=172. Application of Fitzgerald’s Result_Ancient and modern engineering and the Isthmian canal

evaporation data determined by Messrs. Fitzgerald and Kuichling are

sufficient for all ordinary purposes in the North Atlantic States. In

the discussion of the capacity of the Croton watershed Mr. Fitzgerald’s

results will be taken, as the conditions of the Croton watershed in

respect to temperature and atmosphere are affected by the proximity to

the ocean, and other features of the case make it more nearly like the

Metropolitan drainage area near Boston than the more elevated inland

district near Rochester.

If the monthly amounts of evaporation be taken from the preceding

table, and if it further be observed that a volume of water 1

square mile in area and 1 inch thick contains 17,377,536 gallons,

the following table (Table XI) of amounts of evaporation from the

reservoirs in the Croton watershed, including the new Croton Lake, will

result, since the total area of water surface of all these reservoirs

is 16.1 square miles.

TABLE XI.

Jan. 0.96 × 16.1 × 17,377,536 = 268,600,000 gallons.

Feb. 1.05 × ” × ” = 293,800,000 ”

Mar. 1.70 × ” × ” = 475,700,000 ”

April 2.97 × ” × ” = 831,000,000 ”

May 4.46 × ” × ” = 1,247,900,000 ”

June 5.54 × ” × ” = 1,550,100,000 ”

July 5.98 × ” × ” = 1,673,200,000 ”

Aug. 5.50 × ” × ” = 1,538,900,000 ”

Sept. 4.12 × ” × ” = 1,152,800,000 ”

Oct. 3.16 × ” × ” = 884,200,000 ”

Nov. 2.25 × ” × ” = 629,600,000 ”

Dec. 1.51 × ” × ” = 422,500,000 ”

----- --------------

39.20 Total = 10,968,300,000 ”

It will be seen from this table that the total annual evaporation from

all the reservoir surfaces of the Croton watershed, as it will exist

when the new Croton Lake is completed, will be nearly 11,000,000,000

gallons, enough to supply the boroughs of Bronx and Manhattan at the

present rate of consumption for about forty days.

=173. The Capacity of the Croton Watershed.=—The use of the preceding

figures and numbers can be well illustrated by considering the capacity

of the Croton watershed in its relations to the present water needs of

the boroughs of Bronx and Manhattan which that watershed is designed

to supply. The total area of the Croton watershed is 360.4 square

miles, of which 16.1 square miles, as has already been observed, is

water surface. As a matter of fact the run-off observations from that

watershed have been maintained or computed for the thirty-two-year

period from 1868 to 1899, inclusive, covering the evaporation from the

reservoirs and lake surfaces as they have existed during that period.

The later observations, therefore, include the effects of evaporation

from the more lately constructed reservoirs, but none of these data

cover evaporation from the entire surface of the new Croton Lake, whose

excess over that of the old reservoir is nearly one third of the total

water surface of the entire shed. As a margin of safety and for the

purpose of simplification, separate allowance will be made for the

evaporation from all the reservoir and lake surfaces of the entire

watershed as it will exist on the completion of the new Croton Lake, as

a deduction from the run-off. The preceding table (Table XI) exhibits

those deductions for evaporation as they will be made in the next table.

In Table IX the year 1880 yields the lowest run-off of the entire

thirty-two-year period. The total precipitation was 36.92 inches, and

only 34.21 per cent of it was available as run-off. The first column in

Table XII gives the amount of monthly rainfall for the entire year, the

sum of which aggregates 36.92 inches. Each of these monthly quantities

multiplied by .3421 will give the amount of rainfall available for

run-off, and the latter quantity multiplied by the number of square

miles in the watershed (360.4) will show the total depth of available

water concentrated upon a single square mile. If the latter quantity be

multiplied by 17,378,000, the total number of gallons available for the

entire month will result, from which must be subtracted the evaporation

for the same month. Carrying out these operations for each month in the

year, the monthly available quantities for water-supply will be found,

as shown in the last column.

TABLE XII.

(Jan. 3.43 × .3421 = 1.173) × 360.4 × 17,378,000 - 268,600,000 = 7,077,700,000

(Feb. 3.40 × ” = 1.163) × ” × ” - 293,800,000 = 6,989,900,000

(Mar. 3.90 × ” = 1.334) × ” × ” - 475,700,000 = 7,879,000,000

(April 3.57 × ” = 1.221) × ” × ” - 831,000,000 = 6,816,000,000

(May 1.04 × ” = .356) × ” × ” - 1,247,900,000 = 982,000,000

(June 1.40 × ” = .479) × ” × ” - 1,550,100,000 = 1,449,800,000

(July 5.86 × ” = 2.005) × ” × ” - 1,673,200,000 = 10,890,000,000

(Aug. 4.16 × ” = 1.423) × ” × ” - 1,538,900,000 = 7,373,100,000

(Sept. 2.42 × ” = .828) × ” × ” - 1,152,800,000 = 4,032,900,000

(Oct. 2.83 × ” = .968) × ” × ” - 884,200,000 = 5,178,500,000

(Nov. 2.32 × ” = .794) × ” × ” - 629,600,000 = 4,343,100,000

(Dec. 2.59 × ” = .886) × ” × ” - 422,500,000 = 5,126,300,000

-----

36.92

The sum of the twelve monthly available quantities will give the total

number of gallons per year applicable to meeting the water demands of

the boroughs of Bronx and Manhattan.

=174. Necessary Storage for New York Supply to Compensate for

Deficiency.=—At the present time the average daily consumption per

inhabitant of those two boroughs is 115 gallons, and if the total

population be taken at 2,200,000, the total daily consumption will

be 2,200,000 × 115 = 253,000,000 gallons. If the latter quantity be

multiplied by 30.5, the latter being taken as the average number of

days in the month throughout the year, the average monthly draft of

water for the two boroughs in question will be 7,716,500,000 gallons.

The subtraction of the latter quantity from the monthly results in the

preceding table will exhibit a deficiency which must be met by storage

or a surplus available for storage. Table XIII exhibits the twelve

monthly differences of that character.

TABLE XIII.

7,077,700,000 — 7,716,500,000 = - 638,800,000

6,989,900,000 — ” = - 726,600,000

7,879,000,000 — ” = + 162,500,000

6,816,000,000 — ” = - 900,500,000

982,000,000 — ” = - 6,734,500,000

1,449,800,000 — ” = - 6,266,700,000

10,890,000,000 — ” = +3,173,500,000

7,373,100,000 — ” = - 343,400,000

4,032,900,000 — ” = - 3,683,600,000

5,178,500,000 — ” = - 2,538,000,000

4,343,100,000 — ” = - 3,373,400,000

5,126,300,000 — ” = - 2,590,200,000

--------------- ---------------

-27,795,700,000 +3,336,000,000

+ 3,336,000,000

---------------

-24,459,700,000

It is seen from this table that the total monthly deficiencies

aggregate 27,795,700,000 gallons and that there are only two months in

which the run-off exceeds the consumption, the surplus for those two

months being only 3,336,000,000 gallons. The total deficiency for the

year is therefore 24,459,700,000 gallons. Dividing the latter quantity

by the average daily draft of 253,000,000 gallons, there will result

a period of 97 days, or more than one quarter of a year, during which

the minimum annual rainfall would fail to supply any water to the city

at all. These results show that in case of a low rainfall year, like

that of 1880, the precipitation upon the Croton watershed would supply

sufficient water for the boroughs of Bronx and Manhattan at the present

rate of consumption for three fourths of the year only. A distressingly

serious water famine would result unless the year were begun by

sufficient available storage in the reservoirs of the basin at least

equal to 24,459,700,000 gallons. Should such a low rainfall year or

one nearly approaching it be one of a two- or three-year low rainfall

cycle, such a reserve storage would be impossible and the resulting

conditions would be most serious for the city. If an average year, for

which the total rainfall would be about 48 inches preceded such a year

of low rainfall, the conditions would be less serious. The figures

would stand as follows:

Total run-off =

17,377,536 × 360.4 × 22.93 - 17,377,536 × 16.1 × 39.2

= 132,640,000,000 gallons.

Total annual consumption = 92,345,000,000 ”

---------------

Available for storage = 40,295,000,000 ”

Deficiency = 24,459,700,000 ”

---------------

Surplus = 15,835,300,000 ”

The average year would, therefore, yield enough run-off water if stored

to more than make up the deficiency of the least rainfall year by

nearly 16,000,000,000 gallons. In order to secure the desired volume it

would therefore be necessary to have storage capacity at least equal

to 24,459,700,000 gallons; indeed, in order to meet all the exigencies

of a public water-supply it would be necessary to have far more than

that amount. As a matter of fact there are in the Croton watershed

seven artificial reservoirs with a total storage capacity of nearly

41,000,000,000 gallons, besides a number of small ponds in addition

to the new Croton Lake which with water surface at the masonry crest

of the dam has a total additional storage capacity of 23,700,000,000

gallons. The storage capacity of the new Croton Lake may be increased

by the use of flash-boards 4 feet high placed along its crest, so

that with its water surface at grade 200 its total capacity will be

increased to 26,500,000,000 gallons. After the new Croton reservoir is

in use the total storage capacity of all the reservoirs and ponds in

the Croton watershed will be raised to 70,245,000,000 gallons, which

can be further augmented by the Jerome Park reservoir when completed by

an amount equal to 1,900,000,000 gallons. This is equivalent, at the

present rate of consumption, to a storage supply for 285 days for the

boroughs of Manhattan and the Bronx.

=175. No Exact Rule for Storage Capacity.=—This question of the

amount of storage capacity to be provided in connection with public

water-supplies is one which cannot be reduced to an exact rule.

Obviously if the continuous flow afforded from any source is always

greater per day than any draft that can ever be made upon it, no

storage-reservoirs at all would be needed, although they might be

necessary for the purpose of sedimentation. On the other hand, as in

the case of New York City, if the demand upon the supply has reached

its capacity or exceeded it for low rainfall years, it may be necessary

to provide storage capacity sufficient to collect all the run-off of

the watershed. The civil engineer must from his experience and from the

data before him determine what capacity between those limits is to be

secured. When the question of volume or capacity of storage is settled

the mode of distribution of that volume or capacity in reservoirs is

to be determined, and that affects to some extent the potability of

the water. If there is a large area of shallow storage, the vegetable

matter of the soil may affect the water in a number of ways. Again, it

is advisable in this connection to consider certain reservoir effects

as to color and contained organic matter in general.

=176. The Color of Water.=—The potability[7] of water collected from

any watershed is materially affected by its color. Although iron

may produce a brownish tinge, by far the greater amount of color

is produced by dissolved vegetable matter. Repeated examinations

of colored water have shown that discoloration is in many cases at

least a measure of the vegetable matter contained in it. While this

may not indicate that the water is materially unwholesome, it shows

conclusively the existence of conditions which are usually productive

of minute lower forms of vegetation from which both bad taste and odors

are likely to arise.

[7] What is generally known as the “Michigan standard of the purity

of drinking-water,” as specified by the Michigan State Laboratory of

Hygiene, is here given:

“1. The total residue should not exceed 500 parts per

million.

“2. The inorganic residue may constitute the total residue.

“3. The smaller amount of organic residue the better the

water.

“4. The amount of earthy bases should not exceed 200 parts

per million.

“5. The amount of sodium chloride should not exceed 20 parts

per million (i.e., ‘chlorine’ 12.1 parts per million).

“6. The amount of sulphates should not exceed 100 parts per

million.

“7. The organic matter in 1,000,000 parts of the water

should not reduce more than 8 parts of potassium

permanganate (i.e., ‘required oxygen’ 2.2 parts per

million).

“8. The amount of free ammonia should not exceed 0.05 part

per million.

“9. The amount of albuminoid ammonia should not exceed 0.15

part per million.

“10. The amount of nitric acid should not exceed 3.5 parts

per million (i.e., ‘N as nitrate’ .9 part per million).

“11. The best water contains no nitrous acid, and any water

which contains this substance in quantity sufficient

to be estimated should not be regarded as a safe

drinking-water.

“12. The water must contain no toxicogenic germs as

demonstrated by tests upon animals.

“The water must be clear and transparent, free from smell, and without

either alkaline or acid taste, and not above 5 French standard of

hardness.”

This standard is too high to be attained ordinarily in natural waters.

There are two periods in the year of maximum intensity of color, one

occurring in June and the other in November. The former is due to the

abundant drainage of peaty or other excessively vegetable soils from

the spring rains. After June the sun bleaches the water to a material

extent until the autumn, when the dying vegetation imparts more or less

coloring to the water falling upon it. This last agency produces its

maximum effect in the month of November.

There are various arbitrary scales employed by which colors may be

measured and discolored waters compared. Among others, dilute solutions

of platinum and cobalt are used, in which the relative proportions of

those substances are varied so as to resemble closely the colors of the

water. The amount of platinum used is a measure of the color, one unit

of which corresponds to one part of the metal in 10,000 parts of water.

Again, the depth at which a platinum wire 1 mm. (.039 inch) in diameter

and 1 inch long can be seen in the water is also taken as a measure

of the color, the amount of the latter being inversely as the depth.

This method has found extended and satisfactory use in connection with

the Metropolitan Water-supply of Boston, the Cochituate water having a

degree of color represented by .25 to .30, while the Sudbury water has

somewhat more than twice as much. The Cochituate water is practically

colorless.

The origin of the color of water is chiefly the swamps which drain into

the water-supply, or the vegetation remaining upon a new reservoir site

when the surface soil has not been removed before the filling of the

reservoir. The drainage of swamps should not, as a rule, be permitted

to flow into a public water-supply, as it is naturally heavily charged

with vegetable matter and is correspondingly discolored. This matter,

like many others connected with the sanitation of potable public

waters, has been most carefully investigated by the State Board of

Health of Massachusetts in connection with the Boston water-supply.

Its work has shown the strong advisability of diverting the drainage

of large swamps from a public supply as carrying too much vegetable

matter even when highly diluted by clear water conforming to desirable

sanitary standards.

=177. Stripping Reservoir Sites.=—The question of stripping or cleaning

reservoir sites of soil is also one which has been carefully studied

by the Massachusetts State Board of Health. As a consequence large

amounts of money have been expended by the city of Boston in stripping

the soil from reservoir sites to the average depth in some cases of 9

inches for wooded land and 12½ inches for meadow land. This was done

in the case of the Nashua River reservoir having a superficial area of

6.56 square miles at a cost of nearly $2,910,000, or about $700 per

acre. It has been found that the beneficial effect of this stripping

is fully secured if the black loam in which vegetation flourishes is

removed.

[Illustration: Wachusetts Reservoir, showing Stripping of Soil.]

This stripping of soil is indicative of the great care taken to secure

a high quality of water for the city of Boston, but it is not done in

the Croton watershed of the New York supply. It cannot be doubted that

the quality of the Croton supply would have been sensibly enhanced by

a similar treatment of its reservoir sites. Mr. F. B. Stearns, chief

engineer of the Metropolitan Water-supply of Boston, states that in

some cases the effects of filling reservoirs without removing the

soil and vegetable matter have “continued for twenty years or more

without apparent diminution.” On the other hand, water discolored by

vegetable matter becomes bleached to some extent at least by standing

in reservoirs whose sites have been stripped of soil.

=178. Average Depth of Reservoirs should be as Great as Practicable.=—In

the selection of reservoir locations those are preferable where the

average depths will be greatest and where shallow margins are reduced

to a minimum. It may sometimes be necessary to excavate marginal

portions which would otherwise be shallow with a full reservoir.

There should be as little water as possible of a less low-water

depth than 10 or 12 feet, otherwise there may be a tendency to

aquatic vegetable growth. The following table exhibits the areas,

average depths, capacity, and other features of a number of prominent

storage-reservoirs.

COMPARATIVE TABLE OF AREAS, DEPTHS, AND CAPACITIES OF STORAGE

RESERVOIRS WITH HEIGHTS AND LENGTHS OF DAMS.

LEGEND:

(A) = Area Square Miles.

(B) = Average Depth, Feet.

(D) = Capacity, Million Gallons.

------------------------------+-----+---+--------------+-----+-------

Name and Location | | +-------+------+ |

of Reservoir. | (A) |(B)| Above | Above| (C) | (D)

------------------------------+-----+---+-------+------+-----+-------

Swift River, Mass |36.96| 53| 144 | ... |2,470|406,000

Nashua River, Mass | 6.56| 46| 129 | 158 |1,250| 63,068

Nira, near Poona, India | 7.25| 27| 100 | ... |3,000| 41,143

Tansa, Bombay, India | 5.50| 33| 127 | 131 |8,770| 37,500

Khadakvasla, Poona, India | 5.50| 32| 100 | 107 |5,080| 36,737

New Croton, N. Y. | ....| ..| 157 | 225 |1,270| 32,000

(total for six reservoirs) | 2.34| 43|98-128 | ... |4,460| 20,838

reservoirs combined | 5.82| 14|14-65 | ... |.....| 15,867

Vyrnwy, Liverpool, Eng. | 1.75| ..| 84 | 129 |1,350| 14,560

Ware River, Mass. | 1.62| 33| 71 | ... | 785| 11,190

Sodom, N. Y. | ....| ..| 72 | 89 | 500| 9,500

water-works | 1.91| 19| 65 | 70 |1,865| 7,438

Titicus, N. Y. | ....| ..| 105 | 115 |.....| 7,000

water-works | 1.00| 12| 23 | ... |.....| 2,500

Cochituate, Boston water-works| 1.35| 8| .. | ... |.....| 2,160

water-works | 0.29| 25| 52 | ... |1,500| 1,500

------------------------------+-----+---+-------+------+-----+-------

=179. Overturn of Contents of Reservoirs Due to Seasonal Changes of

Temperature.=—It will be noticed that the average depth is less

than about 20 feet in few cases only. If the water is deep, its mean

temperature throughout the year will be lower than if shallow. During

the warmer portion of the year the upper layers of the water are

obviously of a higher temperature than the lower portions, since the

latter receive much less immediate effect from the sun’s rays. As the

upper portions of the water are of higher temperature, they are also

lighter and hence remain at or near the top. For the same reason the

water at the bottom of the reservoir remains there throughout the warm

season and until the cool weather of the autumn begins. The top layers

of water then continue to fall in temperature until it is lower than

that of the water at the bottom, when the surface-water becomes the

heaviest and sinks. It displaces subsurface water lighter than itself,

the latter coming to the surface to be cooled in turn.

This operation produces a complete overturning of the entire reservoir

volume as the late autumn or early winter approaches. It thus brings to

the surface-water which has been lying at the bottom of the reservoir

all summer in contact with what vegetable matter may have been there.

The depleted oxygen of the bottom water is thus replenished with a

corresponding betterment of condition. It is the great sanitary effort

of nature to improve the quality of stored water entrusted to its care,

and it continues until the surface is cooled to a temperature perhaps

lower than that of the greatest density of water.

Another great turn-over in the water of a lake or reservoir covered

with ice during the winter occurs in the spring. When the ice melts,

the resulting water rises a little in temperature until it reaches

possibly its greatest density at 39°.2 Fahr., and then sinks,

displacing subsurface water. This goes on until all the ice is melted

and until all water cooled by it, near the surface, below 39°.2 Fahr.

has been raised to that temperature. The period of summer stagnation

then follows.

=180. The Construction of Reservoirs.=—The natural topography and

sometimes the geology of the locality determines the location of the

reservoir. The first requirement obviously is tightness. If for any

reason whatever, such as leaky banks or bottom, porous subsurface

material, or for any other defect, the water cannot be retained in

the reservoir, it is useless. Some very perplexing questions in this

connection have arisen. Indeed reservoirs have been completed only

to be found incapable of holding their contents. Such results are

evidently not creditable to the engineers who are responsible for them,

and they should be avoided.

[Illustration: YARROW RESERVOIR, LIVERPOOL WATER-SUPPLY]

[Illustration: SAN LEANDRO DAM, SAN FRANCISCO WATER-WORKS]

[Illustration: TITICUS DAM, NEW YORK WATER-SUPPLY]

In order that the bottom of the reservoir may be water-tight it must

be so well supported by firm underlying material that it will not be

injured by the weight of water above it, which in artificial reservoirs

may reach 30 to 100 feet or more in depth. The subsurface material at

the site of any proposed structure of this character must, therefore,

be carefully examined so as to avoid all porous material, crevasses in

rocks, or other open places where water might escape. Objectionable

material may frequently be removed and replaced with that which is

more suitable, and rock crevices and other open places may sometimes

be filled with concrete and made satisfactory. Whatever may be the

conditions existing, the finished bottom of the reservoir should be

placed only on well-compacted, firm, unyielding material.

The character of the reservoir bottom will depend somewhat upon the

cost of suitable material of which to construct it. If a bottom of

natural earth cannot be used, a pavement of stone, brick, or concrete

may be employed from 8 inches to a foot or a foot and a half in

thickness. The reservoir banks must be placed upon carefully prepared

foundations, sometimes with masonry core-walls. They are frequently

composed of clayey and gravelly material mixed in proper proportions

and called puddle, although that term is more generally applied to a

mixture of clay and gravel designed to form a truly impervious wall

in the centre of the reservoir embankment. Some engineers require the

core-wall, as it is called, to be constructed of masonry, with the

earth or gravelly material carried up each side of this wall in layers

6 to 9 inches thick, well moistened and each layer thoroughly rolled

with a grooved roller, or treated in some equivalent manner in order

that the whole mass may not be in strata but essentially continuous

and as nearly impervious as possible. The masonry core-wall should be

founded on bed-rock or its equivalent. Its thickness will depend upon

the height of the embankment. If the latter is not more than 20 or 25

feet high, the core-wall need not be more than 4 to 6 feet thick, but

if the embankment reaches a height of 75 feet or even 100 feet, it must

be made 15 to 20 feet thick, or possibly more, at the base. Its top

should be not less than 4 or 6 feet thick, imbedded in the earth and

carried well above the highest surface of water in the reservoir.

The thickness of the clay puddle-wall employed as the central core

of the reservoir embankment is usually made much thicker than that

of masonry. As a rough rule it may be made twice as thick as the

masonry core at the deepest point and not less than about 6 feet at

the top. The thickness of the puddle core is sometimes varied to meet

the requirements of the natural material in which it is embedded at

different depths.

Frequently, when embankments are under about 20 feet high, the

core-walls may be omitted, excavation having been made at the base of

the embankment down to rock or other impervious material, and if the

entire bank is carried up with well-selected and puddled material.

The interior slopes of reservoir embankments are usually covered with

roughly dressed stone pavement 12 to 18 inches thick, laid upon a

broken stone foundation 8 to 12 inches thick, for a protection against

the wash of waves, the pavement in any case being placed upon the bank

slope after having been thoroughly and firmly compacted. The sloping

and bottom pavements, of whatever material they may be composed, should

be made continuous with each other so as to offer no escape for the

water. In some cases where it has been found difficult to make the

interior surfaces of reservoirs water-tight, asphalt or other similar

water-tight layers have been used with excellent results.

The care necessary to be exercised in the construction of storage or

other reservoirs when earth dams or embankments are used can better be

appreciated when it is realized that almost all such banks, even when

properly provided with masonry or clay-puddle core-walls, are saturated

with water, even on the down-stream side, at least throughout their

lower portions. A board of engineers appointed by the commissioners

of the Croton Aqueduct in the summer of 1901 made a large number

of examinations in the earth embankments in the Croton watershed,

and found that with scarcely an exception those embankments were

saturated throughout the lower portions of their masses, although in

every case a masonry core-wall had been built. The results of those

investigations showed that the water had percolated through the earth

portion of the embankments and even through the core-walls, which had

been carried down to bed-rock. This induced saturation, more or less,

of the material on the down-stream slopes of the embankments. When

material is thus filled with water, unless it is suitably selected, it

is apt to become soft and unstable, so that any superincumbent weight

resting upon it might produce failure. The fact that such embankments

may become saturated with water fixes limits to their heights, since

the surface of saturation in the interior of the bank has generally

a flatter slope than that of the exterior surface. The height of the

embankment therefore should be such that the exterior slope cannot cut

into the saturated material at its foot, at least to any great extent.

From what precedes it is evident that the height of an earth embankment

will depend largely upon the slope of the exterior surface. This slope

is made 1 vertical to 2, 2½, or 3 horizontal. The more gradual slope

is sometimes preferable. It is advisable also to introduce terraces

and to encourage the growth of sod so as to protect the surface from

wash. The inner paved slope may be as steep as 1 vertical to 1½ or 2

horizontal.

[Illustration: BOG BROOK DAM NO. 1.—RESERVOIR 1.]

[Illustration: TITICUS DAM.—RESERVOIR M.]

[Illustration: AMAWALK DAM.—RESERVOIR A.

Earth Dams in Croton Watershed, showing Slopes of Saturation.]

=181. Gate-houses, and Pipe-lines in Embankments.=—It is necessary

to construct the requisite pipe-lines and conduits leading from the

storage-reservoirs to the points of consumption, and sometimes such

lines bring the water to the reservoir. Wherever such pipes-line or

conduits either enter or leave a reservoir gates and valves must be

provided so as properly to control the admission and outflow of the

water. These gate-houses, as they are called, because they contain

the gates or valves and such other appurtenances or details as

are requisite for operation and maintenance, are usually built of

substantial masonry. They are the special outward features of every

reservoir construction, and their architecture should be characteristic

and suitable to the functions which they perform. Where the pipes are

carried through embankments it is necessary to use special precautions

to prevent the water from flowing along their exterior surfaces.

Many reservoirs have been constructed under defective design in this

respect, and their embankments have failed. Frequently small masonry

walls are built around the pipes and imbedded in the bank, so as to

form stops for any initial streams of water that might find their way

along the pipe. In short, every care and resource known to the civil

engineer must be employed in reservoir construction to make its bottom

and its banks proof against leakage and to secure permanence and

stability in every feature.

=182. High Masonry Dams.=—The greatest depths of water impounded in

reservoirs are found usually where it is necessary to construct a high

dam across the course of a river, as at the new Croton dam. In such

cases it is not uncommon to require a dam over 75 to 100 feet high

above the original bed of the river, which is usually constructed of

masonry with foundations carried down to bed-rock in order to secure

suitable stability and prevent flow or leakage beneath the structure.

It is necessary to secure that result not only along the foundation-bed

of the dam, but around its ends, and special care is taken in those

portions of the work.

The new Croton dam is the highest masonry structure of its class yet

built. The crest of its masonry overflow-weir is 149 feet above the

original river-bed, with the extreme top of the masonry work of the

remaining portion of the dam carried 14 feet higher. A depth of earth

and rock excavation of 131 feet below the river-bed was necessary

in order to secure a suitable foundation on bed-rock. The total

maximum height, therefore, of the new Croton dam, from the lowest

foundation-point to the extreme top, is 294 feet, and the depth of

water at the up-stream face of the dam will be 136 feet when the

overflow is just beginning, or 140 feet if 4 feet additional head be

secured by the use of flash-boards. In the prosecution of this class

of work it is necessary not only to reach bed-rock, but to remove all

soft portions of it down to sound hard material, to clean out all

crevices and fissures of sensible size, refilling them with hydraulic

cement mortar or concrete, and to shape the exposed rock surfaces so

as to make them at least approximately normal to the resultant loads

upon them, to secure a complete and as nearly as possible water-tight

bond with the superimposed masonry. If any streams or other small

watercourses should be encountered, they must either be stopped or

led off where they will not affect the work, or, as is sometimes

done, the water issuing from them may be carried safely through the

masonry mass in small pipes. The object is to keep as much water out

of the foundation-bed as possible, so as to eliminate upward pressure

underneath the dam caused by the head of water in the subsequently full

reservoir. It is a question how much dependence can be placed upon the

exclusion of water from the foundation-bed. In the best class of work

undoubtedly the bond can be good enough to exclude more or less water,

but it is probably only safe and prudent so to design the dam as to be

stable even though water be not fully excluded.

[Illustration: Cross-section of New Croton Dam.]

The stability of the masonry dam must be secured both for the reservoir

full and empty. With a full reservoir the horizontal pressure of water

on the up-stream face tends to overturn the dam down-stream. When the

water is entirely withdrawn the pressure under the up-stream edge of

the foundation becomes much greater, so that safety and stability

under both extreme conditions must be assured. There are a number of

systems of computation to which engineers resort in order to secure a

design which shall certainly be stable under all conditions. That which

is commonly employed in this country is based upon two fundamental

propositions, under one of which the pressure at any point in the

entire masonry mass must not exceed a certain safe amount per square

foot, while the other is of a more technical character, requiring that

the centre of pressure shall, in every horizontal plane of the dam,

approach nowhere nearer than one third the horizontal thickness of

the masonry to one edge of it. A further condition is also prescribed

which prevents any portion of the dam from slipping or sliding over

that below it. As a matter of fact when the first two conditions are

assured the third is usually fulfilled concurrently. Obviously there

will be great advantage accruing to a dam if the entire mass of masonry

is essentially monolithic. In order that that may be the case either

concrete or rubble is usually employed for the great mass of the

masonry structure, the exterior surfaces frequently being composed of a

shell of cut-stone, so as to provide a neat and tasteful finish. This

exterior skin or layer of cut masonry need not average more than 1½ to

2½ feet thick.

The pressures prescribed for safety in the construction of masonry dams

vary from about 16,000 to 28,000 or 30,000 pounds per square foot.

Sometimes, as in the masonry dams found in the Croton watershed, limits

of 16,000 to 20,000 pounds per square foot are prescribed for the upper

portions of the dams and a gradually increasing pressure up to 30,000

pounds per square foot in passing downward to the foundation-bed. There

are reasons of a purely technical character why the prescribed safe

working pressure must be taken less on the down-stream or front side of

the dam than on the up-stream or rear face.

The section of a masonry dam designed under the conditions outlined

will secure stability through the weight of the structure alone, hence

it is called a gravity section. In some cases the rock bed and sides

of a ravine in which the stream must be dammed will permit a curved

structure to be built, the curvature being so placed as to be convex

up-stream or against the water pressure. In such a case the dam really

becomes a horizontal arch and, if the curvature is sufficiently sharp,

it may be designed as an arch horizontally pressed. The cross-section

then has much less thickness (and hence less area) than if designed

on a straight line so as to produce a gravity section. A number of

such dams have been built, and one very remarkable example of its kind

is the Bear Valley dam in California; it was built as a part of the

irrigation system.

[Illustration: Foundation Masonry of New Croton Dam.]

CHAPTER XVII.

=183. Gravity Supplies.=—When investigation has shown that a sufficient

quantity of water may be obtained for a required public supply from any

of the sources to which reference has been made, and that a sufficient

storage capacity may be provided to meet the exigencies of low rainfall

years, it will be evident if the water can be delivered to the points

of consumption by gravity, or whether pumping must be employed, or

recourse be made to both agencies.

If the elevation of the source of supply is sufficiently great to

permit the water to flow by gravity either to storage-reservoirs or to

service-reservoirs and thence to the points of consumption, a proper

pipe-line or conduit must be designed to afford a suitable channel. If

the topography permits, a conduit may be laid which does not run full,

but which has sufficient grade or slope to induce the water to flow in

it as if it were an open channel. This is the character of such great

closed masonry channels as the new and old Croton aqueducts of the

New York water-supply and the Sudbury and Wachusetts aqueducts of the

Boston supply. These conduits are of brick masonry backed with concrete

carried sometimes on embankments and sometimes through rock tunnels.

When they act like open channels a very small slope is employed, 0.7 of

a foot per mile being a ruling gradient for the new Croton aqueduct,

and 1 foot per mile for the Sudbury. Where these conduits cross

depressions and follow approximately the surface, or where they pass

under rivers, their construction must be changed so that they will not

only run full, but under greater or less pressure, as the case may be.

=184. Masonry Conduits.=—In general the conduits employed to bring

water from the watersheds to reservoirs at or near places of

consumption may be divided into two classes, masonry and metal,

although timber-stave pipes of large diameter are much used in the

western portion of the country. The masonry conduits obviously cannot

be permitted to run full, meaning under pressure, for the reason that

masonry is not adapted to resist the tension which would be created

under the head or pressure of water induced in the full pipe. They

must rather be so employed as to permit the water to flow with its

upper surface exposed to the atmosphere, although masonry conduits are

always closed at the top. In other words, they must be permitted to

run partially full, the natural grade or slope of the water surface

in them inducing the necessary velocity of flow or current. Evidently

the velocity in such masonry conduits is comparatively small, seldom

exceeding about 3 feet per second. The new and old Croton aqueducts,

the Sudbury and Wachusetts aqueducts of the Metropolitan Water-supply

of Boston, are excellent types of such conveyors of water. They are

sometimes of circular shape, but more frequently of the horseshoe

outline for the sides and top, with an inverted arch at the bottom for

the purpose of some concentration of flow when a small amount of water

is being discharged and for structural reasons.

The interiors of these conduits are either constructed of brick or

they may be of concrete or other masonry affording smooth surfaces.

In the latest construction Portland-cement concrete or that concrete

reinforced with light rods of iron or steel is much used. Bricks, if

employed, should be of good quality and laid accurately to the outline

desired with about ¼-inch joints, so as to offer as smooth a surface as

possible for the water to flow over. In special cases the interiors of

these conduits may be finished with a smooth coating of Portland-cement

mortar. If conduits are supported on embankments, great care must be

exercised in constructing their foundation supports, since any sensible

settlement would be likely to form cracks through which much water

might easily escape. When carried through tunnels they are frequently

made circular in outline. They must occasionally be cleaned, especially

in view of the fact that low orders of vegetable growths appear on

their sides and so obstruct the free flow of water.

=185. Metal Conduits.=—Metal conduits have been much used within the

past fifteen or twenty years. Among the most prominent of these are

the Hemlock Lake aqueduct of the Rochester Water-works, and that of

the East Jersey Water Company through which the water-supply of the

city of Newark, N. J., flows. When these metal conduits or pipes equal

24 to 30 or more inches in diameter they are usually made of steel

plates, the latter being of such thickness as is required to resist

the pressure acting within them. The riveted sections of these pipes

may be of cylindrical shape, each alternate section being sufficiently

small in diameter just to enter the other alternate sections of little

larger diameter, the interior diameter of the larger sections obviously

being equal to the interior diameter of the smaller sections plus twice

the thickness of the plate. Each section may also be slightly conical

in shape, the larger ends having a diameter just large enough to pass

sufficiently over the smaller end of the next section to form a joint.

Large cast-iron pipes are also sometimes used to form these metal

conduits up to an interior diameter of 48 inches. The selection of the

type of conduit within the limits of diameter adapted to both metals is

usually made a matter of economy. The interior of the cast-iron pipe is

smoother than that of the riveted steel, although this is not a serious

matter in deciding upon the type of pipe to be used.

Steel-plate conduits have been manufactured and used up to a diameter

of 9 feet. In this case the pipe was used in connection with

water-power purposes and with a length of 153 feet only, the plates

being ½ inch thick. The steel-plate conduits of the East Jersey Water

Company’s pipes are as follows:

Diameter. Thickness. Length.

48 inches ¼ inch }

48 ” ⁵/₁₆ ” } 21 miles.

48 ” ⅜ ” }

36 ” ¼ ” 5 ”

The diameters and lengths of the metal pipes or conduits of the Hemlock

Lake conduit of the Rochester Water-works are as follows:

36-inch wrought-iron pipe 9.60 miles.

24 ” ” ” 2.96 ”

24 ” cast-iron pipe 15.82 ”

-----

Total 28.39 ”

All metal conduits or pipes are carefully coated with a suitable

asphalt or tar preparation or varnish applied hot and sometimes baked

before being put in place. This is for the purpose of protecting the

metal against corrosion. Cast-iron pipes have been used longer and

much more extensively than wrought-iron or steel, but an experience

extending over thirty to forty years has shown that the latter class of

pipes possesses satisfactory durability and may be used to advantage

whenever economical considerations may be served.

=186. General Formula for Discharge of Conduits—Chezy’s Formula.=—It

is imperative in designing aqueducts of either masonry or metal to

determine their discharging capacity, which in general will depend

largely upon the slope of channel or head of water and the resistance

offered by the bed or interior of the pipe to the flow of water. The

resistance of liquid friction is so much more than all others in this

class of water-conveyors that it is usually the only one considered.

There is a certain formula much used by civil engineers for this

purpose; it is known as Chezy’s formula, for the reason that it was

first established by the French engineer Antoine Chezy about the year

1775, although it is an open question whether the beginnings of the

formula were not made twenty or more years prior to that date. Its

demonstration involves the general consideration of the resistance

which a liquid meets in flowing over any surface, such as that of the

interior of a pipe or conduit, or the bed and banks of a stream.

The force of liquid friction is found to be proportional to the

heaviness of the liquid (i.e., to the weight of a cubic unit, such as

a cubic foot), to the area of wetted surface over which the liquid

flows, and nearly to the square of the velocity with which the liquid

moves. Hence if _lʹ_ is the length of channel, _p_ the wetted portion

of the perimeter of the cross-section, _w_ the weight of a cubic unit

of the liquid, and _v_ the velocity, the total force of liquid friction

for the length _l′_ of channel will be _F = ζwpl′v²_, ζ being the

coefficient of liquid friction. The path of the force _F_ for a unit of

time is _v_, and the work _W_ which it performs in that unit of time is

equal to the weight _wal′_ falling through the height _h′_, _a_ being

the area of the cross-section of the stream.

[Illustration: FIG. 2.]

Hence _W_ = ζ_wplʹv².v_ = _wal′h′._ (7)

_a_ _____________________ ____

ζ_v²v_ = ---- _hʹ_, _v_ = √(1/ζ) (_a/p_) (_h′/v_) = _c_√_rs_. (8)

_p_

In this equation

_____ _a_

_c_ = √(1/ζ); _r_ = ---- = hydraulic mean radius;

_p_

_hʹ_

_s_ = ----- = sine of inclination of stream’s bed.

_v_

As the motion of the water is assumed to be uniform, the head lost by

friction for the total length of channel _l_ is the total fall _h_, and

by equation (8), since

_h′ h_

--- = _s_ = ---,

_v l_

_v² l_

_h_ = ---- ---------. (9)

_c²_ (_a/p_)

If, as in the case of the ordinary cast-iron water-pipes of a public

supply system, the cross-section _a_ is circular,

_a_ (π_d²_/4) _d_

--- = --------- = ---,

_p_ π_d_ 4

and

4.2_g l v² l v²_

_h_ = ----- --- ------ = _f_ --- -----, (10)

_c² d_ 2_g d_ 2_g_

in which _f_ = 8_g_ ÷ _c²_.

The quantity _f_ is sometimes called the “friction factor.” For smooth,

new pipes from 4 feet down to 3 inches in diameter its value may be

taken from .015 to .03. An approximate mean value may be taken at .02.

The last member of equation (8) is Chezy’s formula, and it is one of

the most used expressions in hydraulic engineering. Some values for

the coefficient _c_ will presently be given. The quantity _r_ found

by dividing the area of the cross-section of the stream by the wetted

portion of its perimeter is called the “hydraulic mean radius,” or

simply the “mean radius.” The other quantity, _s_, appearing in the

formula is, as shown by the figure, the sine of the inclination of the

bed of the stream.

In order to determine the discharge of any pipe, conduit, or open

channel carrying a known depth of water, it is only necessary to

compute _r_ and _s_ from known data and select such a value of the

coefficient _c_ as may best fit the circumstances of the particular

case in question. The substitution of those quantities in Chezy’s

formula, i.e., equation (8), will give the mean velocity _v_ of the

water which, when multiplied by the area of cross-section of the

stream, will give the discharge of the latter per second of time. It

is customary to compute _r_ in feet. The coefficient _c_ is always

determined so as to give velocity in feet per second of time. Hence if

the area of the cross-section of the stream, _a_, is taken in square

feet, as is ordinarily the case, the discharge _av_ will be in cubic

feet per second.

[Illustration: Progress View of Construction of New Croton Dam.]

=187. Kutter’s Formula.=—The coefficient _c_ in Chezy’s formula is

not a constant quantity, but it varies with the mean radius _r_, with

the sine of inclination _s_, and with the character of the bottom and

sides of the open channel, i.e., with the roughness of the interior

surface of the closed pipe. Many efforts have been made and much labor

expended in order to find an expression for this coefficient which may

accurately fit various streams and pipes. These efforts have met with

only a moderate degree of success. The form of expression for _c_ which

is used most among engineers is that known as Kutter’s formula, as it

was established by the Swiss engineer W. R. Kutter. This formula is as

follows:

( 1.811 .00281)

___ ( ------ + 41.65 + ------)

√_r_ ( _n s_ )

_c_ = ---- (------------------------)

_n_ ( ___ )

( √_r_ .00281 )

( ----- + 41.65 + ------ )

( _n s_ )

The quantity _n_ in this formula is called the “coefficient of

roughness,” since its value depends upon the character of the surface

over which the water flows. It has the following set of values for the

surfaces indicated:

_n_ = 0.009 for well-planed timber;

_n_ = 0.010 for neat cement;

_n_ = 0.011 for cement with one third sand;

_n_ = 0.012 for unplaned timber;

_n_ = 0.013 for ashlar and brickwork;

_n_ = 0.015 for unclean surfaces in sewers and conduits;

_n_ = 0.017 for rubble masonry;

_n_ = 0.020 for canals in very firm gravel;

_n_ = 0.025 for canals and rivers free from stones and weeds;

_n_ = 0.030 for canals and rivers with some stones and weeds;

_n_ = 0.035 for canals and rivers in bad order.

=188. Hydraulic Gradient.=—Before illustrating the use of Chezy’s

formula in connection with masonry and metal conduits, of which mention

has already been made, it is best to define another quantity constantly

used in connection with closed iron or steel pipes. This quantity is

called the “hydraulic gradient.” If a closed iron or steel pipe is

running full of water and under pressure and if small vertical tubes

be inserted in the top of the pipe with their lower ends bent so as

to be at right angles to its axis, the water will rise to heights in

the tubes depending upon the pressures of water in the pipe or conduit

at the points of insertion. Such tubes with the water columns in them

are called piezometers. They are constantly used in connection with

water-pipes in order to show the pressures at the points where they are

inserted. A number of such pipes being inserted along an iron pipe or

conduit, a line may be imagined to be drawn through the upper surfaces

of the columns of water, and that line is called the “hydraulic

gradient.” It represents the upper surface of water in an open channel

discharging with the same velocity existing in the closed pipe.

In case Chezy’s formula is used to determine the velocity of discharge

in a closed pipe running under pressure, the sine of inclination _s_

must be that of the hydraulic gradient and not the sine of inclination

of the axis of the closed pipe. In the determination of this quantity

_s_ by the use of piezometer tubes, if a straight pipe remains of

constant section between any two points, it is only necessary to insert

the tubes at those points and observe the difference in levels of the

water columns in them. That difference of levels or elevations will

represent the height which is to be divided by the length of pipe or

conduit between the same two points in order to determine the sine _s_.

[Illustration: Progress View of Construction of New Croton Dam.]

The hydraulic gradient plays a very important part in the construction

of a long pipe-line or conduit. If any part of the pipe should rise

above the hydraulic gradient, the discharge would no longer be full

below that point. It is necessary, therefore, always to lay the pipe or

the closed conduit so that all parts of it shall be below the hydraulic

gradient. Caution is obviously necessary to lay a pipe carrying water

deep enough below the surface of the ground in cold climates to protect

the water against freezing. At the same time if the pipe-line is a long

one it must follow the surface of the ground approximately in order to

save expensive cutting. There will, therefore, generally be summits

in pipe-lines, and inasmuch as all potable water carries some air

dissolved in it, that air is liable to accumulate at the high points or

summits. If that accumulation goes on long enough, it will seriously

trench upon the carrying capacity of the pipe and decrease its flow. It

is therefore necessary to provide at summits what are called blow-off

cocks to let the air escape. At the low points of the pipe-line, on the

contrary, the solid matter, such as sand and dirt, carried by the water

is liable to accumulate, and it is customary to arrange blow-offs also

at such points, so as to enable some of the water to escape and carry

with it the sand and dirt.

[Illustration: IN LOOSE EARTH.]

[Illustration: IN ROCK.

Weston Aqueduct. Sections of Aqueduct and Embankment.]

[Illustration: SECTION OF EMBANKMENT.]

[Illustration: ON EMBANKMENT.

Weston Aqueduct. Sections of Aqueduct and Embankment. Gradient, 1 in

5000.]

=189. Flow of Water in Large Masonry Conduits.=—In order to apply

Chezy’s formula first to the flow of the masonry aqueducts of the New

York and Boston water-supplies, it is necessary to have the outlines of

those conduits so that the wetted perimeter and hence the mean radius

may be determined for any depth of water in them.

[Illustration: OUTLINES OF AQUADUCTS.

FIG. 3.]

The figure shows the desired cross-sections drawn carefully to scale.

Table XIV has been computed and arranged from data taken from various

official sources so as to show the depth, mean velocity, discharge per

second and per twenty-four hours, and the coefficient used in Chezy’s

formula, together with the coefficient of roughness _n_ in Kutter’s

formula for the conduits shown in the figure.

This table exhibits in a concise and clear manner the use of Chezy’s

formula in this class of hydraulic work.

TABLE XIV.

LEGEND:

(A) = Depth, in Feet.

(B) = Hydraulic Radius _r_, Feet.

(D) = Mean Velocity, Feet.

--------------------------+----+-----+--------+-------+------

Aqueducts. | (A)| (B) | _s_. | (C) | (D)

--------------------------+----+-----+--------+-------+------

† New Croton (1899) |8.42|3.974|.0001326| 153.3 | 3.52

years’ use) | .. |2.338| ” | 131.3 | 2.312

‡ ” ” | .. |1 | ” | 119.3 | 1.374

‡ ” ” | .. |1.5 | ” | 126.3 | 1.781

‡ ” ” | .. |2 | ” | 129.8 | 2.114

‡ ” ” | .. |2.5 | ” | 132 | 2.404

‡ ” ” | .. |3 | ” | 133.4 | 2.661

‡ ” ” | .. |3.5 | ” | 134 | 2.887

‡ ” ” | .. |4 | ” | 134.4 | 3.095

Old Croton (1899) clean |6 |2.338| .. | 133.4 | 2.958

not clean |6 |2.338| .. | 123.2 | ..

” ” not clean |7.33|2.368| .. | 118.2 | ..

Dorchester Bay tunnel | .. |1.875| .. | 119 |

” ” | .. |2.338| .. | 125.0 | ..

clean (approx.) | .. | .. | .. | 144.9 |

Sudbury, clean | .. | .5 |.000189 | 116.9 | 1.14

” ” | .. |1.0 | ” | 127.0 | 1.74

” ” | .. |1.5 | ” | 133.3 | 2.24

” ” | .. |2.0 | ” | 137.8 | 2.68

” ” | .. |2.5 | ” | 140.4 | 3.04

--------------------------+----+-----+--------+-------+------

--------------------------+----------------------+--------

| Discharge. |

--------------------------+----------------------+

|Cubic Feet| Gallons | _n_ in

Aqueducts. | per | per |Kutter’s

| Second. | 24 Hours. |Formula.

--------------------------+----------+-----------+--------

† New Croton (1899) | 371.6 |240,200,000|

† ” ” (after two | | |

years’ use) | .. | .. | .0133

‡ ” ” | | |

Old Croton (1899) clean | 122.8 | 79,400,000| .0133

” ” ordinary | | |

condition; | | |

not clean | .. | 73,300,000|

” ” not clean | .. | 85,600,000|

Dorchester Bay tunnel | | |

” ” | .. | .. | .014

Wachusetts, new; probably | | |

clean (approx.) | | |

Sudbury, clean | | |

” ” | | |

--------------------------+----------+-----------+--------

† From report by J. R. Freeman to B. S. Coler, 1899.

‡ From report of New York Aqueduct Commission.

=190. Flow of Water through Large Closed Pipes.=—The masonry conduits

to which consideration has been given in the preceding paragraphs

carry water precisely as in an open canal, but the closed conduits or

pipes of steel plates and cast-iron, like the Hemlock Lake conduit at

Rochester and the East Jersey conduit of the Newark Water-works, are of

an entirely different type, as they carry water under pressure. Hence

the slope or sine of inclination _s_ belongs to the hydraulic gradient

rather than to the grade of the pipe itself. Where the pipe-line is a

long one its average grade frequently does not differ much from the

hydraulic gradient, but the latter quantity must always be used. As

in the case of the masonry conduits, the coefficient _c_ in Chezy’s

formula will vary considerably with the degree of roughness of the

interior surface of the pipe, with the slope _s_, and with the mean

radius _r_. An important distinction must be made between riveted steel

pipes and those of cast-iron, for the reason that the rivet-heads

on the inside of the former exert an appreciable influence upon the

coefficient _c_. The rivet-heads add to the roughness or unevenness of

the interior of the pipe. Table XV gives the elements of the flow or

discharge in the two pipe-lines which have been taken as types, as

determined by actual measurements; it also exhibits similar elements

for timber-stave pipes, to which reference will be made later.

[Illustration: CROTON AQUEDUCT

IN EARTH.]

As would be expected, the velocity of flow in these pipes may be and

generally is considerably higher than the velocity of movement in

masonry channels. Both Tables XV and XVI give considerable range of

coefficients computed and arranged from authoritative sources, and

the coefficients _c_ for Chezy’s formula represent the best hydraulic

practice in connection with such works at the present time. In using

the formula for any special case, great care must be taken to select

a value for _c_ which has been established for conditions as closely

as possible to those in question. This is essential in order that the

results of estimated discharges may not be disappointing, as they

sometimes have been where that condition so necessary to accuracy has

not been fulfilled.

TABLE XV.

VALUES OF COEFFICIENT _c_.

LEGEND:

(A) = Hydraulic Radius _r_.

(B) = Hydraulic Gradient.

------------------------------+-----------------+-----+-------+------

| | | |

Pipe-line. | Diameter. | | |

| | (A) | (B) | (C)

------------------------------+-----------------+-----+-------+------

Hemlock Lake |36″ wrought-iron | 9″ |.000411| 1.532

” ” |24″ wr’t and cast| 6″ |.00239 | 3.448

Rush Lake to Mt. Hope |24″ cast-iron | 6″ |.00255 | 3.448

------------------------------+-----------------+-----+-------+------

Sudbury aqueduct |48″ ” ” | 12″ | | 3.738

” ” |48″ ” ” | 12″ | | 4.965

” ” |48″ ” ” | 12″ | | 6.195

” ” |48″ ” ” | 12″ | | 3.738

” ” |48″ ” ” | 12″ | | 4.965

” ” |48″ ” ” | 12″ | | 6.195

------------------------------+-----------------+-----+-------+------

East Jersey Water Co. |48″ steel riveted| 12″ |.002 | 4.62

| pipe | | |

Timber-stave pipe, Ogden, Utah|72″.5 | | | .5

” ” ” ” ” |72″.5 | | | 1.0

” ” ” ” ” |72″.5 | | | 1.5

” ” ” ” ” |72″.5 | | | 2.0

” ” ” ” ” |72″.5 | | | 2.5

” ” ” ” ” |72″.5 | | | 3.0

” ” ” ” ” |72″.5 | | | 3.5

” ” ” ” ” |72″.5 | | | 4.0

------------------------------+-----------------+-----+-------+------

LEGEND:

(A) = Coefficient _c_.

(B) = Cubic Feet per Second.

------------------------------+-------+--------+---------+---------

| | Discharge. |

Pipe-line. | +--------+---------+

| (A) | (B) | (C) | Remarks.

------------------------------+-------+--------+---------+---------

Hemlock Lake | 87.3 |10.83124|7,000,000|

” ” | 99.7 |10.83124|7,000,000| 1892.

Rush Lake to Mt. Hope | 96.5 |10.83124|7,000,000+---------

Sudbury aqueduct |140.14 | | |

” ” |142.11 | | | Pipe new

” ” |144.09 | | | 1880.

| | | +---------

| | | | After

| | | | cleaning,

” ” |139.94†| | | 1894-95.

” ” |141.74†| | | Before

” ” |143.16†| | | cleaning,

| | | |_c_ = 108

| | | +---------

East Jersey Water Co. |103.3 | 58.02 |7,500,000| 1891.

Timber-stave pipe, Ogden, Utah| 72 | | | 1897.

” ” ” | 96 | | |

” ” ” |109 | | |

” ” ” |115 | | |

” ” ” |119 | | |

” ” ” |122 | | |

” ” ” |124 | | |

” ” ” |126 | | |

------------------------------+-------+--------+---------+---------

† These values correspond to the formula _c_ = 131.88_v_⁰˙⁰⁴⁵.

TABLE XVI.

___

VALUES OF _c_ IN _v_ = _c_√_rs_.

--------------+------------+-----+-----+-----+-----+-----+-----

| No. | 1 | 2 | 3 | 4 | 5 | 6

--------------+------------+-----+-----|-----+-----+-----+-----

| | | 4 | | | |

| Age | New |Years| New | New | New | New

--------------+------------+-----+-----+-----+-----+-----+-----

Feet/sec. | Inches | 36 | 36 | 38 | 38 | 42 | 42

--------------+------------+-----+-----+-----+-----+-----+-----

0.5 | | | | | | |

1 | | 86 | | | | | 96

1.48 | | | | | | |

1.5 | | 90.6| | | | |103

2.0 | | 95.2| | | | |107.9

2.44 | | | | | |115.9|

2.5 | | 99.4| | | | |111

3 | |103.3| | | | |112.6

3.23 | | | |114 | | |

3.27 | | | |116.6| | |

3.32 |_c_ in _v_ =| | | | | |

3.5 | ___ |107 | | | | |113

3.52 | _c√rs_. | | | | | |

3.9 | | | | |109.2| |

3.96 | | | | | | |

4 | |110.6| | | | | 112.8

4.5 | |114 | | | | | 111.8

4.93 | | |106.3| | | |

5 | |117.2| | | | | 110.8

5.5 | |120.4| | | | | 110.2

6 | |123.6| | | | | 110

12.6 | | | | | | |

--------------+------------+-----+-----+-----+-----+-----+------

coefficient | | .014| .013| .013| .013| .013| .013

--------------+------------+-----+-----+-----+-----+-----+----+-----

| No. | 7 | 8 | 9 | 10 | 11 |12 | 13

--------------+------------+-----+-----+-----+-----+-----+----+-----

| | | | 4 | 4 | | | 5

| Age | New | New |Years|Years| New | New|Years

--------------+------------+-----+-----+-----+-----+-----+----+-----

Feet per sec. | Inches | 42 | 48 | 48 | 48 | 48 | 72 | 103

--------------+------------+-----+-----+-----+-----+-----+----+-----

0.5 | | | | | | |110 |126.5

1 | |101 |101.2| 78 | 97.2| 97.1|110 |116.6

1.48 | | | | | | | |

1.5 | |102.8|105.4| 84.6|100.8| 98.7|111 |112.7

2.0 | |104.3|108.8| 89.6|103.3|100.3|110 |110.3

2.44 | | | | | | | |

2.5 | |105.5|111.2| 92.4|104.9|101.6|108 |108.8

3 | |106.4|111.8| 93 |105.3|102.2|108 |107.7

3.23 | | | | | | | |

3.27 | | | | | | | |

3.32 |_c_ in _v_ =| | | | | | |

3.5 | ___ |107.2|113.4| 93.2|104.8|103.6|110 |106.9

3.52 | _c√rs_. | | | | | | |

3.9 | | | | | | | |

3.96 | | | | | | | |

4 | |107.8|113.2| 94 |104 |104.2|111 |106.2

4.5 | |108.2|112.4| 94.2|103.7|104.7| |105.6

4.93 | | | | | | | |

5 | |108.4|112 | 94.4|103.7|105.1| |

5.5 | |108.5|111.7| 94.7|103.7|105.2| |

6 | |108.5|111.6| 94.9|103.7|105.2| |

12.6 | | | | | | | |

--------------+------------+-----+-----+-----+-----+-----+----+-----

coefficient | | .013| .013| .016| .014| .014|.014| .015

--------------+------------+-----+-----+-----+-----+-----+----+-----

Exp. Nos. 1-2. Clemens Herschel, 1802. East Jersey Conduit,

cylindrical joints.

Nos. 3-4. E. Kuichling, 1895. New Rochester conduit,

cylindrical joints.

No. 5. I. W. Smith, 1896. Portland, Oregon, water-works.

Nos. 6-7. Clemens Herschel, 1896. East Jersey conduit,

taper joints.

No. 8. Clemens Herschel, 1892. East Jersey conduit,

cylindrical joints.

Nos. 9-10. Clemens Herschel, 1896. East Jersey conduit,

cylindrical joints.

No. 11. Clemens Herschel, 1896. East Jersey conduit,

taper joints.

No. 12. Marx, Wing, Hoskins, 1897. Pioneer El. Power Co.,

Ogden, Utah.

No. 13. Clemens Herschel, 1887. Holyoke, Mass.,

testing flume.

[Illustration: CROTON AQUEDUCT

IN ROCK.]

=191. Change of Hydraulic Gradient by Changing Diameter of Pipe.=—It

has already been seen, in the case of closed pipes or conduits, that

the hydraulic gradient with slope _s_ governs the velocity of flow, and

also that all parts of the pipe-line must be kept below that gradient.

It is sometimes desirable, in order to meet conditions either of

topography or of flow, to raise or lower the hydraulic gradient over

the whole or some portion of the pipe-line. This can easily be done

to any needed extent by varying the diameter of the pipe. An increase

in diameter will in general decrease the velocity of the water and

increase its pressure, thus increasing correspondingly the height of

the columns of water in the piezometer tubes. As the top surface of the

latter determines the hydraulic gradient, it is seen that increasing

the diameter of a portion of the pipe-line will correspondingly

raise the gradient over the same portion. Thus by a proper relative

variation of diameters the hydraulic gradient of a given pipe-line may

readily be controlled within sufficient limits to meet any ordinary

requirements of this character.

=192. Control of Flow by Gates at Upper End of Pipe-line.=—Obviously,

if the pressure in the pipe-line is diminished, less thickness of metal

will be required to resist it, and a corresponding degree of economy

may be reached by a decrease in the quantity of metal. In the 21 miles

of 48-inch steel-plate pipe of the East Jersey Water Company there is

a fall of 340 feet; if, therefore, the flow through that pipe were

regulated by a gate or gates at its lower end, the lower portion of the

line would be subjected to great intensity of pressure. If, however,

the flow through the pipe is controlled by a gate or gates at its

upper end, enough water only may be admitted to enable it to flow full

with the velocity due to the hydraulic gradient. By such a procedure

the pressure upon the pipe over and above that which is necessary to

produce the gradient is avoided. This condition is not only judicious

in the reduction of the amount of metal required, but also in reducing

both the leakage and the tendency to further leakage, which is largely

increased by high pressures. This feature of control of pressure in a

long pipe-line with considerable fall is always worthy of most careful

consideration.

=193. Flow in Old and New Cast-iron Pipes—Tubercles.=—The velocity of

flow through cast-iron mains or conduits or through the cast-iron pipes

of a distribution system of public water-supply depends largely upon

the condition of the interior surface of the pipes as affected by age.

All cast-iron pipes before being shipped from the foundry where they

are manufactured are immersed in a hot bath of suitable coal-tar pitch

composition in order to protect them from corrosion. After having been

in use a few years this coating on the interior of the pipes is worn

off in spots and corrosion at once begins. The iron oxide produced

under these circumstances forms projections, or tubercles as they are

called, of greatly exaggerated volume and out of all proportion to

the actual weight of oxide of iron. When the pipes are emptied these

tubercles are readily removed by scraping, but before their removal

they greatly obstruct the flow of water through the pipes. Indeed this

obstruction is so great that the discharging capacity of cast-iron

mains must be treated in view of its depreciation from this source.

Table XVII exhibits the value of the coefficient _c_ to be used in

Chezy’s formula for all cast-iron pipes having been in use for the

periods shown.

TABLE XVII.

TABLE OF VALUES OF _f_ AND _c_.

LEGEND:

(A) = Diameter, Inches.

(B) = Hydraulic Radius _r_, Inches.

(D) = Coefficient _c_.

(E) = Coefficient _f_.

---------+-------------------------+-----+----+-----+-----+------

| | | | | |

| | (A) |(B) | (C) | (D) | (E)

| | | | | |

---------+-------------------------+-----+----+-----+-----+------

Darcy |New Pipe | 3.22| .8 | 0.29| 78.5| .0418

| | | |10.71|100.0| .0257

---------+-------------------------+-----+----+-----+-----+------

Darcy |Old cast-iron pipe lined | 9.63|2.41| 1.00| 72.5| .0489

| with deposit | | |12.42| 74.0| .0468

---------+-------------------------+-----+----+-----+-----+------

Darcy |Pipe above cleaned | 9.63|2.41| 0.91| 90.0| .0316

| | | |14.75| 98.0| .0269

---------+-------------------------+-----+----+-----+-----+------

Brush |Cast-iron pipe tar-coated|20 |5 | 2.00|114.0| .0197

| and in service 5 years. | | | 3.00|110.0| .0214

---------+-------------------------+-----+----+-----+-----+------

Darrach |Cast-iron pipe in service|20 |5 | 2.71| 67.5| .0568

| 11 years | | | 5.11| 83.0| .0376

---------+-------------------------+-----+----+-----+-----+------

Darrach |Cast-iron pipe in service|36 |9 | 1.58| 60.0| .0716

| 7 years | | | 2.37| 66.0| .0586

---------+-------------------------+-----+----+-----+-----+------

Obviously it is not possible to clean the smaller pipes of a

distribution system, but large cast-iron conduits may be emptied at

suitable periods and have their interior surfaces cleaned of tubercles

or other accumulations. At the same time, if necessary, a new coal-tar

coating can be applied.

Table XVIII exhibits the values of the coefficient _c_ to be used in

Chezy’s formula for new and clean coated cast-iron pipes. It represents

the results of actual hydraulic experience and is taken from Hamilton

Smith’s “Hydraulics.” A comparison between this table and that which

precedes will show how serious the effect of tubercles may be on the

discharging capacity of a cast-iron pipe.

____

In using Chezy’s formula, _v_ = _c_√_rs_,

in connection with either Table XVII or XVIII, the slope or sine of

inclination _s_ of the hydraulic gradient may be readily computed

by equation (10), which gives the head lost by friction in a closed

circular pipe as

_l v²_

_h_ = _f_ - --- ----.

_d_ 2_g_

It is only necessary in a straight pipe or one nearly straight to

compute the quantity

_h f v²_

_s_ = --- = --- ------.

_l d_ 2_g_

TABLE XVIII.

____

VALUES OF _c_ IN FORMULA: _v_ = _c__√_rs_.

--------+------+-------+-------+-------+-------+-------+-------

Velocity| Diameters in Feet (_d_ = 4_r_).

_v_, |

Feet per|------+-------+-------+-------+-------+-------+-------

Second.| .05 | .1 | 1 | 1.5 | 2 | 2.5 | 3

--------+------+-------+-------+-------+-------+-------+-------

1 | | 80.0 | 96.1 | 102.8 | 108.8 | 112.7 | 116.7

2 | 77.8 | 88.9 | 104.0 | 110.9 | 116.2 | 120.3 | 123.8

3 | 82.4 | 93.7 | 108.7 | 115.6 | 120.8 | 124.8 | 128.3

4 | 85.6 | 97.0 | 112.0 | 118.9 | 124.0 | 128.1 | 131.5

5 | 87.6 | 99.3 | 114.4 | 121.3 | 126.5 | 130.6 | 134.1

6 | 89.1 | 101.0 | 116.3 | 123.2 | 128.6 | 132.6 | 136.3

7 | 90.0 | 102.4 | 118.0 | 125.0 | 130.4 | 134.6 | 138.2

8 | 90.0 | 103.3 | 119.3 | 126.4 | 132.0 | 136.3 | 140.0

9 | 90.7 | 104.0 | 120.4 | 127.7 | 133.3 | 137.7 | 141.6

10 | 90.8 | 104.5 | 121.4 | 128.8 | 134.5 | 139.0 | 142.9

11 | 90.9 | 104.7 | 122.0 | 129.7 | 135.6 | 140.2 | 144.2

12 | 91.0 | 104.8 | 122.5 | 130.4 | 136.4 | 141.1 | 145.2

13 | 91.0 | 105.0 | 122.9 | 131.0 | 137.1 | 141.9 | 146.1

14 | 91.0 | 105.0 | 123.2 | 131.5 | 137.6 | 142.5 | 146.7

15 | 91.0 | 105.0 | 123.6 | 131.8 | 138.0 | 142.9 | 147.2

20(?)| | | 123.9 | 132.9 | | |

--------+------+-------+-------+-------+-------+-------+-------

Velocity| Diameters in Feet (_d = 4r_).

_v_, |

Feet per+------+-------+-------+-------+-------+-------

Second.| 3.5 | 4 | 5 | 6 | 7 | 8

--------+------+-------+-------+-------+-------+-------

1 |120.2 | 123.0 | 127.8 | 131.8 | 134.8 | 137.5

2 |127.0 | 129.9 | 134.3 | 138.0 | 141.0 | 143.3

3 |131.4 | 134.2 | 138.6 | 142.3 | 145.4 | 147.6

4 |134.6 | 137.4 | 141.9 | 145.5 | 148.6 | 151.0

5 |137.1 | 140.0 | 144.7 | 148.1 | 151.2 | 153.6

6 |139.4 | 142.3 | 146.9 | 150.5 | 153.5 |

7 |141.5 | 144.5 | 149.0 | 152.7 | |

8 |143.3 | 146.3 | 151.0 | 154.9 | |

9 |145.0 | 148.1 | 152.8 | 156.7 | |

10 |146.4 | 149.7 | 154.6 | | |

11 |147.7 | 151.0 | | | |

12 |148.8 | 152.3 | | | |

13 |149.8 | 153.2 | | | |

14 |150.5 | 154.0 | | | |

15 |151.1 | 154.6 | | | |

20(?)| | | | | |

--------+------+-------+-------+-------+-------+-------

=194. Timber-stave Pipes.=—In the western part of the country long

conduits or pipe-lines are frequently constructed of timber called

redwood. Staves of suitable thickness, sometimes 1¾ inches, are

accurately shaped and finished with smooth surfaces so as to form large

pipes of any desired diameter. These staves are held rigidly in place

with steel bands drawn tight with nuts on screw ends, so as to close

tightly the joints between them. Such wooden conduits are rapidly and

cheaply built and are very durable. They have the further advantage

of requiring no interior coating, as the timber surface remains

indefinitely unaffected by the water flowing over it. The latter part

of Table XV shows coefficients for Chezy’s formula which may be used

for such a class of timber conduits. As the interior surfaces of such

closed conduits are always very smooth, the coefficients are seen to

be relatively large, and such pipes are, therefore, well adapted to

maintain unimpaired discharging capacity for great lengths of time.

CHAPTER XVIII.

=195. Pumping and Pumps.=—When it is impossible to secure water at

sufficient elevation to be delivered to the points of consumption by

gravity, it is necessary to resort to pumping in order to raise it

to the desired level. Indeed it is sometimes necessary to resort to

pumping in connection with a gravity supply in order to deliver water

to the higher parts of the distribution system, the lower points being

supplied by gravity. This combination of gravity supply with pumping

is not unusual. That part of New York north of Thirty-fourth Street

between Lexington and Fifth avenues, north of Thirty-fifth Street

between Fifth and Sixth avenues, north of Fifty-first Street between

Sixth and Ninth avenues, north of Fifty-fifth Street between Ninth and

Tenth avenues, north of Fifty-eighth Street between Tenth and Eleventh

avenues, and north of Seventy-second Street between Eleventh Avenue

and the North River, with elevation of 60 feet or more above mean high

tide-water, is supplied from the high-service reservoir near High

Bridge, the water being elevated to it from the Croton supply by the

pumping-station at the westerly end of the bridge. The elevation of the

water surface in the High Bridge reservoir is 208 feet, and that of the

large reservoir in Central Park 115 feet, above mean high tide-water.

Some specially high points on the northern part of Manhattan Island are

supplied from the High Bridge tower, whose water surface is 316 feet

above mean high tide.

[Illustration]

[Illustration: Skeleton Pumps.]

The pumps employed for the purpose of elevating water to

distributing-reservoirs are among the finest pieces of machinery built

by engineers at the present time. They are usually actuated by steam

as a motive power, the steam being supplied from suitable boilers or

batteries of boilers in which coal is generally used as fuel. The

modern pumping-engine is in reality a combination of three classes of

machinery, the boilers, the steam-engines, and the pumps. There are

various types of boilers as well as of engines and pumps, all, when

judiciously designed and arranged, well adapted to the pumping-engine

process. The pumps are generally what are called displacement

pumps; that is, the water in the pump-cylinder is displaced by the

reciprocating motion of a piston or plunger. These pumps may be either

double-acting or single-acting; in the former case, as the piston or

plunger moves in one direction it forces the water ahead of it into

the main or pipe leading up to the reservoir into which the water is

to be delivered, while the water rising from the pump-well follows back

of the piston or plunger to the end of its stroke. When the motion

is reversed the latter water is forced on its way upward through the

main, while the water rises from the pump-well into the other end of

the water-cylinder. In the case of single-acting pumps water is drawn

up into the water-cylinder from the pump-well during one stroke and

forced up through the main during the next stroke, one operation only

being performed at one time. The pump-well is a well or tank, usually

of masonry, into which the water runs by gravity and from which the

pump raises it to the reservoir. For the purposes of accessibility and

convenience in repairing, the pump is always placed at an elevation

above the water in the pump-well, the pressure of the atmosphere on the

water in the well forcing the latter up into the pump-cylinder as the

piston recedes in its stroke. The height of a column of water 1 square

inch in section representing the pressure of the atmosphere per square

inch is about 34 feet, but a pump-cylinder should not be placed more

than about 18 feet above the surface of the water in the pump-well in

order that the water may rise readily as it follows the stroke of the

plunger.

In the operation of the ordinary pump the direction of the water as it

flows into and out of the pump-cylinder must necessarily be reversed,

and this is true also with the type of pump called the differential

plunger-pump, which is really a single-acting pump designed so as to

act in driving the water into the main like a double-acting pump,

i.e., both motions of the plunger force water through the main, but

only one draws water from the pump-well into the pump-cylinder. Valves

may be so arranged in the pump-piston as to make the progress of the

water through the pump continuous in one direction and so avoid the

irregularities and shocks which necessarily arise to some extent from a

reversal of the motion of the water.

The steam is used in the steam-cylinders of a pumping-engine precisely

as in every other type of steam-engine. At the present time compound

or triple-expansion engines are generally used, among the well-known

types being the Worthington duplex direct-acting pump without crank or

fly-wheel, the Gaskill crank and fly-wheel pumping-engine, the Allis

and the Leavitt pumping-engines, both of the latter employing the crank

and fly-wheel and both may be used as single- or double-acting pumps,

usually as the latter. The characteristic feature of the well-known

Worthington pumping-engine is the movement of the valves of each of the

two engines by the other for the purpose of securing a quiet seating of

the valves and smooth working.

One of the most important details of the pumping-engine is the

system of valves in the water-cylinder, and much ingenuity has been

successfully expended in the design of proper valve systems. These

pump-valves must, among other things, meet the following requirements

as efficiently as possible: they must close promptly and tightly, so

that no water may pass through them to create slip or leakage; they

should have a small lift, so as to allow prompt closing, and large

waterways, to permit a free flow through them with little resistance;

they must also be easily operated, so as to require little power,

and, like all details of machinery, they should be simple and easily

accessible for repairing when necessary.

As steam is always used expansively, its force impelling the plunger

will have a constant value during the early portion of the stroke

only, and a much less value, due to the expansion of the steam, at

and near the end of the stroke, while the head of water against which

the pump operates is practically constant. There is, therefore, an

excess of effort during the first part of the stroke and a deficiency

during the latter part. Unless there should be some means of taking

up or cushioning this difference, the operation of the pump would be

irregular during the stroke and productive of water-hammer or blows to

the engine. Two means are employed to remove this undesirable effect,

i.e., the fly-wheel and the air-chamber, or both. In the one case the

excess of work performed by the steam in the early part of the stroke

is stored up as energy in the accelerated motion of the fly-wheel and

given out by the latter near the end of the stroke, thus producing the

desired equalization. The air-chamber is a large reservoir containing

air, attached to and freely communicating with the force-main or pipe

near its connection with the pumps. In this case the excess of work

performed at the beginning of the stroke is used in compressing the

air in the air-chamber, sufficient water entering to accomplish that

purpose. This compressed air acts as a cushion, expanding again at the

end of the stroke and reinforcing the decreasing effort of the steam.

=196. Resistances of Pumps and Main—Dynamic Head.=—Obviously the

water flowing through the pipes, pump-cylinders, and pump-valves

will experience some resistance, and it is one purpose in good

pumping-engine design to make the progress of the water through the

pump so direct and free as to reduce these losses to a minimum.

Similarly the large pipe or main, called the force-main, leading

from the pump up to the reservoir into which the water is delivered,

sometimes several thousand feet long, will afford a resistance of

friction to the water flowing through it. The head which measures

this frictional loss is given by equation (10) on page 239. All these

resistances will increase rapidly with the velocity with which the

water flows through the pipes and other passages, as do all hydraulic

losses. It is obviously advisable, therefore, to make this velocity

as low as practicable without unduly increasing the diameter of the

force-main. This velocity seldom exceeds about 3 feet per second.

[Illustration: Allis Pump.]

[Illustration: Section of Allis Pumping-Engine.]

The static head against which the pumping-engine operates is the

vertical height or elevation between the water surfaces in the

pump-well and the reservoir. The head which represents the resistances

of the passages through the pump and force-main, when added to the sum

of the static head and the head due to the velocity in the force-main,

gives what is called the dynamic head; it represents the total head

against which the pump acts. If _h_ represents the static head, _hʹ_

the head due to all the resistances, and _h″_ the head due to the

velocity in the force-main, then the dynamic head will be

_l v² v² v²_

_H_ = _h + hʹ + h″_ = _h_ + _f_ --- ---- + _n_---- + ----,

_d_ 2_g_ 2_g_ 2_g_

in which _f_ has a value of about .015 and _n_ is a coefficient which

when multiplied by the velocity head will represent the loss of head

incurred by the water in passing through the pump-cylinder and valves.

The latter quantity is variable in value; but it is seldom more than a

few feet.

=197. Duty of Pumping-engines.=—It is thus seen that the collective

machines and force-main forming the pumping system afford opportunity

for a number of serious losses of energy found chiefly in the boiler,

the engine, and the pump. The excellence of a pumping-plant, including

the boilers, may obviously be measured by the amount of useful work

performed by a standard quantity, as 100 pounds of coal. Sixty or more

years ago, in the days of the old Cornish pumping-engine, the standard

of excellence or “duty” was the number of foot-pounds of work, i.e.,

the number of pounds lifted one foot high, performed by one bushel of

coal. As early as 1843 the Cornish pumping-engine reached a duty, per

bushel of coal, of 107,500,000 foot-pounds. These pumping-engines were

single-acting, the steam raising a weight the descent of which forced

the water up the delivery-pipe.

At a later date and until about ten years ago the usual standard or

criterion applied to pumping-engines for city water-works was the

amount of work performed in lifting water for each 100 pounds of

coal consumed; this result was also called the “duty” of the engine.

In order to determine the duty of a pumping-engine it was thus only

necessary to observe carefully for a given period of time, i.e.,

twenty-four hours or some other arbitrary period, the amount of coal

consumed, the condition of the furnace-fires at the beginning and end

of the test being as nearly the same as possible, and measure at the

same time the total amount of water discharged into the reservoir.

The total weight of water raised multiplied by the total number of

feet of elevation from the water surface in the pump-well to that in

the reservoir would give the total number of foot-pounds of useful

work performed. This quantity divided by the number of hundred pounds

of coal consumed would then give what is called the “duty” of the

pumping-engine.

=198. Data to be Observed in Pumping-engine Tests.=—Obviously it is

necessary to observe a considerable number of data with care. No

pump works with absolute perfection. A little water will run back

through the valves before they are seated, and there will be a little

leakage either through the valves or through the packing around the

piston or plunger, or both sources of leakage may exist. That leakage

and back-flow represent the amount of slip or water which escapes

to the back of the plunger after having been in front of it. In

well-constructed machinery this slip or leakage is now very small and

may be but a small fraction of one per cent. Inasmuch as the amount

of work performed by the steam will be the same whether this slip

or leakage exists or not, the latter is now frequently ignored in

estimating the duty of pumping-engines, the displacement of the piston

or plunger itself being taken as the volume of water pumped at each

stroke.

Again, in discussing the efficiency of the steam portion of the

machinery the amount of partial vacuum maintained in the vacuum-pump,

which is used to move the water of the condensed steam, is affected

by atmospheric pressure, as is the work which is performed. Hence

in complete engine tests it is necessary to observe the height of

the barometer during the test. It is also necessary to observe the

temperature of feed-water supplied to the boiler, and to use accurate

appliances for ascertaining with the greatest exactness practicable

the weight of dry steam used in the steam-cylinders and the amount of

water which it carries. It is not necessary for the present purpose

to discuss with minuteness these details, but it is evident from the

preceding observations that the complete test of a pumping-engine

involves the accurate observation of many data and their careful use in

computations. The determination of the duty alone is but a simple part

of those computations, and the duty is all that is now in question.

=199. Basis of Computations for Duty.=—It was formerly necessary in

giving the duty of a pumping-engine to state whether the 100 pounds of

coal was actually coal as shovelled into the furnace, or whether it was

that coal less the weight of ash remaining after combustion. It was

also necessary to specify the quality of coal used, because the heating

capacity of different coals may vary materially. For these different

reasons the statement of the duty of a pumping-engine in terms of a

given weight of coal consumed involved considerable uncertainty, hence

in 1891 a committee of the American Society of Mechanical Engineers,

appointed for the purpose, took into consideration the best method

of determining and stating the duty of a pumping-engine. The report

of that committee may be found in vol. XII of the Transactions of

that Society. The committee recommended that in a duty test 1,000,000

heat-units (called British Thermal Units or, as abbreviated, frequently

B.T.U.) should be substituted for 100 pounds of coal. In other words,

that the following should be the expression for the duty:

foot-pounds of work done

Duty = ----------------------------------- × 1,000,000.

total number of heat-units consumed

For some grades of coal in which 1,000,000 heat-units would be

available for every 100 pounds the numerical value of the duty

expressed in the new terms would be unchanged, but for other grades of

coal the new expression of the duty might be considerably different.

=200. Heat-units and Ash in 100 Pounds of Coal, and Amount of Work

Equivalent to a Heat-unit.=—The following table exhibits results

determined by Mr. George H. Barrus (Trans. A. S. M. E., vol. XIV. page

816), giving an approximate idea of the total number of heat-units

which are made available by the combustion of 100 pounds of coal of the

kinds indicated:

Semibitumintous:

George’s Creek Cumberland, Percentage of Ash.

1,287,400 to 1,421,700 6.1 to 8.6

Pocahontas,

1,360,800 to 1,460,300 3.2 to 6.2

New River,

1,385,800 to 1,392,200 3.5 to 5.7

Bituminous:

Youghiogheny, Pa., lump,

1,294,100 5.9

Youghiogheny, Pa., slack,

1,166,400 10.2

Frontenac, Kan.,

1,050,600 17.7

Cape Breton Caledonia,

1,242,000 8.7

Anthracite:

1,152,100 to 1,318,900 9.1 to 10.5

[Illustration: Worthington Pump.]

Each unit or B.T.U. represents the amount of heat required to raise

one pound of water at 32° Fahr. 1° Fahr., and it is equal to 778

foot-pounds of work. In other words, 778 foot-pounds of work is said

to be the mechanical equivalent of one heat-unit. The amount of work,

therefore, which one pound of dry steam is capable of performing at

any given pressure and at the corresponding temperature may readily

be found by multiplying the number of available heat-units which it

contains, and which may be readily computed if not already known, by

778, or as in a pumping-engine duty trial, knowing by observation the

number of pounds of steam at a given pressure and temperature supplied

through the steam-cylinders, the number of heat-units supplied in

that steam is at once known or may easily be computed. Then observing

or computing the total weight of water raised by the pumping-engine,

as well as the total head (the dynamic head) against which the

pumping-engine has worked, the total number of foot-pounds of work

performed can be at once deduced. This latter quantity divided by the

number of million heat-units will give the desired duty.

[Illustration: Section of Worthington Pump.]

=201. Three Methods of Estimating Duty.=—At the present time it is

frequently, and perhaps usually, customary to give the duty in terms

of 100 pounds of coal consumed, as well as in terms of 1,000,000

heat-units. Frequently, also, the duty is expressed in terms of 1000

pounds of dry steam containing about 1,000,000 heat-units. As has

sometimes been written, the duty unit is 100 for coal, 1000 for steam,

and 1,000,000 for heat-units.

=202. Trial Test and Duty of Allis Pumping-engine.=—The following data

are taken from a duty test of an Allis pumping-engine at Hackensack,

N. J., in 1899 by Prof. James E. Denton. This pumping-engine was built

to give a duty not less than 145,000,000 foot-pounds for each “1000

pounds of dry steam consumed by the engine, assuming the weight of

water delivered to be that of the number of cubic feet displaced by the

plungers on their inward stroke, i.e., to be 145,000,000 foot-pounds

at a steam pressure of 175 pounds gauge.” The capacity of the engine

was to be 12,000,000 gallons per twenty-four hours at a piston speed

not exceeding 217 feet per minute. The engine was of the vertical

triple-expansion type with cylinders 25.5 inches, 47 inches, and 73

inches in diameter with a stroke of 42¹/₁₆ inches, the single-acting

plunger being 25.524 inches in diameter. The following data and figures

illustrate the manner of computing the duty:

DUTY PER 1000 POUNDS OF DRY STEAM BY PLUNGER DISPLACEMENT.

1. Circumference of plungers, _Cl_ 80.1875 ins.

2. Length of stroke, 7 42.0625 ins.

3. Number of plungers (single-acting) 3

4. Aggregate displacement of plunger per revolution =

3_C²l_

------ = _d_ 64,4557.1 cu. ins.

4π

5. Revolutions during 24 hours, _N_ 43,337

6. Weight of one cubic foot of water, _w_ 62.42 lbs.

7. Total head pumped against, _H_ 266.61 ft.

8. Total feed-water per 24 hours, _W_ 160,354 lbs.

9. Duty per 1000 lbs. of feed-water =

_d × w H × N_ × 1000

------ × -------------

1728 _W_

266.61 × 43,337 × 1000

= 2,331,976 × ---------------------- = 168,027,200 ft.-lbs.

160,354

10. Percentage of moisture in steam at

engine-throttle valve 0.3 per cent.

168,027,200

11. Duty per 1000 lbs. of dry steam, ----------- = 168,532,800

0.997 ft.-lbs.

DUTY PER MILLION HEAT-UNITS.

12. Average steam pressure at throttle above atmosphere. 173 lbs.

13. Average feed-water temperature. 78°.5 Fahr.

14. Total heat in one pound of steam containing

0.3 per cent. of moisture above 32° Fahr. 1,194.2 B. T. U.

15. Heat per lb. of feed-water above 32° Fahr. 46.5 ”

-------

16. Heat supplied per lb. of feed-water

above 32° Fahr. 1,147.7 ”

17. Duty per lb. of feed-water. 168,027.2 ft.-lbs.

18. Duty per million B. T. U. 146,403,614 ”

=203. Conditions Affecting Duty of Pumping-engines.=—Manifestly the

duty of a pumping-engine by whatever standard it may be measured will

vary with the conditions under which it is made. A new engine running

under the favoring circumstances of a short-time test may be expected

to give a higher duty than when running under the ordinary conditions

of usage one month after another. Hence it can scarcely be expected

that the monthly performance, and much less the yearly performance, of

an engine will show as high results as when tested for a day or two or

for less time.

=204. Speeds and Duties of Modern Pumping-engines.=—The following table

gives the piston or plunger speeds of a number of the best modern

pumping-engines, and the corresponding duties, with the standards by

which those duties are measured.

LEGEND:

(A) = Piston Speed in Feet per Minute.

(B) = Duty in Foot-pounds.

-------------------------------+------+-----------+-----------------

Engine. | (A) | (B) | Expressed in

-------------------------------+------+-----------+-----------------

Ridgewood Station, Brooklyn, | | |

Worthington engine |164.0 |137,953,585| 1000 lbs. of

| | | dry steam

14th St. pumping-station, | | |

Chicago; built by Lake Erie | | |

Engine Works |210.54|133,445,000| Million B.T.U.

Allis engine at Hackensack, | | |

N. J. |210.65|146,403,416| ” ”

Snow pump at Indianapolis |214.6 |150,100,000| ” ”

Leavitt pump at Chestnut Hill | |144,499,032| ” ”

Nordberg at Wildwood |256.0 |162,132,517| ” ”

Allis at Chestnut Hill, tested | | |

May 1, 1900 |192.5 |157,002,500| Million B.T.U.

Allis at St. Louis, tested | | |

February 26, 1900 |197.16|158,077,324| ” ”

Barr at Waltham, Mass. |194.28|128,865,000| 1000 lbs. of

| | | dry steam

Allis at St. Paul, Minn. |189.0 |144,463,000| ” ” ”

Lake Erie Engine Works at | | |

Buffalo |207.7 |135,403,745| Million B.T.U.

These results show that material advances have been made in

pumping-engine designs within a comparatively few years.

CHAPTER XIX.

=205. Distributing-reservoirs and their Capacities.=—The water of a

public supply seldom runs from the storage-reservoir directly into

the distributing system or is pumped directly into it, although such

practices may in some cases be permissible for small towns or cities.

Generally distributing-reservoirs are provided either in or immediately

adjacent to the distributing system of pipes, meaning the water-pipes

large and small which are laid through the streets of a city or town,

and the service-pipes leading from the latter directly to the consumers.

The capacity ordinarily given to these distributing-reservoirs is not

controlled by any rigid rule, but depends upon the local circumstances

of each case. If they are of masonry and covered with masonry arches,

as required for the reception of some filtered waters, they are made as

small as practicable on account of their costs. If, on the contrary,

they are open and formed of suitably constructed embankments, like the

distributing-reservoirs of New York City in Central Park and at High

Bridge, they are and should be of much greater capacity. The storage

volume of the High Bridge reservoir amounts to 11,000,000 gallons,

while that of the Central Park reservoir is 1,000,000,000 gallons.

Again, the capacity of the old receiving-basin in Central Park is

200,000,000 gallons. These reservoirs act also as equalizers against

the varying draft on the system during the different portions of the

day and furnish all desired storage for the demands of fire-streams,

which, while it lasts, may be a demand at a high rate. It may be

approximately stated under ordinary circumstances that the capacity of

distributing-reservoirs for a given system should equal from two or

three to eight or ten days supply. It is advantageous to approach the

upper of those limits when practicable. The volume of water retained in

these reservoirs acts in some cases as a needed storage, while repairs

of pumping-machinery or other exigencies may temporarily stop the flow

into them. The larger their capacity the more effectively will such

exigencies be met.

=206. System of Distributing Mains and Pipes.=—Gate-houses must be

placed at the distributing-reservoirs within which are found and

operated the requisite gates controlling the supply into the reservoir

and the outflow from it into the distributing system. The latter

begins at the distributing-reservoir where there may be one or two

or more large mains, usually of cast-iron. These mains conduct the

water into the branching system of pipes which forms a network over

the entire city or town. A few lines of large pipes are laid so as

to divide the total area to be supplied into convenient portions

served by pipes of smaller diameter leading from the larger, so that

practically every street shall carry its line or lines of piping from

which every resident or user may draw the desired supply. Obviously,

as a rule, the further the beginning of the distributing system is

departed from in following out the ramifications of the various lines

the smaller will the diameter of pipe become. The smallest cast-iron

pipe of a distributing system is seldom less than 3 inches, and

sometimes not less than 4 or 6 inches. There should be no dead ends

in any distributing system. By a dead end is meant the end of a line

of pipes, which is closed so that no water circulates through it.

Whenever a branch pipe ceases it should be extended so as to connect

with some other pipe in the system in order to induce circulation. The

entire distributing system should therefore, in its extreme as well

as central portions, constitute an interlaced system and not a series

of closed ends. This is essential for the purity and potability of

the water-supply. A circulation in all parts of the entire system is

essential and it should be everywhere secured.

The diagram shows a portion of the distributing system of the city of

New York. It will be noticed that there is a complete connection of

the outlying portions, so as to make the interlacing and corresponding

circulation as complete and active as possible.

[Illustration: FIG. 4.—New York City Distributing System.]

=207. Diameters of and Velocities in Distributing Mains and Pipes.=—In

laying out a distributing system it will not be possible to base the

diameters at different points on close computations for velocity or

discharges based upon considerations of friction or other resistances,

as the conditions under which the pipes are found are too complicated

to make such a method workable. Approximate estimates may be made as

to the number of consumers to be supplied at a given section of a main

pipe, and consequently what the diameter should be to pass the required

daily supply so that the velocity may not exceed certain maximum limits

known to be advisable. Such estimates may be made at a considerable

number of what may be termed critical points of the system, and the

diameters may be ascertained in that manner with sufficient accuracy.

In this field of hydraulics a sound engineering judgment, based upon

experience, is a very important element, as it is in a great many other

engineering operations.

It will follow from these considerations that as a rule the larger

diameters of pipe in a given distributing system will belong to the

greater lengths, and it will be found that the velocities of water in

the various parts of a system will seldom exceed the following limits,

which, although stated with some precision, are to be regarded only as

approximate:

For 4-inch pipe 23 feet per second.

” 6 ” ” 23 ” ” ”

” 8 ” ” 17 ” ” ”

” 11 ” ” 12 ” ” ”

” 12 ” ” 12 ” ” ”

” 16 ” ” 9 ” ” ”

” 20 ” ” 8 ” ” ”

” 24 ” ” 7 ” ” ”

” 30 ” ” 7 ” ” ”

” 36 ” ” 7 ” ” ”

” 48 ” ” 7 ” ” ”

” 60 ” ” 7 ” ” ”

=208. Required Pressures in Mains and Pipes.=—In designing distributing

systems it is very essential so to apportion the pipes as to secure

the requisite pressure at the various street services. Like many other

features of a water-supply system no exact rules can be given, but it

may be stated that at the street-level a pressure of at least 20 to 30

pounds should be found in resident districts, and from 30 to 35 or 40

pounds in business districts. The character and height of buildings

affect these pressures to a large extent. Old pipe systems usually

have many weak points, and while pressures requisite to carry water

to the top of three- or four-story buildings are needed, any great

excess above that would be apt to cause breaks and result in serious

leakages. If the distributing system is one in which the pressure for

fire-streams is to be found at the hydrants, then greater pressures

than those named must be provided. In such cases the pressures in pipes

at the hydrants should range from 60 to 100 pounds.

=209. Fire-hydrants.=—Fire-hydrants must be placed usually at street

corners, if the blocks are not too long, and so distributed as to

control with facility the entire district in which they are found.

Unless fire-engines are used to create their own pressure, the lower

the pressure at the hydrant the nearer together the hydrants must be

placed. It is obvious, however, that when the pressure of the system

is depended upon for fire-streams it is desirable to have the pressure

comparatively high, so far as the hydrants are concerned, as under

those conditions they may be placed farther apart and a less number

will be required.

=210. Elements of Distributing Systems.=—The following table gives

a number of statistics, exhibiting the elements of the distributing

system of a considerable number of cities, including some pumping and

meter data pertinent to the costs of pumping on the one hand and the

extension of the use of meters on the other.

=172. Application of Fitzgerald’s Results to the Croton Watershed.=—The