CRUDE ESTIMATE OF SPACE HEATED BY 1 SQ. FT. OF DIRECT HOT-WATER HEATING SURFACE.

lation, but both of these quantities must be considered in order to give results which are even approximately correct.

In any locality it would seem that the rules which are in common use when modified as to the condition of buildings in which they have been successfully applied would be of considerable value; for that reason the preceding tables are given showing the relation of radiating surface to cubic feet of space to be heated as stated by various authorities; it will be noticed, however, that there is such extreme variation in the amount of heating surface required for the same conditions that the results are almost valueless, and indicate that wide variation is common in the practice of different designers.

119. The Amount of Surface Required for Indirect Heating. For this case the heat received by the rooms is all supplied by air which passes over the radiating surfaces and is heated by convection. A large number of tests have been quoted of these heaters, both with natural and mechanical draft

(see Article 52, page 79). From these experiments it is seen that the amount of heat given off by one square foot of surface varies with the velocity of the air, as shown by the table on page 84 and also in the diagram Fig. 187, the use of which has been explained. From the table on page 84 it will be noticed that with natural circulation the velocity in feet per second will vary from 2.97 for a height of 5 feet to 8.4 for a height of 50 feet, and the corresponding convection expressed in heat-units per degree difference of temperature per square foot per hour, which in the preceding table is termed the coefficient, varies from 3 to 6.

If

The entering air is brought into the room usually at a temperature 20 to 40 degrees above that in the room. this entering air is about 100 degrees, I heat-unit will warm 58 cubic feet I degree, an amount about 5 per cent greater than when the entering air was 70 (see Table VIII).

From these data we can readily compute the number of cubic feet of air which must be supplied to bring in the necessary heat, and the size of heating-surface required. The amount of heat to be supplied must be sufficient to compensate for loss from the room, which is approximately equal to the glass surface + the exposed walled surface multiplied by the difference between the temperature of the room and the outside air, or it may be obtained more exactly from Wolff's data, page 57. The number of cubic feet of air required will be found by dividing this quantity by the excess of temperature of the heated air over that of the air in the room and multiplying this result by 58.

The extent of heating surface in square feet will be obtained by dividing the number of cubic feet of air as obtained by the previous calculation by the number of cubic feet heated by one square foot of surface. If air is heated to 100° F. each heat-unit will warm 58 cubic feet one degree.

These results are better expressed in shape of formulæ from which tables suited for practical application may be computed. Lett equal the temperature of the room, t' that of the outside air, " that of the mean temperature of the air surrounding the heating surface, 7' that of the heated air, 7 that of the radiating surface, H the heat required per hour per degree difference of temperature to supply loss from the room, a the

heat given off from 1 sq. ft. radiating surface per degree difference of temperature. We have the following formula:

Loss from the room per hour (t − t)H = (t − t) (G + }W) nearly; (1) Heat brought in by 1 cu. ft. of air 1/58( T' — t); .

Heat given off from 1 sq. ft. of radiating surface per hour

(2)

Cubic feet of air heated by 1 sq. ft. of radiating surface per hour

The table,* page 212, computed from the above formulæ for various conditions gives a series of factors which, multiplied into the building loss H per degree difference of temperature, will give the radiating surface required; it also gives the number of cubic feet of air heated the required amount per square foot of radiating surface per hour.

To use the table, we need simply to know, in addition to temperatures, the probable coefficient of heat transmission, all other conditions being given. For ordinary indirect heating, first floor, the velocity of air can be considered as 2 to 4 feet per second, and the corresponding value of this coefficient as 2. For higher floors the velocity is higher, and coefficients may be taken as 3. (See page 84.) As an example, assume outside temperature zero, inside temperature 70°, and the air leaving the indirect at 100°, the factor with which to multiply the building loss to obtain radiating surface is 0.69. This is practically 3.00 times that for direct heating. Computing the radiating surface required for the same room as that considered in the case of direct heating (page 206), in which there was 48 square feet of glass and 320 square feet of exposed wall surface, and in which the total loss of heat per degree difference of temperature was 128 heat-units, the indirect surface required would be this quantity multiplied by the factor 0.69, which is 88 square feet, or about one half more than required in the calculation for direct heating. For the

* In the table the term coefficient is used for the heat transmitted per degree

TABLE OF FACTORS TO OBTAIN INDIRECT HEATING SURFACE AND OF CUBIC FEET OF AIR HEATED PER SQUARE FOOT OF SURFACE PER HOUR.

ROOM 70° FAHR., OUTSIDE AIR O FAHR., STEAM PRESSURE O LBS., STEAM TEMPERATURE 212° FAHR.

ROOM 70° FAHR., OUTSIDE AIR O FAHR., STEAM PRESSURE 5 LBS., STEAM. TEMPERATURE 219° FAHR.

ROOM 60° FAHR., OUTSIDE AIR O° FAHR., STEAM PRESSURE O LBS., STEAM

ROOM 70° FAHR., OUTSIDE AIR O° FAHR., HOT WATER AT TEMPERATURE.

ROOM 70° FAHR., OUTSIDE AIR O FAHR., HOT WATER AT TEMPERATURE

*To find surface of heater multiply loss from room for one degree difference of temperature by the factor for the given condition. Results computed by formula (6).

second and third stories the factors are to be found in the column in which the coefficient is 3.

The following table gives the number of cubic feet of air required per hour in indirect heating to maintain the proper temperature, as computed by formulæ (4), for each heat-unit lost from walls and windows of room for a temperature of 60° or 70° above outside air. The total air required will be found by multiplying the values, as given in the table, by the total heat lost per degree difference of temperature from the room. This loss is designated by H in formulæ (4), and is approximately equal to the glass plus the exposed wall surface expressed in square feet. (See page 59.)

CUBIC FEET OF AIR PER HEAT-UNIT FROM WAlls.

Thus to find the number of cubic feet of air required to warm a room to 70° in zero weather, in which the glass plus one fourth the exposed wall surface equals 128, and air is introduced 30° above that in the room, multiply 135, as given in the table, by 128.

It is usual to allow 50 per cent more surface for indirect than for direct heating, although some engineers allow only. 25 per cent more.

In concluding this subject it may be remarked that the amount of heat which is given off from indirect heating surfaces would seem from the experiments to depend largely