Part 48

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 quantities 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 W² C H [Delta]D = -------- (26) A³

in which

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 W² C H d^{1} = available draft = KH - -------- (27) A³

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 ASSUMING 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

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.

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.

Assuming 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 passage upward through the stack, this ratio is 8. Using this factor in formula (25), and transposing, the height of the chimney becomes,