on construction. With the surface erected closely together the amount is small. By better arrangement of the surfaces, so that all parts are made hot, and an ample opportunity is provided for circulation of the air, the coefficient of heat transmission may be much increased. If extended-surface radiators are used and the entire surface figured as effective, the coefficient should be taken about 10 per cent less than assumed by the writer in the computation. For forced draft the coefcient may be safely taken as 4 and 6, or about 100 per cent greater than for natural circulation.

The following tables are collected from various authorities, and are of interest as showing character of "rule of thumb" practice in providing indirect heating surface for rooms of various kinds. It will be noted that the amount specified for the same work differs more than 50 per cent, which shows the crudeness of estimates of this character.

CRUDE ESTIMATE OF SPACE HEATED BY 1 SQ. FT. OF INDIRECT STEAM-HEATING SURFACE.

CRUDE ESTIMATE OF SPACE HEATED BY I SQ. FT. OF INDIRECT HOT-WATER HEATING SURFACE.

120. Summary of Approximate Rules for Estimating Radiating Surface. As the temperature required for buildings of various classes varies but little, and as the heating surface is usually estimated to be sufficient to heat buildings during zero weather to a temperature of 70 degrees, some very simple rules can be given which are founded on a rational basis, and which with certain modifications, as explained (page 57), for those which are especially exposed, will be found to give good results in practice which agree closely with those used by the best heating engineers. They are as follows:

First. The amount of heat required to supply that lost from the room per degree difference of temperature is approximately equal to the area of the glass in square feet plus 1/4 the exposed wall surface. (See page 59.)

Second. The heat necessary to supply loss from ventilation for dwelling-houses, first floor, is 2/55 of the cubic contents per hour for living rooms;

3/55 of the cubic contents for halls;

1/55 of the cubic contents for upper stories.

For churches, auditoriums, the loss to supply ventilation should be taken as 3/55 to 6/55 of the cubic contents; for offices, banks, etc., 1/55 to 2/55 of the cubic contents, depending upon circumstances.

Third. To find the radiating surface for direct steam-heating, multiply the sum of the numbers as given by rules First and Second by 1/4.

Fourth. To obtain the radiating surface for direct hotwater heating, multiply the sum of the numbers as given by rules First and Second by 0.4. These rules may both be summed up in the following concise form:

RULE. For heating to 70 degrees in zero weather, direct heating Radiating surface is equal to the sum of the glass surface plus 1/4 the exposed wall surface plus 1/55 to 3/55 the cubic contents, for rooms as explained, multiplied by 1/4 for lowpressure steam-heating or by 0.4 for hot-water heating.

NOTE. When air is introduced at 100 degrees Fahr., 58 should be used instead of 55. This difference is, however, usually negligible.

For indirect heating the following rules will give quite satisfactory results when the temperature of the room is to be maintained at 70° with outside air at zero and the heated air brought in at a temperature 30° above that in the room. In this calculation the surface of the steam radiator is supposed to be 212°, that of the hot-water radiator 170° Fahr. The coefficients are taken from the preceding table.

RULE. The radiating surface for indirect heating is equal to the glass surface plus one fourth the exposed wall surface in square feet multiplied by the following factors:

The total amount of air supplied will be given by the fol

lowing

RULE. The air in cubic feet per hour is found by multiplying the radiating surface, computed as in above rule, by the following factors:

If this is insufficient for ventilating purposes more air must be introduced, which must be heated to 70° F., and this will require approximately an additional foot of surface for each additional 250 cubic feet of air heated by steam, or for each additional 150 cubic feet heated by hot water.

These rules will be found quite simple in application, and they may be easily committed to memory. For rooms which are poorly constructed or especially exposed these results should be increased the same proportional amount as for direct radiating surfaces. For temperatures lower or higher than 70° the table of factors p. 212 may be used with facility.

121. Flow of Water and Steam.-It seems necessary to say a few words respecting the general laws which apply before considering the practical application. The velocity with which water flows in a pipe is computed from the same general laws as those applying to the fall of bodies. The velocity is produced, however, not by actually falling through a given distance, but by a difference of pressure, which must be expressed, not in pounds per square inch, but in feet of head. This head is in every case to be found by multiplying the difference of pressure by the height required for the given fluid to make one pound of pressure. If we denote by h the difference of head as described, by g the force of gravity= 32.16, by v the velocity in feet per second, we would have in case of no friction

v = √2gh.

The quantity discharged per second would be found in every case by multiplying the velocity by the area of the orifice in square feet.

In the flow of water in pipes there is considerable friction,

which acts to reduce the velocity and the amount discharged; this increases with the length and decreases with the diameter of the pipe. For the actual flow we depend upon experimental results. An approximate formula, attributed by Robert Briggs* to Prof. Unwin, which is sufficiently accurate for computing the flow of water in pipes is as follows:

Let the velocity in feet per second, V the velocity of feet per minute, q = the quantity discharged in cubic feet per second, that discharged per minute, /= the length of pipe in feet, h = the head in feet, D the diameter in feet, d the diameter in inches.

=

=

The friction caused by bends and by passing through valves and into entrance of pipes is of considerable amount, and often requires consideration. It can be considered as producing the same resistance to flow as though the pipe had been increased in length certain distances as follows: 90-degree elbow is equivalent to increase in length of the pipe 40 diameters, globe valve 60 diameters, entrance of a pipe in tee or elbow 60 diameters, entrance in straight coupling 20 diameters.

The flow of steam in pipes presents some problems slightly different from that of flow of air (Articles 31 and 32), but in many respects the two cases are similar. There is a tendency for the steam to condense, which changes the volume flowing and affects the results greatly. The effect of condensation and friction is to reduce the pressure in the pipe an amount proportional to the velocity and also to the distance, and these losses are greater as the pipe is smaller. There

* Steam-heating for Buildings, p. 75, by Briggs.