line. For example, considering once more the case of 1000 h.p. oil-fired boilers operating at 50 per cent. overload, and requiring 0.5 in. draft at the chimney base, we have, as before, 90,000 lb. of flue gas per hour at a temperature of 500°F. Following the horizontal line corresponding to 90,000 lb. per hour, until it crosses the vertical dotted line, we

find that the cheapest chimney to build for this capacity will be between 60 in. and 66 in. diameter. It is customary to build stacks with diameters equal to some multiple of 6 in. We may therefore select 66 in. as the required diameter. The diagram shows that under the assumed conditions the draft for a 66-in. stack, 100 ft. high, will be 0.555 in. Since the draft required is only 0.5 in., the height of the stack may be reduced in proportion, making it 90 ft. high instead of 100 ft. It is thus found that the proper size of chimney for the conditions of the problem is 66 in. diameter and 90 ft. high.

In the table in Fig. 162 the chimney of least first cost is indicated by printing in bold type the draft obtained from the proper size of chimney for each given capacity.

FIG. 165.-The power plant in the Woolworth Building, New

York, has the tallest chimney in

the world. The height of the stack is determined by that of the building, but in some cases the stack must be built extra high in order to discharge well above surrounding buildings.

Sometimes stacks must be built higher than would otherwise be necessary, in order to discharge well above surrounding buildings, in which case a smaller diameter may be used than would be required for a lower stack. In tall office buildings the height of the stack is determined by the height of the building itself. It is not generally known that the tallest chimney in the world is the one provided for the power plant of the Woolworth Building in New York.

Chimneys that have small diameters in proportion to their

height are somewhat objectionable on account of the variability of the draft. At the full load of 1000 boiler h.p., as we have seen, a 54 in. x 140 ft. stack gives the same draft as a 66 in. x 90 ft. stack. At light loads, however, the 54 in. x 140 ft. stack will give a much greater draft, for it still has its full height, but the friction loss is much less. This increase of draft at light loads requires special care on the part of the boiler fireman to adjust his dampers for proper air regulation. Corrections in Chimney Height for Altitude. We shall next consider the necessary corrections to be made in the dimensions of proposed chimneys in their relation to altitude above the sea. All chimney dimensions and tables have been computed on the basis of sealevel pressures. From our equation of draft readings previously derived, it is seen that the draft depends directly upon the atmospheric pressure. Hence it is evident that since the higher the altitude, the less the pressure, the stack must be lengthened in proportion to the barometric readings. Thus if H is the proper height of a chimney at sea level or barometric pressure P., then H1 the proper height at the altitude P1 above sea level is as follows:

1

or if r is a factor obtained by dividing the barometric reading at sea level by the barometric reading at the proposed point of installation,

H1 = TH

This reasoning is 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.

An important point to consider in the construction of the stack is how the altitude will affect the cross-sectional area. At high altitudes the air becomes less dense, hence the area should be larger in order to pass the required weight of air needed in com

bustion of the fuel, for the same weight of air is needed for proper fuel combustion, no matter what the altitude may be.

In the flow of gases through pipes, it has been found that the weight passing any given section per minute is

Where K is constant; p is the difference in pressure between two ends of pipe; D the density; d the diameter of pipe in inches; and L the length of pipe. Since these quantities will later disappear in self-cancelling pairs from this equation, the noting of the particular units involved in measurement is not necessary. In applying this formula to gases flowing through a stack, the quan

tity (1+3.6) is practically unity, the quantity L becomes equal

d

1

to H and H1 in the respective cases, and p is the same in each case. Hence we have

But W must equal W1 for the same economy of fuel burning.

1

K(

H

Hi

Rule for Altitude Correction.-Hence to properly proportion a chimney for a given altitude above sea level, first pick the height and diameter for the boiler capacity on the assumption that the installation is to be made at sea level. Next determine the height for the altitude desired by making the ratio of the new height to the sea-level determination inversely proportional to the barometric readings. The stack diameter is then increased so that

the stack at the higher altitude should have the same frictional resistance as that used at sea-level. This new diameter is determined by multiplying the diameter obtained on the basis of sea-level assumption by the ratio r of barometric heights raised to the 26th power as above deduced.

An Example of Chimney Design at Altitude. Since it is now seen that the factor or ratio of sea-level pressure to the pressure at altitude enters as a first and a two-fifths power, a chart is herewith given by means of which this factor may be quickly raised to the power desired for altitudes up to 10,000 ft., without any reference to barometric pressures.

As an example, let us find the proper proportions of a chimney to amply provide for a 1000 boiler horsepower installation situated 8000 ft. above sea-level.

We have hitherto found that the proper dimensions at sealevel for such an installation are 66 in. in diameter for a height of 90 ft. Applying our rule set forth above, we find from the chart that r for 8000 ft. is 1.357. Hence the proper height is 122 ft. at this altitude, and since r raised to the 25th power is found from the chart to be 1.130 the proper diameter is 74.5 in.

CHAPTER XXX

ACTUAL DRAFT REQUIRED FOR FUEL OIL

For every kind of fuel and rate of combustion there is a certain draft with which the best general results are obtained. A comparatively light draft is best for burning bituminous coals and the amount to use increases as the percentage of volatile matter diminishes and the fixed carbon increases, being highest for the small sizes of anthracites. Numerous other factors such as the thickness of fires, the percentage of ash and the air spaces in the grates bear directly on this question of the draft best suited to a given combustion rate.

For fuel oil, the question of draft required is greatly simplified by the fact that the air does not have to be drawn in through a thick bed of fuel and there are no ashes or clinkers to further complicate the matter. The resistance offered to the entrance of air to the furnace is caused by the checkerwork furnace floor, and as the openings in the checkerwork can be altered at will, it is evident that the amount of draft required in the furnace will depend largely on the arrangement of checkerwork adopted.

For a furnace arrangement such as shown on page 158, in which the total net area of free air space amounts to 3 to 311⁄2 sq. in. per rated horsepower of the boiler, the draft required in the furnace amounts to the following, approximately:

The draft in the furnace is only a small proportion of the total draft that must be supplied by the chimney, for it is necessary to add to the furnace draft the draft loss caused by the friction of the gases in passing through the boilers, breechings and flues leading to the chimney.