In every system of machinery deriving energy from a natural waterfall
there exist the following parts:--
1. A supply channel or head race, leading the water from the highest
accessible level to the site of the machine. This may be an open channel
of earth, masonry or wood, laid at as small a slope as is consistent
with the delivery of the necessary supply of water, or it may be a
closed cast or wrought-iron pipe, laid at the natural slope of the
ground, and about 3 ft. below the surface. In some cases part of the
head race is an open channel, part a closed pipe. The channel often
starts from a small storage reservoir, constructed near the stream
supplying the water motor, in which the water accumulates when the motor
is not working. There are sluices or penstocks by which the supply can
be cut off when necessary.
2. Leading from the motor there is a tail race, culvert, or discharge
pipe delivering the water after it has done its work at the lowest
convenient level.
3. A waste channel, weir, or bye-wash is placed at the origin of the
head race, by which surplus water, in floods, escapes.
4. The motor itself, of one of the kinds to be described presently,
which either overcomes a useful resistance directly, as in the case of a
ram acting on a lift or crane chain, or indirectly by actuating
transmissive machinery, as when a turbine drives the shafting, belting
and gearing of a mill. With the motor is usually combined regulating
machinery for adjusting the power and speed to the work done. This may
be controlled in some cases by automatic governing machinery.
§ 169. _Water Motors with Artificial Sources of Energy._--The great
convenience and simplicity of water motors has led to their adoption in
certain cases, where no natural source of water power is available. In
these cases, an artificial source of water power is created by using a
steam-engine to pump water to a reservoir at a great elevation, or to
pump water into a closed reservoir in which there is great pressure. The
water flowing from the reservoir through hydraulic engines gives back
the energy expended, less so much as has been wasted by friction. Such
arrangements are most useful where a continuously acting steam engine
stores up energy by pumping the water, while the work done by the
hydraulic engines is done intermittently.
§ 170. _Energy of a Water-fall._--Let H_t be the total fall of level
from the point where the water is taken from a natural stream to the
point where it is discharged into it again. Of this total fall a
portion, which can be estimated independently, is expended in
overcoming the resistances of the head and tail races or the supply
and discharge pipes. Let this portion of head wasted be [h]_r. Then
the available head to work the motor is H = H_t - [h]_r. It is this
available head which should be used in all calculations of the
proportions of the motor. Let Q be the supply of water per second.
Then GQH foot-pounds per second is the gross available work of the
fall. The power of the fall may be utilized in three ways. (a) The GQ
pounds of water may be placed on a machine at the highest level, and
descending in contact with it a distance of H ft., the work done will
be (neglecting losses from friction or leakage) GQH foot-pounds per
second. (b) Or the water may descend in a closed pipe from the higher
to the lower level, in which case, with the same reservation as
before, the pressure at the foot of the pipe will be p = GH pounds per
square foot. If the water with this pressure acts on a movable piston
like that of a steam engine, it will drive the piston so that the
volume described is Q cubic feet per second. Then the work done will
be pQ = GHQ foot-pounds per second as before. (c) Or lastly, the water
may be allowed to acquire the velocity v = [root](2gH) by its descent.
The kinetic energy of Q cubic feet will then be ½GQv²/g = GQH, and if
the water is allowed to impinge on surfaces suitably curved which
bring it finally to rest, it will impart to these the same energy as
in the previous cases. Motors which receive energy mainly in the three
ways described in (a), (b), (c) may be termed gravity, pressure and
inertia motors respectively. Generally, if Q ft. per second of water
act by weight through a distance h1, at a pressure p due to h2 ft. of
fall, and with a velocity v due to h3 ft. of fall, so that h1 + h2 +
h3 = H, then, apart from energy wasted by friction or leakage or
imperfection of the machine, the work done will be
GQh1 + pQ + (G/g) Q (v²/2g) = GQH foot pounds,
the same as if the water acted simply by its weight while descending H
ft.
§ 171. _Site for Water Motor._--Wherever a stream flows from a higher to
a lower level it is possible to erect a water motor. The amount of power
obtainable depends on the available head and the supply of water. In
choosing a site the engineer will select a portion of the stream where
there is an abrupt natural fall, or at least a considerable slope of the
bed. He will have regard to the facility of constructing the channels
which are to convey the water, and will take advantage of any bend in
the river which enables him to shorten them. He will have accurate
measurements made of the quantity of water flowing in the stream, and he
will endeavour to ascertain the average quantity available throughout
the year, the minimum quantity in dry seasons, and the maximum for which
bye-wash channels must be provided. In many cases the natural fall can
be increased by a dam or weir thrown across the stream. The engineer
will also examine to what extent the head will vary in different
seasons, and whether it is necessary to sacrifice part of the fall and
give a steep slope to the tail race to prevent the motor being drowned
by backwater in floods. Streams fed from lakes which form natural
reservoirs or fed from glaciers are less variable than streams depending
directly on rainfall, and are therefore advantageous for water-power
purposes.
§ 172. _Water Power at Holyoke, U.S.A._--About 85 m. from the mouth of
the Connecticut river there was a fall of about 60 ft. in a short
distance, forming what were called the Grand Rapids, below which the
river turned sharply, forming a kind of peninsula on which the city of
Holyoke is built. In 1845 the magnitude of the water-power available
attracted attention, and it was decided to build a dam across the
river. The ordinary flow of the river is 6000 cub. ft. per sec.,
giving a gross power of 30,000 h.p. In dry seasons the power is 20,000
h.p., or occasionally less. From above the dam a system of canals
takes the water to mills on three levels. The first canal starts with
a width of 140 ft. and depth of 22 ft., and supplies the highest
range of mills. A second canal takes the water which has driven
turbines in the highest mills and supplies it to a second series of
mills. There is a third canal on a still lower level supplying the
lowest mills. The water then finds its way back to the river. With the
grant of a mill site is also leased the right to use the water-power.
A mill-power is defined as 38 cub. ft. of water per sec. during 16
hours per day on a fall of 20 ft. This gives about 60 h.p. effective.
The charge for the power water is at the rate of 20s. per h.p. per
annum.
§ 173. _Action of Water in a Water Motor._--Water motors may be divided
into water-pressure engines, water-wheels and turbines.
Water-pressure engines are machines with a cylinder and piston or ram,
in principle identical with the corresponding part of a steam-engine.
The water is alternately admitted to and discharged from the cylinder,
causing a reciprocating action of the piston or plunger. It is admitted
at a high pressure and discharged at a low one, and consequently work is
done on the piston. The water in these machines never acquires a high
velocity, and for the most part the kinetic energy of the water is
wasted. The useful work is due to the difference of the pressure of
admission and discharge, whether that pressure is due to the weight of a
column of water of more or less considerable height, or is artificially
produced in ways to be described presently.
Water-wheels are large vertical wheels driven by water falling from a
higher to a lower level. In most water-wheels, the water acts directly
by its weight loading one side of the wheel and so causing rotation. But
in all water-wheels a portion, and in some a considerable portion, of
the work due to gravity is first employed to generate kinetic energy in
the water; during its action on the water-wheel the velocity of the
water diminishes, and the wheel is therefore in part driven by the
impulse due to the change of the water's momentum. Water-wheels are
therefore motors on which the water acts, partly by weight, partly by
impulse.
Turbines are wheels, generally of small size compared with water wheels,
driven chiefly by the impulse of the water. Before entering the moving
part of the turbine, the water is allowed to acquire a considerable
velocity; during its action on the turbine this velocity is diminished,
and the impulse due to the change of momentum drives the turbine.
In designing or selecting a water motor it is not sufficient to consider
only its efficiency in normal conditions of working. It is generally
quite as important to know how it will act with a scanty water supply or
a diminished head. The greatest difference in water motors is in their
adaptability to varying conditions of working.
_Water-pressure Engines._
§ 174. In these the water acts by pressure either due to the height of
the column in a supply pipe descending from a high-level reservoir, or
created by pumping. Pressure engines were first used in mine-pumping on
waterfalls of greater height than could at that time be utilized by
water wheels. Usually they were single acting, the water-pressure
lifting the heavy pump rods which then made the return or pumping stroke
by their own weight. To avoid losses by fluid friction and shock the
velocity of the water in the pipes and passages was restricted to from 3
to 10 ft. per second, and the mean speed of plunger to 1 ft. per second.
The stroke was long and the number of strokes 3 to 6 per minute. The
pumping lift being constant, such engines worked practically always at
full load, and the efficiency was high, about 84%. But they were
cumbrous machines. They are described in Weisbach's _Mechanics of
Engineering_.
The convenience of distributing energy from a central station to
scattered working-points by pressure water conveyed in pipes--a system
invented by Lord Armstrong--has already been mentioned. This system has
led to the development of a great variety of hydraulic pressure engines
of very various types. The cost of pumping the pressure water to some
extent restricts its use to intermittent operations, such as working
lifts and cranes, punching, shearing and riveting machines, forging and
flanging presses. To keep down the cost of the distributing mains
very high pressures are adopted, generally 700 lb. per sq. in. or 1600
ft. of head or more.
In a large number of hydraulic machines worked by water at high
pressure, especially lifting machines, the motor consists of a direct,
single acting ram and cylinder. In a few cases double-acting pistons and
cylinders are used; but they involve a water-tight packing of the piston
not easily accessible. In some cases pressure engines are used to obtain
rotative movement, and then two double-acting cylinders or three
single-acting cylinders are used, driving a crank shaft. Some
double-acting cylinders have a piston rod half the area of the piston.
The pressure water acts continuously on the annular area in front of the
piston. During the forward stroke the pressure on the front of the
piston balances half the pressure on the back. During the return stroke
the pressure on the front is unopposed. The water in front of the piston
is not exhausted, but returns to the supply pipe. As the frictional
losses in a fluid are independent of the pressure, and the work done
increases directly as the pressure, the percentage loss decreases for
given velocities of flow as the pressure increases. Hence for
high-pressure machines somewhat greater velocities are permitted in the
passages than for low-pressure machines. In supply mains the velocity is
from 3 to 6 ft. per second, in valve passages 5 to 10 ft. per second, or
in extreme cases 20 ft. per second, where there is less object in
economizing energy. As the water is incompressible, slide valves must
have neither lap nor lead, and piston valves are preferable to ordinary
slide valves. To prevent injurious compression from exhaust valves
closing too soon in rotative engines with a fixed stroke, small
self-acting relief valves are fitted to the cylinder ends, opening
outwards against the pressure into the valve chest. Imprisoned water can
then escape without over-straining the machines.
In direct single-acting lift machines, in which the stroke is fixed, and
in rotative machines at constant speed it is obvious that the cylinder
must be filled at each stroke irrespective of the amount of work to be
done. The same amount of water is used whether much or little work is
done, or whether great or small weights are lifted. Hence while pressure
engines are very efficient at full load, their efficiency decreases as
the load decreases. Various arrangements have been adopted to diminish
this defect in engines working with a variable load. In lifting
machinery there is sometimes a double ram, a hollow ram enclosing a
solid ram. By simple arrangements the solid ram only is used for small
loads, but for large loads the hollow ram is locked to the solid ram,
and the two act as a ram of larger area. In rotative engines the case is
more difficult. In Hastie's and Rigg's engines the stroke is
automatically varied with the load, increasing when the load is large
and decreasing when it is small. But such engines are complicated and
have not achieved much success. Where pressure engines are used
simplicity is generally a first consideration, and economy is of less
importance.
§ 175. _Efficiency of Pressure Engines._--It is hardly possible to
form a theoretical expression for the efficiency of pressure engines,
but some general considerations are useful. Consider the case of a
long stroke hydraulic ram, which has a fairly constant velocity v
during the stroke, and valves which are fairly wide open during most
of the stroke. Let r be the ratio of area of ram to area of valve
passage, a ratio which may vary in ordinary cases from 4 to 12. Then
the loss in shock of the water entering the cylinder will be (r -
1)²v²/2g in ft. of head. The friction in the supply pipe is also
proportional to v². The energy carried away in exhaust will be
proportional to v². Hence the total hydraulic losses may be taken to
be approximately [zeta]v²/2g ft., where [zeta] is a coefficient
depending on the proportions of the machine. Let f be the friction of
the ram packing and mechanism reckoned in lb. per sq. ft. of ram area.
Then if the supply-pipe pressure driving the machine is p lb. per sq.
ft., the effective working pressure will be
p - G[zeta]v²/2g - f lb. per sq. ft.
Let A be the area of the ram in sq. ft., v its velocity in ft. per
sec. The useful work done will be
(p - G[zeta]v²/2g - f)Av ft. lb. per sec.,
and the efficiency of the machine will be
[eta] = (p - G[zeta]v²/2g - f)/p.
This shows that the efficiency increases with the pressure p, and
diminishes with the speed v, other things being the same. If in
regulating the engine for varying load the pressure is throttled,
part of the available head is destroyed at the throttle valve, and p
in the bracket above is reduced. Direct-acting hydraulic lifts,
without intermediate gearing, may have an efficiency of 95% during the
working stroke. If a hydraulic jigger is used with ropes and sheaves
to change the speed of the ram to the speed of the lift, the
efficiency may be only 50%. E. B. Ellington has given the efficiency
of lifts with hydraulic balance at 85% during the working stroke.
Large pressure engines have an efficiency of 85%, but small rotative
engines probably not more than 50% and that only when fully loaded.
[Illustration: FIG. 171.]
§ 176. _Direct-Acting Hydraulic Lift_ (fig. 171).--This is the simplest
of all kinds of hydraulic motor. A cage W is lifted directly by water
pressure acting in a cylinder C, the length of which is a little greater
than the lift. A ram or plunger R of the same length is attached to the
cage. The water-pressure admitted by a cock to the cylinder forces up
the ram, and when the supply valve is closed and the discharge valve
opened, the ram descends. In this case the ram is 9 in. diameter, with a
stroke of 49 ft. It consists of lengths of wrought-iron pipe screwed
together perfectly water-tight, the lower end being closed by a
cast-iron plug. The ram works in a cylinder 11 in. diameter of 9 ft.
lengths of flanged cast-iron pipe. The ram passes water-tight through
the cylinder cover, which is provided with double hat leathers to
prevent leakage outwards or inwards. As the weight of the ram and cage
is much more than sufficient to cause a descent of the cage, part of the
weight is balanced. A chain attached to the cage passes over a pulley at
the top of the lift, and carries at its free end a balance weight B,
working in T iron guides. Water is admitted to the cylinder from a 4-in.
supply pipe through a two-way slide, worked by a rack, spindle and
endless rope. The lift works under 73 ft. of head, and lifts 1350 lb at
2 ft. per second. The efficiency is from 75 to 80%.
The principal prejudicial resistance to the motion of a ram of this
kind is the friction of the cup leathers, which make the joint between
the cylinder and ram. Some experiments by John Hick give for the
friction of these leathers the following formula. Let F = the total
friction in pounds; d = diameter of ram in ft.; p = water-pressure in
pounds per sq. ft.; k a coefficient.