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as equal approximately to of the square root of the radiating surface in square feet.

If the temperature of the water be supposed to change 20° in passing through the radiators, the required area of the main would be one half of that given by the table; if 150°, two thirds, etc.

In hot-water heating the return-pipe must have the same diameter as the supply-pipe, since there is no sensible change in bulk between the hot and cold water.

We may take as a practical rule, applicable when less than 200 feet in length: The diameter of main supply- or return-pipe in a system of direct hot-water heating should be one pipe-size greater than the square root of the number of square feet of radiating surface divided by 9 for the first story, by 10 for the second story, and by II for the third story of a building; for indirect hot-water multiply above results by 1.5.

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125. Size of Ducts and Ventilating-flue for Conveying Air. The method of computing the sizes of flues would evidently be that of dividing the total amount of air which is required in a given time by that delivered or discharged through a flue one square foot in area. A table has been given for cubic feet of air delivered in ventilating-pipes, see Chapter I, pages 45 to 52. The air required can be found as explained in Article 119, page 211, formula 4, or by consulting the table, page 213, which gives the factors to be multiplied by the area of glass plus the exposed wall surface when the air enters at various temperatures above that in the room.

As an illustration, consider the same problem as in previous cases, viz., that of a room with 48 square feet of glass surface and 320 square feet of exposed wall surface, and from which the heat loss per degree difference of temperature is 128. Supposing air in room to be 70° F. and that supplied by flue to be 100° F., we see by table page 213, that for every heat-unit as above there will be required 135 cubic feet of air per hour, and for this case we will require 135 X 128 = 17,280 cubic feet per hour. If excess of temperature of air in flue over that outside be considered as 50°, and height of flue as 10 feet, the discharge per square foot of flue (see table page 45) will be 242 feet per minute, or 14,520 per hour. Hence the required area of the flue will be 17,280 divided by 14,520 = 1.19 square feet

= 171 square inches.

In a similar manner areas of flues may

be computed for any given case.

As the velocity of flow increases with difference of temperature between outside air and that in the flue, and is les sened when this difference is small, it is better to assume a mean difference of temperature so low that the computation will certainly afford plenty of air for ventilation.

AREA OF FLUE IN SQUARE INCHES REQUIRED TO SUPPLY GIVEN AMOUNT OF HEAT.

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21000 300 720

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195 183 163

652

28000 400 960
35000 500 1200 865
52500 750 1800 1290 1060
70000 1000 2400 1730 1410
87500 1250 3000 2160 1760
105000 1500 3600 2580 2120
140000 2000 4800 3460 2440
175000 2500 6000 4320 3150 2730 2310
210000 3000 7200 5190 4230 3270 2780 2450 2110

564 436 369

327

281

261 244 218

715 545 462

408

352

326 306 273

825 693

612

527

457 458 408

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Table is computed by finding air required to supply heat by formula 4, page 211, when outside air is o°, inside air 70', and heated air 100°, and dividing this by the air supplied by a flue one square foot in area for the given height and a difference of temperature of 30°, as obtained in table page 45. Ventilating flues for a given height should be taken one quarter larger than the values given in the table. See note on page 246.

* See page 57.

+ Approximately equal to area of glass plus one fourth the exposed wallsurface. See page 59.

The table on p. 233 is computed by the method explained for different heights of flue and for a difference of temperature of the air in the flue over that in the space into which it discharges of 30° F.

For difference of temperature other than 30° multiply results in the table by the following factors to obtain the area of the flue:

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For usual conditions of residence heating in which the air in the supply-flue is 30° above the temperature of the air in the room, and that in the ventilating-flue 20°, we may compute the approximate area in square inches of the supply- and ventilating-duct, by multiplying each heat-unit per degree difference of temperature lost from the walls by a series of simple factors which are easily memorized.

TABLE OF FACTORS FOR AREA OF AIR-FLUES.

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As an example, find the required area of heat- and ventilating-ducts for a room with 200 square feet of exposed wallsurface and 30 square feet of glass: 30 plus one fourth of 200 is 80, the approximate building loss per degree. This quantity multiplied by factors in columns (3) and (5) gives respective areas of flues in square inches with sufficient exactness for ordinary requirements. The factors afford a ready means of computation in the absence of an extended table, similar to that on page 233.

In some instances the amount of air can be computed as a function of the cubic contents of the room, especially when required for ventilation alone. For ventilation purposes the problem of proportioning the air-passages is solved simply by computing, first, the air required, on the basis of 1800 cubic feet. per hour for each person who will occupy the room; second, the number of times the air will be changed per hour, by dividing this result by the volume of the room. This method

is considered fully in Article 38, pagė 53, and a table is given for computing the area of the flue in square inches for different velocities of the moving air.

In applying this method to practical problems, it is best to proportion the ducts so that in no case will the required velocity of the air in the flue exceed 12 feet per second or 43,200 feet per hour, an amount not likely to be reached without a fan or blower, and one which corresponds to a pressure of nearly 0.1 inch of water (pages 42 to 53).

126. Dimensions of Registers.-The registers should be so proportioned that the velocity of the entering air will not be sufficient to produce a sensible draft; that is, the area must be such that the velocity shall not exceed 3 to 5 feet per second or 10,800 to 18,000 lineal feet per hour. The writer thinks that very excellent results are obtained by proportioning the registers for first floor so as to give velocity of 2 feet per second, and those of higher floors and at entrance to ventilating-shafts 3 feet per second.* The results above, except for entrances to ventilating-shafts on the top floor, are less than is usually produced by natural draft, so that the area computed by dividing the total amount of air required by the number which expresses the velocity gives satisfactory results.

The above rules are for effective or clear opening, and this will be found in each case to be about two thirds of the nominal or rated size of the register as shown in the table given in Article 144.

By computing, from the data given, the number of changes of air per hour in room, the table page 53 can be used as explained to determine the effective area in square inches required for each 1000 cubic feet of space.

* See page 52, Article 38.

As an example illustrating use of this table, suppose, in a room containing 2500 cubic feet, air to be changed four times per hour, and that velocity in air-flue be 6 feet per second, in ventilating-shaft 4 feet, through fresh-air register 2.5 feet, through ventilating-register 3 feet.

The table on page 53 gives the net area for each 1000 cubic feet of space, so that for above conditions the results as found in the table must be multiplied by 2.5. We should have, taking 2.5 times the tabulated values, the following results:

Net area supply-flue 67.5 sq. in.; ventilating-shaft 100 sq. in.; fresh-air register 166 sq. in.; ventilating-register 136.5 sq. in.

The nominal area of the register to be used should be about 50 per cent greater than the net area; it may be taken from the table given in Article 144. The velocity corresponding to 2.5 feet per second is taken as the mean of that given in the table for 2 and 3.

It is best to make flue dimensions about one inch greater than obtained by calculation, to allow for surface friction.

127. Summary of Various Methods of Computing Quantities Required for Heating.-The following table gives the required size of steam-pipes and of steam-boiler or hot-water heater, for various amounts of radiating surface. The proportions given will apply to residence heating or where the length of main pipe is not over 200 feet. The value given for the steam-main is that for the single-pipe system when no return. is needed. For the system of separate steam- and return-pipes the diameter of the steam-main should be taken of that given, that of the return as in table page 227. The cubic space heated is given if the ratio to radiating surface be known; this is an approximation only, although it may often serve a useful purpose when experience has been gained of heat required in constructions of similar nature in the same locality.

About two thirds as much air is warmed by hot-water as by steam radiators, and flues should be about two thirds as large as given in the table on page 238.

128. Heating of Greenhouses.-Greenhouses and conservatories are heated in some cases by steam and in other cases by hot water, and there is quite a difference of opinion held by florists respecting the relative merits of these two

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