The height and diameter of a properly designed chimney depend upon the
amount of fuel to be burned, its nature, the design of the flue, with
its arrangement relative to the boiler or boilers, and the altitude of
the plant above sea level. There are so many factors involved that as
yet there has been produced no formula which is satisfactory in taking
them all into consideration, and the methods used for determining stack
sizes are largely empirical. In this chapter a method sufficiently
comprehensive and accurate to cover all practical cases will be
developed and illustrated.
Draft is the difference in pressure available for producing a flow of
the gases. If the gases within a stack be heated, each cubic foot will
expand, and the weight of the expanded gas per cubic foot will be less
than that of a cubic foot of the cold air outside the chimney.
Therefore, the unit pressure at the stack base due to the weight of the
column of heated gas will be less than that due to a column of cold air.
This difference in pressure, like the difference in head of water, will
cause a flow of the gases into the base of the stack. In its passage to
the stack the cold air must pass through the furnace or furnaces of the
boilers connected to it, and it in turn becomes heated. This newly
heated gas will also rise in the stack and the action will be
continuous.
The intensity of the draft, or difference in pressure, is usually
measured in inches of water. Assuming an atmospheric temperature of 62
degrees Fahrenheit and the temperature of the gases in the chimney as
500 degrees Fahrenheit, and, neglecting for the moment the difference in
density between the chimney gases and the air, the difference between
the weights of the external air and the internal flue gases per cubic
foot is .0347 pound, obtained as follows:
Weight of a cubic foot of air at 62 degrees Fahrenheit = .0761 pound
Weight of a cubic foot of air at 500 degrees Fahrenheit = .0414 pound
------------------------
Difference = .0347 pound
Therefore, a chimney 100 feet high, assumed for the purpose of
illustration to be suspended in the air, would have a pressure exerted
on each square foot of its cross sectional area at its base of .0347 ×
100 = 3.47 pounds. As a cubic foot of water at 62 degrees Fahrenheit
weighs 62.32 pounds, an inch of water would exert a pressure of 62.32 ÷
12 = 5.193 pounds per square foot. The 100-foot stack would, therefore,
under the above temperature conditions, show a draft of 3.47 ÷ 5.193 or
approximately 0.67 inches of water.
The method best suited for determining the proper proportion of stacks
and flues is dependent upon the principle that if the cross sectional
area of the stack is sufficiently large for the volume of gases to be
handled, the intensity of the draft will depend directly upon the
height; therefore, the method of procedure is as follows:
1st. Select a stack of such height as will produce the draft required by
the particular character of the fuel and the amount to be burned per
square foot of grate surface.
2nd. Determine the cross sectional area necessary to handle the gases
without undue frictional losses.
The application of these rules follows:
Draft Formula--The force or intensity of the draft, not allowing for the
difference in the density of the air and of the flue gases, is given by
the formula:
/ 1 1 \
D = 0.52 H × P |--- - -----| (24)
\ T T_{1}/
in which
D = draft produced, measured in inches of water,
H = height of top of stack above grate bars in feet,
P = atmospheric pressure in pounds per square inch,
T = absolute atmospheric temperature,
T_{1} = absolute temperature of stack gases.
In this formula no account is taken of the density of the flue gases, it
being assumed that it is the same as that of air. Any error arising from
this assumption is negligible in practice as a factor of correction is
applied in using the formula to cover the difference between the
theoretical figures and those corresponding to actual operating
conditions.
The force of draft at sea level (which corresponds to an atmospheric
pressure of 14.7 pounds per square inch) produced by a chimney 100 feet
high with the temperature of the air at 60 degrees Fahrenheit and that
of the flue gases at 500 degrees Fahrenheit is,
/ 1 1 \
D = 0.52 × 100 × 14.7 | --- - --- | = 0.67
\ 521 961 /
Under the same temperature conditions this chimney at an atmospheric
pressure of 10 pounds per square inch (which corresponds to an altitude
of about 10,000 feet above sea level) would produce a draft of,
/ 1 1 \
D = 0.52 × 100 × 10 | --- - --- | = 0.45
\ 521 961 /
For use in applying this formula it is convenient to tabulate values of
the product
/ 1 1 \
0.52 × 14.7|--- - -----|
\ T T_{1}/
which we will call K, for various values of T_{1}. With these values
calculated for assumed atmospheric temperature and pressure (24) becomes