8624
---- = 22 pounds.
400
For 50 per cent overload the combustion rate will be approximately 60
per cent greater than this or 1.60 × 22 = 35 pounds per square foot of
grate surface per hour. The furnace draft required for the combustion
rate, from the curve, Fig. 34, is 0.6 inch. The loss in the boiler will
be 0.4 inch, in the flue 0.1 inch, and in the turns 2 × 0.05 = 0.1 inch.
The available draft required at the base of the stack is, therefore,
_Inches_
Boiler 0.4
Furnace 0.6
Flues 0.1
Turns 0.1
---
Total 1.2
Since the available draft is 80 per cent of the theoretical draft, this
draft due to the height required is 1.2 ÷ .8 = 1.5 inch.
The chimney constant for temperatures of 60 degrees Fahrenheit and 550
degrees Fahrenheit is .0071 and from formula (30),
1.5
H = ----- = 211 feet.
.0071
Its diameter from curve in Fig. 33 is 96 inches if unlined, and 102
inches inside if lined with masonry. The cross sectional area of the
flue should be approximately 70 square feet at the point where the total
amount of gas is to be handled, tapering to the boiler farthest from the
stack to a size which will depend upon the size of the boiler units
used.
Correction in Stack Sizes for Altitudes--It has ordinarily been assumed
that a stack height for altitude will be increased inversely as the
ratio of the barometric pressure at the altitude to that at sea level,
and that the stack diameter will increase inversely as the two-fifths
power of this ratio. Such a relation has been based on the assumption of
constant draft measured in inches of water at the base of the stack for
a given rate of operation of the boilers, regardless of altitude.
If the assumption be made that boilers, flues and furnace remain the
same, and further that the increased velocity of a given weight of air
passing through the furnace at a higher altitude would have no effect on
the combustion, the theory has been advanced[53] that a different law
applies.
Under the above assumptions, whenever a stack is working at its maximum
capacity at any altitude, the entire draft is utilized in overcoming the
various resistances, each of which is proportional to the square of the
velocity of the gases. Since boiler areas are fixed, all velocities may
be related to a common velocity, say, that within the stack, and all
resistances may, therefore, be expressed as proportional to the square
of the chimney velocity. The total resistance to flow, in terms of
velocity head, may be expressed in terms of weight of a column of
external air, the numerical value of such head being independent of the
barometric pressure. Likewise the draft of a stack, expressed in height
of column of external air, will be numerically independent of the
barometric pressure. It is evident, therefore, that if a given boiler
plant, with its stack operated with a fixed fuel, be transplanted from
sea level to an altitude, assuming the temperatures remain constant, the
total draft head measured in height of column of external air will be
numerically constant. The velocity of chimney gases will, therefore,
remain the same at altitude as at sea level and the weight of gases
flowing per second with a fixed velocity will be proportional to the
atmospheric density or inversely proportional to the normal barometric
pressure.
To develop a given horse power requires a constant weight of chimney gas
and air for combustion. Hence, as the altitude is increased, the density
is decreased and, for the assumptions given above, the velocity through
the furnace, the boiler passes, breeching and flues must be
correspondingly greater at altitude than at sea level. The mean
velocity, therefore, for a given boiler horse power and constant weight
of gases will be inversely proportional to the barometric pressure and
the velocity head measured in column of external air will be inversely
proportional to the square of the barometric pressure.
For stacks operating at altitude it is necessary not only to increase
the height but also the diameter, as there is an added resistance within
the stack due to the added friction from the additional height. This
frictional loss can be compensated by a suitable increase in the
diameter and when so compensated, it is evident that on the assumptions
as given, the chimney height would have to be increased at a ratio
inversely proportional to the square of the normal barometric pressure.
In designing a boiler for high altitudes, as already stated, the
assumption is usually made that a given grade of fuel will require the
same draft measured in inches of water at the boiler damper as at sea
level, and this leads to making the stack height inversely as the
barometric pressures, instead of inversely as the square of the
barometric pressures. The correct height, no doubt, falls somewhere
between the two values as larger flues are usually used at the higher
altitudes, whereas to obtain the ratio of the squares, the flues must be
the same size in each case, and again the effect of an increased
velocity of a given weight of air through the fire at a high altitude,
on the combustion, must be neglected. In making capacity tests with coal
fuel, no difference has been noted in the rates of combustion for a
given draft suction measured by a water column at high and low
altitudes, and this would make it appear that the correct height to use
is more nearly that obtained by the inverse ratio of the barometric
readings than by the inverse ratio of the squares of the barometric
readings. If the assumption is made that the value falls midway between
the two formulae, the error in using a stack figured in the ordinary way
by making the height inversely proportional to the barometric readings
would differ about 10 per cent in capacity at an altitude of 10,000
feet, which difference is well within the probable variation of the size
determined by different methods. It would, therefore, appear that ample
accuracy is obtained in all cases by simply making the height inversely
proportional to the barometric readings and increasing the diameter so
that the stacks used at high altitudes have the same frictional
resistance as those used at low altitudes, although, if desired, the
stack may be made somewhat higher at high altitudes than this rule calls
for in order to be on the safe side.
The increase of stack diameter necessary to maintain the same friction
loss is inversely as the two-fifths power of the barometric pressure.
Table 54 gives the ratio of barometric readings of various altitudes to
sea level, values for the square of this ratio and values of the
two-fifths power of this ratio.