for capacity of steam-mains are computed for steam 10 pounds above atmospheric pressure, and the frictional resistance 6 inches of water column. Tables computed from the same formula and covering other conditions will be found in "Steam-heating," by Robert Briggs, and can be consulted when desired.

123. Size of Return-pipes, Steam-heating.-The size of return-pipes, if figured from the actual volume of water to be carried back, would be smaller than is safe to use, largely because of air which is contained in the steam-pipes, and which does not change in volume when the steam is condensed. For this reason it is necessary to use dimensions which have been proved by practical experience to be satisfactory. When the steam-main is large, the diameter of the return-pipe will prove satisfactory if taken one size less than one half that of the steam-pipe; but if the steam-main is small, for instance, 5 inches or less, the return-pipe should be but one or two sizes smaller. The return-pipe should never be less than I inch, in order to give satisfactory results. The following table suggests sizes of returns which will prove satisfactory for sizes of main steam-pipes as given:

The size of return-pipes, if computed on basis of reduction in volume due to condensation of the steam, supposing the steam to have a gauge-pressure of 40 pounds and that one half its volume is air, would be, neglecting friction, about one sixth of that of the main steam-pipe, which is much smaller than would be considered safe in practice.

* Van Nostrand's Science Series, No. 68.

Main and Return-pipes for Indirect Heating Surfaces.-The indirect heating surfaces require about twice as much heat as the same quantity of direct radiating surface, and hence, for same resistance in the pipe, the area should be twice that required in direct heating. It will usually be sufficiently accurate to use a pipe whose diameter is 1.4 times greater than that for direct heating.

Reliefs and Drip-pipes.-The size of drip-pipes necessary to convey the water of condensation from a main steam to a return cannot be obtained by computation, as there is much uncertainty regarding the amount of water that will flow through.

As the flow through the relief tends to increase the pressure in the return, it may also serve to lessen the velocity of flow beyond the point of junction, provided the size is greater than necessary to carry off the water of condensation from the steam-main. Drip-pipes should be united to the return in such a manner as to re-enforce rather than impede the circulation, which result can usually be attained by joining the pipes with 60 or 45 degree fittings.

The writer would recommend the employment of the following sizes of drip-pipes as ample for usual conditions:

DIAMETER OF DRIP-PIPE FOR STEAM-MAINS OF VARIOUS LENGTHS.

124. Size of Pipes for Hot-water Radiators.-Method of computation of the velocity with which circulation will take place in a hot-water heating-system without friction has been considered in Article 121, page 220. In some instances this

velocity is increased by bubbles or particles of steam which pass up the main risers and reduce the specific gravity of the water in the ascending pipes to such an extent that the actual velocity produced is much in excess of what would have been possible had no steam formed. This condition is undesirable, as it is usually accompanied with more or less noise and a very high temperature in the boiler, and should not serve as a basis for designing main-pipes to be used in hot-water heating apparatus. It should not be recommended that heaters be run in such a manner as to produce steam in any part of the circulation.

The heat which is given off from radiating surfaces of various kinds has already been considered (page 204), and as each thermal unit given off by the surface is obtained by the cooling of one pound of water one degree in temperature, it is easy to compute from the data already given (1) the weight of water required, and (2) the number of cubic feet needed to heat each square foot of radiating surface.

The following table gives the data necessary for computing the volume of water required to supply radiating surface for various conditions likely to occur in heating:

By dividing the number of cubic feet to be supplied per hour by the velocity with which the water moves per hour we obtain the area of the pipe in square feet.

The general case from which practical tables may be computed can best be considered by the use of formulæ, as follows:

Let equal the weight of water per cubic foot, let H equal total heat per square foot per hour from radiator, R total radiating surface, Q number of cubic feet of water per hour, A area of pipe in square feet, a area of pipe in square inches, v velocity in feet per second as given in table, page 221, Vequal velocity in feet per hour, T loss of temperature of water in radiator. We have the following formulæ :

By taking special values corresponding to temperatures of water and of surrounding air we can reduce these formulæ to simple forms. Thus, if the temperature of the radiator is 180° and of the room 70°, the total heat-units given off per hour, H, will be 165. If we further assume that the water in the radiator cools during the circulation a certain amount, say 10 degrees, T will equal 10, weight of water w will equal 60.5 pounds, and we shall have formulæ 8 and 9:

(8) R = 92av.
R
92v

(9) a =

For the above condition the radiating surface is equal to 92 times the area of the main pipe in square inches times the velocity of the water in feet per second; and further, the area in square inches is equal to the radiating surface divided by 92 times the velocity. The velocity in feet per second will depend upon the height, the difference of temperature, and amount of friction.

The following table gives relations of radiating surfaces to areas of main pipes, friction neglected. For distances less than 200 ft. sufficient allowance for friction will be made by making the main one size larger than required by table.

AREA AND DIAMETER OF HOT-WATER HEATING-MAIN, DIRECT RADIATION.*

In the above table column (1) gives the height in feet; column (2) the velocity corresponding to the head for a reduction in temperature of 10° F.; column (3) is the area in square inches, neglecting friction, for each 100 square feet of radiating surface; column (4) is the corresponding diameter of pipe required for each square foot of surface, and is to be multiplied by the number of square feet of radiating surface to give the diameter for any given case; the actual diameter should be one pipe size greater; column (5) is the equivalent head which would produce the same velocity if falling freely in the air.

The preceding table is in the same form as that given for diameters of steam-main. If we consider 10 feet as the average height or head producing circulation for the first floor, it will be seen that we shall need, neglecting friction, one square inch in area in our main pipe for each 100 square feet of radiation, or the diameter of our pipe would be found for this case

* As illustrating the use of the table, compute the area of main pipe needed to supply 350 square feet of direct radiation situated 25 feet above the heater. The area is obtained by multiplying 3.5 by 0.65, which will equal 2.28 square inches. The diameter can be found from this, or it may be obtained from column (4), by multiplying the square root of 350 by 0.091. The square root of 350 is 18.7, the product is 1.7. The pipe used, if the distance is about 200 feet, should be 2 inches in diameter.