the maximum and the minimum temperature during every 24-hour period.

The auxiliary consumption of W, and W, are the hot water requirements, etc., and which are independent of the actual heating requirements of the building. This amount can vary between summer and winter, depending upon the nature of the apparatus used. Many buildings are connected up so that the condensate heats all, or nearly all, of the hot water required for the building in the winter time; but in the summer time steam is required. In other cases (hotels, for instance), a practically constant amount of steam is used for cooking purposes. For this reason, judgment should be exercised so that consistent factors are obtained.

No claim is made for absolute accuracy, the formula merely giving results that connot be as readily obtained in any other manner. To show its application, the following are examples:

W, was summed as being 1,300 lbs. as that was the amount used during 1916 in August, and was used for hot water, the only auxiliary load.

It will be noted that the actual requirements are somewhat higher than the calculated totals, but this is explainable by the fact that a 2° higher temperature was maintained. This would have taken even more steam, but for the fact that the condensate, in the case of the central station service plant, was used in economy coils and it was estimated that one item about cancelled the other.

APPLYING FORMULA WHEN METER HAS

STOPPED.

In the following case, the meter had stopped between the two 10-day meter reading intervals, and it was felt necessary to have some "educated" guess, so the formula was applied from the following data and with the results as given.

During period "B," December 30 to January 11, 1917, the steam metered was 137,000 lbs., but the meter was found stopped, (E2 = 22.5) January 11 to 22. Applying the formula for this period gave 210,000 lbs.

1916.

N Number of days.

For heating plants in larger buildings the design of the chimney approaches that of the stacks used for power plants and the quality of fuel is quite liable to be of more or less inferior grade. Under such conditions the height and area become of prime importance since upon the proper size and height of a chimney depend the satisfactory operation of the entire heating plant. It is the purpose of the balance of this article to deal with the numerous factors entering into the matter of sizing the chimneys in a practical manner and with the avoidance, as far as possible, of all the complicated calculations usually found involved in such design.

FRICTION LOSSES.

It must be understood that a chimney or stack filled with hot air or heated gases has a lower pressure at its base than the outside air, owing to the tendency of the heated gases to rise. Now this tendency to ascend is what is known as the "theoretical draft" and its calculation is comparatively simple; the trouble is that as soon as the gas actually commences to rise the element of friction comes into play, this friction being the result of the rubbing of the gases against the sides of the chimney and varying according to the weight of the

gases and the velocity with which they pass along the surface. This friction also depends upon the length and quality of the surface passed over otherwise the height of the chimney. For a given set of conditions this friction can also be computed and the "theoretical draft" less the "friction loss in the stack" will give the "available draft" at the base of the stack.

But this is not the only friction loss which must be overcome by the chimney "theoretical draft." The other losses consist of the friction of the air passing through the fire, all around the gas passages of the boiler, the resistance of the bends into the breeching, in passing along the breeching, and the bend into the chimney, itself.

The total draft necessary (i.e., "theoretical draft") must be equal to, or greater than, the sum of all the friction losses encountered by the air from the time it enters the ash pit until it leaves the top of the stack so that, besides the friction loss in the stack itself, other losses must be considered. Such losses are usually expressed in inches of water and are so treated in this discussion.

The first of these losses and one of the most variable encountered is the loss of draft in passing through the grates and fire bed. This varies with the fuel, its size, and the quantity it

is desired to burn per square foot of grate. This quantity per square foot of grate is in turn governed by the efficiency of the boiler, the horsepower of the boiler and the desired amount of overload to be provided.

In order to give the designer an idea of the various draft losses encountered and of the number of pounds of coal required for any set of conditions Tables III and IV have been prepared, Table III being the number of pounds of coal per hour for the development of various horsepowers at several rates (4 to 7 lbs.) of pounds of coal per boiler horsepower developed. In the righthand column is shown the number of pounds of air per second necessary for the combustion of the required coal to produce this horsepower, the reason for rating this air in pounds per second being for greater facility in applying formulas to the chimney friction loss, as will be seen later. The number of cubic feet per pound of coal upon which these pounds of air are computed consist of

Therefore if the total produced horsepower, pounds of coal per horsepower, number of pounds of coal per square foot of grate and the kind of fuel together with its size are either known quantities or can be assumed, a fair approximation of the draft loss through the fire under these conditions can be readily determined.

Under normal conditions and efficiency it is usual to assume about 5 lbs. of coal per horsepower developed.

OTHER FRICTION LOSSES.

The next loss to be considered is that resulting from the gases passing around the various baffles and through the paths of travel maintained in the different types of boilers. Actual experiment has shown that this draft loss in water-tube boilers seldom exceeds 0.25 in. when a boiler is developing full rating; 0.40 in. when run at 50% overload; and 0.70 in. when operating at 100% overload. In horizontal return tubular boilers the loss is about 0.2, 0.3, and 0.45 in., respectively, while in vertical boilers it runs 0.1, 0.15, and 0.2 in. only. Owing to the fact that heating boilers are seldom if ever figured at being run upon any overload capacity it may be assumed that 0.25 to 0.30 in. wall cover any draft loss which the ordinary heating engineer will be required to consider. Economizers have a draft loss of about 0.3 in.

The losses resultant from the gases passing around bends after leaving the boiler are considerable and, therefore, the easier the bends of the breeching are made and the slower the velocity of the gases, the smaller will be the loss. The 90° change of direction usually made by

25

30

35

1.00

0.65

0.90

1.20

.35

.45

0.58

.28

.38

.45

.20

.27

.34

.14

by the gases in passing from the boiler uptake into the horizontal flue and the 90° horizontal bend from the horizontal flue into the stack and the 90° change from the horizontal direction to the vertical direction in the stack itself all count against the draft and result in the certain loss. It has been found by experiment that in steel flues the loss for each right angle turn is approximately 0.05 in. and that the loss for the straight round or square flue itself due to the friction of the gases along the sides, tops and bottom is about 0.1 in. per 100 lin. ft., while in concrete flues the losses for bends of 90° are 0.1 in. and, for straight flues of 100 ft. length 0.2 inches. So that the total loss of draft say for 150 ft. of steel flue and five right angle bends between the boiler uptake and the stack, including the change of direction into the stack, will be 0.1 X 150/100 + 0.05 in. X5, or 0.15 + 0.25, or 0.4 in. Having obtained all the draft friction losses up to the point where the gases enter the base of the stack it only remains to compute the friction in the stack in order to obtain the total of all friction losses.

The friction loss in the stack, however, is extremely variable in this way. For a given number of pounds of air per second passing up a stack the velocity will, of course, vary as the diameter is increased or decreased, the smaller diameter resulting in a higher velocity. and a greater friction loss, and the larger diameter giving a lower velocity and a smaller friction loss. From this it is readily seen that there is a relation between the height and the diameter, one being to a more or less extent dependent upon the other. Thus, if a stack of a

given height and 3 ft. in diameter has a theoretical draft of 1 in. its friction loss could also be 1 in. provided that the weight of gas to be handled were of sufficient quantity; therefore, the available draft (which has previously been shown as equal to the difference between the "theoretical draft" in the chimney and its "friction loss") would be in this case 1 in. 1 in., or zero, so that there would be practically no pull at the base of the chimney, provided that the gas up to the quantity required were supplied from some other source. However, if the stack diameter were increased to 4 ft. the velocity would be correspondingly lessened, resulting in a falling off of the friction loss perhaps to 0.5 in., leaving 0.5 available at the bottom to overcome the other draft losses; increasing the diameter again would result in a still smaller friction loss and a still higher available draft at the base of the chimney. But how far should the increasing of the diameter be carried?

TWO METHODS OF PRODUCING DRAFT.

It must be understood that the draft can be produced in two ways. On the first chimney the "friction loss" equaling the "theoretical draft," an increase in the height would only result in a proportional increase in the "theoretical draft" and the "friction loss." Since these amounts are equal, the proportional increases will be equal and the results would be equal. On the second chimney, however, if the height were increased 50% the "theoretical draft" would be increased 50% and the "friction loss" increased 50%, resulting in the "available draft" being also increased 50% so that on the 4 ft. stack an increase could be secured for the "available draft" either by increasing the height, or increasing the diameter (using the same height), or by a combination of both. Thus it can be seen that several chimneys of varying diameters in height can be constructed, each of which would give the same "available draft" at the base when handling the same amount of gases, with all other conditions equal, it only being necessary to increase the height sufficiently to make up for the added friction when the

diameter is reduced or, conversely, to increase the diameter so as to reduce the friction as the height is decreased and the "theoretical draft" therefore weakened.

DRAFT LOSSES MUST BE EQUALLED BY "THEORETICAL draft.”

But there is one point upon which no mistake should be made and that is that the draft losses in the fire, boiler, breeching, bends, and stack must be equalled or exceeded by the "theoretical draft" and no enlargement of a stack which is of insufficient height can ever make up for a "theoretical draft" which is less than the friction losses between the ash pit and the base of the chimney, since the chimney friction must always be added to these and it is not possible to produce a chimney large enough so that its friction loss will be zero. Therefore, a certain height of stack must be used to meet given conditions of draft loss and no increase of diameter will allow a stack of less height to be used.

THE QUESTION OF HEIGHT AND DIAMETER.

In

This brings up the point of whether it is cheaper to build a stack higher than absolutely necessary using a smaller diameter, or to build it only as high as it is absolutely necessary to meet the intensity of draft requirements and to increase the diameter accordingly. answer to this it may be said that, where conditions permit, a stack is most economically built when made only of the height absolutely required to produce the required intensity of "available draft" and when built large enough to take care of the amount of gases to be handled with only a reasonable loss for friction. There are cases in high buildings where stacks must be carried up a certain distance in order to get above the roof of the building and in these instances there is no option but to use the height of stack necessary, at the same time cutting down the diameter so that the stack friction will build up a draft resistance which will counter-balance the excess of intensity and still produce the proper and desired "available draft" result in the boiler room.