The best way to determine the minimum temperature on which to calculate the heat losses is to compare the average temperature of the locality under consideration with the one in which you reside and are familiar. In New York the minimum temperature (Table 5) is 6 deg. F. and in Detroit, -24 deg. F., while the averages are 40.1 deg. F. and 35.3 deg. F., yet all contracts are let on the basis of sufficient radiation for the room temperature in 0 deg. F. weather, in both places.

If radiation is provided for the minimum outside temperature, it will be at an unnecessary expense. Boiler, chimney, and grate should be of sufficient size to take care of the lowest temperature periods by raising the temperature of the radiation, or pressure of the heating medium.

The combined coefficient, U, may be defined as the amount of heat absorbed or given off per square foot of surface per hour, by radiation and convection under certain conditions of air movement, for each degree difference in temperature between the surface and the average temperature of the air. If the air movement is different on the two sides of a wall, the value of the combined coefficient will of course, be different owing to the fact that the heat loss by convection is different. Let Ki = the combined coefficient for the inside wall; K = the combined coefficient for the outside wall; Kit - t1) the heat absorbed by the inside wall per sq. ft. per hr.; and Ka(t2- to) = the heat given off by the outside wall surface per sq. ft. per hr. Then

=

temperature

in which t and t1 = temperature of the inside air and inside wall surface respectively, and t1 and t2 = of the outside air and outside wall surface respectively. K2 is taken gener

The average value of K1 is 1.34 and K2 increases with the velocity of wind over the surface. ally at 3 times that of the inside wall surface. Following are the multipliers of K2 for various wind velocities.

The amount of heat that will be transmitted through a material having parallel surfaces due to a difference in temperature between those surfaces is termed the conductivity of the material. The amount of heat that a given material will transmit is directly proportional to the difference in temperature between the surfaces and inversely proportional to the thickness. Let C = coefficient of conductivity or B.t.u. transmitted per square foot per hour per inch of thickness per 1-deg.F. difference in temperature of the two surfaces; t1 = temperature of the inside wall surface; t2 = temperature of the outside wall surface; and X = thickness of the wall in inches. Then C (1 t2)

=

heat transmitted by conduction per sq. ft. per hr.

TABLE 6.-COEFFICIENTS TO BE USED IN DETERMINING "U" FOR DIFFERENT MATERIALS

6. Calculation of Heat Transmission Through Walls, Roofs, and Floors.-The amount of heat received by the inside wall surface, the amount conducted through the wall, and the amount emitted must all be equal. Let U the heat transmission of the actual wall per square foot per hour per degree difference in temperature on the two sides. Then

Since

=

-- "Cement
G-8 K=0.93
3"Cork board
C=0.32

Outside

Us

13" Brick wall

-0.0746

FIG. 2.

-Air space and stud
Clapboards, K2-4.2
Building paper

Lath and plaster, K=0.93
For wood, C=/
For cement, C-8
Still air, K=1.4
lair,

2"Hollow file

C-0.99
Plaster

U=

52*093*0.99*8

=0.20

4" Concrete.

K=1.3, C=8.3

U=1

13+42+ 83+ 843-0.555

FIG. 6.

for paper and very thin substances may be neglected. If the wall is composed of several layers of different materials in contact with an air space of thicknesses X1, X2, X2, etc., then

K1, K2, and C being taken from Table 6 for the particular materials involved. Figs. 1, 2, 3, 4, 5, and 6 illustrate the methods of computing U for various types of walls, floors, and roofs.

It is customary for engineers to increase heat losses by a factor, called the exposure factor. Such an increase, however, is unnecessary if the above method is followed and the proper values used. The values in Table 7 have been calculated in accordance with the method above advocated, using results of the Illinois tests. If the values given are used with judgment, good results will be obtained. A typical heat loss schedule is given in Table 13, pp. 1096 and 1097.

1 Method described is taken from the Univ. of Ill. Bull. 102, entitled "A Study of the Heat Transmission of Building Materials," by A. C. Willard and L. C. Lichty.

This

It has been recommended that the temperature difference usually considered under roots be increased. should be done with judgment since, as a rule, the top floor, with the roof loss properly figured, will have too much radiation.

The first floor where doors occur usually has too little radiation. This is especially true when the doors are opened often. The elevator shaft and doors aggravate this condition as the hot air rises to the top floor.

The following temperature differences may be taken for attic rooms:

Closed attic-metal or slate roofs.

Closed attic-cement tile roofs..

Cellars kept closed....

14 deg. F.

23 deg. F.

32 deg. F.

Thus, the heat loss per hour estimated for a room having a floor 11⁄2-in. thick over a cellar, assuming room heated to 70 deg. F., may be calculated as follows:

Heat loss per hour

(0.3413) (70-32) = 13.0 B.t.u. per sq. ft. Heat loss from floors that are laid directly on the ground may be estimated on the assumption that the ground temperature is 50 deg. F. The loss per hour through 4 in. of concrete for an inside temperature of 65 deg. F. is

7. Heat Loss by Infiltration.-Heat loss by infiltration is estimated in many cases by the number of air changes arbitrarily assumed. It is also estimated by measuring the periphery

of the window casing, assuming a 32 or 6-in. crack, with the wind blowing at a certain velocity. This is largely dependent on the character and grade of the building construction. The results of these determinations are, at best, inaccurate and there is no reason for going into refinements of calculation beyond the limit of error of the assumptions.

Three methods are given for determining the infiltration loss: (1) Assume arbitrarily a number of complete air changes of cubic contents of the buildings or rooms; (2) assume a 16 or 2-in. crack all around the windows with a given wind velocity to determine the air change; and (3) assume the proper crack or opening 16 in. and determine the relation of this infiltration in the form of a ratio of square feet of glass to cubic contents.

TABLE 8.-RESULTS OF EXPERIMENTS ON AIR INFILTRATION

In Table 7 the air infiltration is calculated, assuming 0.147 cu. ft. per minute per running foot of 6-in. crack per mile velocity, the air velocity at 13 miles per hour, the air at 0 deg. F., or 0.086 lb. per cu. ft. (see Table 3), and specific heat at 0.24 B.t.u. (see Art. 3). The B.t.u. per hour per degree difference per running foot of crack = 60 min. × 13 mi. per hr. × 0.147 cu. ft. per min. per ft. per mile X 0.086 × 0.242.4 B.t.u. per deg. per ft., or 1.2 B.t.u. per deg. per ft. for 2-in. crack. Windows on only two sides of room should be figured as the draft will be outward on the leeward side.

TABLE 10.-RELATION OF AIR CHANGES TO CUBIC CONTENTS

Double the above amounts for rooms having doors to outside opened frequently, as on ground floors.

8. Heat Supplied by Persons, Lights, and Machinery.—The following allowances may be made for persons and lights when required, but as buildings have to be heated at times when these sources of heat may be absent, as Sundays, they should be made with care. It would probably be safer to omit them when figuring the radiation, as is generally done, and shut off some of the heating surface when these sources of heat are present. The heat given off by persons is not considered except in assembly halls. These halls are generally figured for 50 deg. F. in 0-deg. weather when the audience is not present.

TABLE 11

Man at rest...

Man at work..

400 B.t.u. per hr.
500 B.t.u. per hr.

Electric lamps: B.t.u. per hr. = watts per lamp X number X 3.415 Motors and machinery convert some of their energy into heat if located in the same room. Rubber and chocolate rolls and similar classes of machinery produce great quantities of heat. 9. Measurement of Flow of Fluids. There are three fluids used in heating, for which pipe sizes have to be determined, viz., steam, water, and air. The power required for circulation and loss in head due to friction has to be known in determining the proper sizes of conduits. All fluids flowing in conduits obey the same laws and with corrections for density, the variables in the formulas are the same.

The potential head, or measured head, is the vertical distance measured from some base line to the center of the pipe at the point under consideration. In the measurement of the flow of gases, as air or steam, the pressure at the point of flow has to be taken into account in determining the density.

R

=

length in feet;

A

in which h= loss of head in friction; f = coefficient of friction, G.02 for water (average) but it actually varies with the diameter of pipe and velocity; l hydraulic radius, or the perimeter divided by the area;

=

The above formulas have been superseded by exponential formulas determined by plotting the values on logarithmic paper and determining the angle of inclination of the straight lines.

Diagram 1, by H. V. Carpenter, was published in "Power" Dec. 17, 1912. It gives steam discharge in pounds per minute, size of pipe, and drop in pressure per 100 ft., for sizes of pipe from 1 to 20 in. and is plotted from Unwin's or Babcock's formula, and verified by tests by R. C. Carpenter.

in which V= velocity of the steam in feet per minute; P= drop in pressure in length L; d = inches; y = density of the steam in pounds per cubic foot; and W

minute.

=

diameter of pipe in

weight of steam delivered in pounds per

This chart is for high pressure steam. For a 3-in. pipe, the discharge is seen to be 33 lb. per min., with 210 lb. average absolute pressure and 0.30 lb. drop per 100 ft. of pipe. For any lower pressure as 80 lb., follow between the inclined lines as shown, obtaining a discharge of 21 lb. per min.