Under the same temperature conditions this chimney at an atmospheric pressure of 10 pounds per square inch (which corresponds to an alt.i.tude 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 a.s.sumed atmospheric temperature and pressure (24) becomes
D = KH. (25)
For average conditions the atmospheric pressure may be considered 14.7 pounds per square inch, and the temperature 60 degrees Fahrenheit. For these values and various stack temperatures K becomes:
_Temperature Stack Gases_ _Constant K_ 750 .0084 700 .0081 650 .0078 600 .0075 550 .0071 500 .0067 450 .0063 400 .0058 350 .0053
Draft Losses--The intensity of the draft as determined by the above formula is theoretical and can never be observed with a draft gauge or any recording device. However, if the ashpit doors of the boiler are closed and there is no perceptible leakage of air through the boiler setting or flue, the draft measured at the stack base will be approximately the same as the theoretical draft. The difference existing at other times represents the pressure necessary to force the gases through the stack against their own inertia and the friction against the sides. This difference will increase with the velocity of the gases.
With the ashpit doors closed the volume of gases pa.s.sing to the stack are a minimum and the maximum force of draft will be shown by a gauge.
As draft measurements are taken along the path of the gases, the readings grow less as the points at which they are taken are farther from the stack, until in the boiler ashpit, with the ashpit doors open for freely admitting the air, there is little or no perceptible rise in the water of the gauge. The breeching, the boiler damper, the baffles and the tubes, and the coal on the grates all r.e.t.a.r.d the pa.s.sage of the gases, and the draft from the chimney is required to overcome the resistance offered by the various factors. The draft at the rear of the boiler setting where connection is made to the stack or flue may be 0.5 inch, while in the furnace directly over the fire it may not be over, say, 0.15 inch, the difference being the draft required to overcome the resistance offered in forcing the gases through the tubes and around the baffling.
One of the most important factors to be considered in designing a stack is the pressure required to force the air for combustion through the bed of fuel on the grates. This pressure will vary with the nature of the fuel used, and in many instances will be a large percentage of the total draft. In the case of natural draft, its measure is found directly by noting the draft in the furnace, for with properly designed ashpit doors it is evident that the pressure under the grates will not differ sensibly from atmospheric pressure.
Loss in Stack--The difference between the theoretical draft as determined by formula (24) and the amount lost by friction in the stack proper is the available draft, or that which the draft gauge indicates when connected to the base of the stack. The sum of the losses of draft in the flue, boiler and furnace must be equivalent to the available draft, and as these quant.i.ties can be determined from record of experiments, the problem of designing a stack becomes one of proportioning it to produce a certain available draft.
The loss in the stack due to friction of the gases can be calculated from the following formula:
f W C H [Delta]D = -------- (26) A
in which
[Delta]D = draft loss in inches of water, W = weight of gas in pounds pa.s.sing per second, C = perimeter of stack in feet, H = height of stack in feet, f = a constant with the following values at sea level: .0015 for steel stacks, temperature of gases 600 degrees Fahrenheit.
.0011 for steel stacks, temperature of gases 350 degrees Fahrenheit.
.0020 for brick or brick-lined stacks, temperature of gases 600 degrees Fahrenheit.
.0015 for brick or brick-lined stacks, temperature of gases 350 degrees Fahrenheit.
A = Area of stack in square feet.
[Ill.u.s.tration: 24,420 Horse-power Installation of Babc.o.c.k & Wilc.o.x Boilers and Superheaters, Equipped with Babc.o.c.k & Wilc.o.x Chain Grate Stokers in the Quarry Street Station of the Commonwealth Edison Co., Chicago, Ill.]
This formula can also be used for calculating the frictional losses for flues, in which case, C = the perimeter of the flue in feet, H = the length of the flue in feet, the other values being the same as for stacks.
The available draft is equal to the difference between the theoretical draft from formula (25) and the loss from formula (26), hence:
f W C H d^{1} = available draft = KH - -------- (27) A
Table 53 gives the available draft in inches that a stack 100 feet high will produce when serving different horse powers of boilers with the methods of calculation for other heights.
TABLE 53
AVAILABLE DRAFT
CALCULATED FOR 100-FOOT STACK OF DIFFERENT DIAMETERS a.s.sUMING STACK TEMPERATURE OF 500 DEGREES FAHRENHEIT AND 100 POUNDS OF GAS PER HORSE POWER
FOR OTHER HEIGHTS OF STACK MULTIPLY DRAFT BY HEIGHT 100
+-----+-------------------------------------------------------------------+ |Horse| | |Power| Diameter of Stack in Inches | +-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | |36 |42 |48 |54 |60 |66 |72 |78 |84 |90 |96 |102|108|114|120|132|144| +-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 100 |.64| | | | | | | | | | | | | | | | | | 200 |.55|.62| | | | | | | | | | | | | | | | | 300 |.41|.55|.61| | | | | | | | | | | | | | | | 400 |.21|.46|.56|.61| | | | | | | | | | | | | | | 500 | |.34|.50|.57|.61| | | | | | | | | | | | | | 600 | |.19|.42|.53|.59| | | | | | | | | | | | | | 700 | | |.34|.48|.56|.60|.63| | | | | | | | | | | | 800 | | |.23|.43|.52|.58|.61|.63| | | | | | | | | | | 900 | | | |.36|.49|.56|.60|.62|.64| | | | | | | | | |1000 | | | |.29|.45|.53|.58|.61|.63|.64| | | | | | | | |1100 | | | | |.40|.50|.56|.60|.62|.63|.64| | | | | | | |1200 | | | | |.35|.47|.54|.58|.61|.63|.64|.65| | | | | | |1300 | | | | |.29|.44|.52|.57|.60|.62|.63|.64|.65| | | | | |1400 | | | | | |.40|.49|.55|.59|.61|.63|.64|.65|.65| | | | |1500 | | | | | |.36|.47|.53|.58|.60|.62|.63|.64|.65|.65| | | |1600 | | | | | |.31|.43|.52|.56|.59|.62|.63|.64|.65|.65| | | |1700 | | | | | | |.41|.50|.55|.58|.61|.62|.64|.64|.65| | | |1800 | | | | | | |.37|.47|.54|.57|.60|.62|.63|.64|.65| | | |1900 | | | | | | |.34|.45|.52|.56|.59|.61|.63|.64|.64| | | |2000 | | | | | | | |.43|.50|.55|.59|.61|.62|.63|.64| | | |2100 | | | | | | | |.40|.49|.54|.58|.60|.62|.63|.64| | | |2200 | | | | | | | |.38|.47|.53|.57|.59|.61|.62|.64| | | |2300 | | | | | | | |.35|.45|.52|.56|.59|.61|.62|.63| | | |2400 | | | | | | | |.32|.43|.50|.55|.58|.60|.62|.63| | | |2500 | | | | | | | | |.41|.49|.54|.57|.60|.61|.63| | | |2600 | | | | | | | | | |.47|.53|.56|.59|.61|.62|.64|.65| |2700 | | | | | | | | | |.45|.52|.55|.58|.60|.62|.64|.65| |2800 | | | | | | | | | |.44|.59|.55|.58|.60|.61|.64|.65| |2900 | | | | | | | | | |.42|.49|.54|.57|.59|.61|.63|.65| |3000 | | | | | | | | | |.40|.48|.53|.56|.59|.61|.63|.64| |3100 | | | | | | | | | |.38|.47|.52|.56|.58|.60|.63|.64| |3200 | | | | | | | | | | |.45|.51|.55|.58|.60|.63|.64| |3300 | | | | | | | | | | |.44|.50|.54|.57|.59|.62|.64| |3400 | | | | | | | | | | |.42|.49|.53|.56|.59|.62|.64| |3500 | | | | | | | | | | |.40|.48|.52|.56|.58|.62|.64| |3600 | | | | | | | | | | | |.47|.52|.55|.58|.61|.63| |3700 | | | | | | | | | | | |.45|.51|.55|.57|.61|.63| |3800 | | | | | | | | | | | |.44|.50|.54|.57|.61|.63| |3900 | | | | | | | | | | | |.43|.49|.53|.56|.60|.63| |4000 | | | | | | | | | | | |.42|.48|.52|.56|.60|.62| |4100 | | | | | | | | | | | |.40|.47|.52|.55|.60|.62| |4200 | | | | | | | | | | | |.39|.46|.51|.55|.59|.62| |4300 | | | | | | | | | | | | |.45|.50|.54|.59|.62| |4400 | | | | | | | | | | | | |.44|.49|.53|.59|.62| |4500 | | | | | | | | | | | | |.43|.49|.53|.58|.61| |4600 | | | | | | | | | | | | |.42|.48|.52|.58|.61| |4700 | | | | | | | | | | | | |.41|.47|.51|.57|.61| |4800 | | | | | | | | | | | | |.40|.46|.51|.57|.60| |4900 | | | | | | | | | | | | | |.45|.50|.57|.60| |5000 | | | | | | | | | | | | | |.44|.49|.56|.60| +-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
FOR OTHER STACK TEMPERATURES ADD OR DEDUCT BEFORE MULTIPLYING BY HEIGHT 100 AS FOLLOWS[52]
For 750 Degrees F. Add .17 inch.
For 700 Degrees F. Add .14 inch.
For 650 Degrees F. Add .11 inch.
For 600 Degrees F. Add .08 inch.
For 550 Degrees F. Add .04 inch.
For 450 Degrees F. Deduct .04 inch.
For 400 Degrees F. Deduct .09 inch.
For 350 Degrees F. Deduct .14 inch.
[Graph: Horse Power of Boilers against Diameter of Stack in Inches
Fig. 33. Diameter of Stacks and Horse Power they will Serve
Computed from Formula (28). For brick or brick-lined stacks, increase the diameter 6 per cent]
Height and Diameter of Stacks--From this formula (27) it becomes evident that a stack of certain diameter, if it be increased in height, will produce the same available draft as one of larger diameter, the additional height being required to overcome the added frictional loss.
It follows that among the various stacks that would meet the requirements of a particular case there must be one which can be constructed more cheaply than the others. It has been determined from the relation of the cost of stacks to their diameters and heights, in connection with the formula for available draft, that the minimum cost stack has a diameter dependent solely upon the horse power of the boilers it serves, and a height proportional to the available draft required.
a.s.suming 120 pounds of flue gas per hour for each boiler horse power, which provides for ordinary overloads and the use of poor coal, the method above stated gives:
For an unlined steel stack--
diameter in inches = 4.68 (H. P.)^{2/5} (28)
For a stack lined with masonry--
diameter in inches = 4.92 (H. P.)^{2/5} (29)
In both of these formulae H. P. = the rated horse power of the boiler.
From this formula the curve, Fig. 33, has been calculated and from it the stack diameter for any boiler horse power can be selected.
For stoker practice where a large stack serves a number of boilers, the area is usually made about one-third more than the above rules call for, which allows for leakage of air through the setting of any idle boilers, irregularities in operating conditions, etc.
Stacks with diameters determined as above will give an available draft which bears a constant ratio of the theoretical draft, and allowing for the cooling of the gases in their pa.s.sage upward through the stack, this ratio is 8. Using this factor in formula (25), and transposing, the height of the chimney becomes,
d^{1} H = ----- (30) .8 K
Where H = height of stack in feet above the level of the grates, d^{1} = available draft required, K = constant as in formula.