seems to be very little exact data regarding the steady flow of steam in pipes, and it has been customary for writers to assume that the same laws which apply to the flow of water hold true. in this case, and that the same methods can be used in computing quantities. These results are certainly safe, although no doubt giving sizes somewhat larger than strictly necessary for the purposes required.

In estimating the size of steam-pipe for power purposes is customary to figure the area of cross-section, such as giving a velocity of flow not exceeding 100 feet per second. This velocity is generally accompanied by a reduction of pressure in a straight pipe of about one pound in 100 feet. For steamheating purposes the general practice is to use a much larger pipe and lower velocity, so that the total reduction in pressure on the whole system is much less; the effect of a drop in pressure of one pound will cause the water to stand in the return pipe in a gravity system 2.4 ft. above the water-level in the boiler.

The velocity of water and steam in a gravity system of heating is due to a different cause from that in the case just considered, for the reason that the pressure upon the heater acts uniformly in all directions, and exerts the same force to prevent the flow into the boiler from the return, as to produce the flow into the main. For such cases the sole cause of circulation must be the difference in weight of the heated bodies, hot water, or steam in the ascending column and the cooler and heavier body in the descending column. The velocity induced by a given force will be reduced in proportion as the mass moved is greater. In the case of steam-heating the difference between the weight in the ascending and descending column is so great that the velocity will not be essentially different from that of free fall, provided correction is made for loss of head due to friction, etc., as explained, but in case of hot water the theoretical velocity produced will be found very small.

The case is very similar to the well-known problem in mechanics in which two bodies A and B of unequal weights are connected by a cord passing over the frictionless pulley C (Fig. 190).

The heavier body B in its descent draws up the lighter body A. In this case the moving force is to the force of gravity as the difference in the weights is to the sum of the weights, and the velocity is the square root of twice the force into the height.

In other words, if ƒ equals the moving force, we have by proportion

which, substituted in place of ƒ in formula v = √2fh, gives the following as the velocity:

ข

2g (BA)h
B+ A

FIG. 190.

h being the height fallen through.

A

B

In applying this to the case of hot-water heating we have, instead of the descent and ascent of two solids of different weights, the descent and ascent of columns of water connected as shown in Fig. 191, the heated water rising in the branch AF and the cooler water descending in the branch BC. The force which produces the motion is the difference in weight of water in the two columns; the quantity moved is the sum of the weight of water in both columns. This is equal to the difference in weight of I cubic foot of the heated and cooled water divided by the sum, multiplied by the total height of water in the system, so that if W1 represents the weight of 1 cubic foot in the column BC, and W represents the weight of 1 cubic foot in the column AF, and h represents the total height of the system, then the velocity of circulation will be, in feet per second,

In this formula no allowance whatever is made for friction, consequently the results obtained by its use will be much in excess of that actually found in pipes. The amount of friction will depend upon the length of pipe and its diameter. As result of experiment the writer found considerable variation

in different measurements of velocity, but in no case did he find a velocity greater than that indicated by the formula. The following table is calculated from the formula without allowance for loss by friction. The computation is made with the colder water at 160 degrees F., although little difference would be found in calculations at other temperatures.

VELOCITY IN FEET PER SECOND IN HOT-WATER PIPES.

A

This table is of interest for the reason that most computations of the velocity of circulation of hot water have entirely neglected the effect that the mass or weight of the water moved has on the velocity, and hence the results as computed have been many times greater than actually found. The method usually employed in computing this velocity has been to consider the denser and lighter fluids occupying the relative positions shown in Fig. 192, the lighter fluid being in one branch of the U tube, the heavier in the other. If the cock be opened, equilibrium will be established, and the lighter liquid will stand in the branch higher than the heavier a distance sufficient to balance the difference in weight. If we suppose (1) the cock closed and

* See Hood's work on "Warming Buildings," page 27. knows, this theory has not before been questioned.

D

FIG. 192.

B

So far as the writer

enough of the heavier material added to the shorter column, so that the heights in each are the same; (2) the cock opened, then the heavier liquid will move downward and drive the lighter liquid upward with a velocity said to be equal to that which a body would acquire in falling through the distance equal to the difference in heights when the columns were in equilibrium. This gives too great results, because it neglects the effect of the mass of the bodies moved. If friction be considered, we should have as a probable expression of velocity, using the same notation as on page 218,

122. Size of Pipes to supply Radiating Surfaces.—The method of computing the size of pipes required for steam heating would be as follows: First find the amount of steam by dividing the total number of heat-units given out by 1 square foot of radiating surface by the latent heat in I pound of steam, this will give the weight of steam required per square foot; this multiplied by the number of cubic feet in I pound of steam will give the volume which will be required for each square foot of radiating surface. Knowing this quantity the size of pipe may be computed from the considerations already given, either by formulæ of Article 121 or by assuming the velocity of flow as equal that due to the head, corrected for friction; 25 to 50 feet per second can in nearly every case be realized. As an illustration; compute the size of main steampipe required to supply 1000 feet of radiating surface with steam at a temperature of 212 degrees when the surrounding temperature of the air is 70: For this case I square foot of radiating surface can be assumed ordinarily as giving off (1.8 times 142) 255 heat-units. To supply 1000 feet of surface 255,000 heat-units per hour would be required; as each pound of steam during condensation (see steam table) will give up 966 heat-units, we will need for this purpose 264 pounds per hour; and as each pound of steam at this temperature makes 26.4 cubic feet, we will require 6970 cubic feet of steam per hour, or 1.94 cubic feet per second.

If we proportion the pipes so that the velocity shall not

exceed 25 feet per second, the area of the pipe must be 0.077 square foot, which equals 11.1* square inches. For this we would require a pipe 4 inches in diameter. If we had assumed the velocity to be 50 feet per second, the area would have been 5.6 square inches and the diameter 3 inches; if we had assumed a velocity of 100 feet per second, the arca required would have been 2.8 square inches and the diameter of the pipe required would have been somewhat less than 2 inches. The friction in a pipe when steam is moving at a velocity of 100 feet per second causes a reduction in pressure of about 11⁄2 pounds in 100 feet, a velocity of 50 feet per second causes about as much, and a velocity of 25 feet about as much. Indirect surfaces of the same extent usually require twice as much steam and a pipe with area twice as great as that needed for direct radiation.

For the single-pipe system of heating an additional amount of space must be provided in the steam main to permit the return of the water of condensation. The actual space occupied by the water is small compared with that taken by the steam, but in order to afford room for the free flow of the currents of water and steam in opposite directions, experience indicates that about 50 per cent more area should be provided than is required in the separate return or double pipe system of heating.

By similar computations we obtain the following factors, which are to be multiplied by the radiating surface to obtain areas and diameters of steam-heating mains in inches:

TABLE FOR AREA AND DIAMETER OF STEAM-MAIN.

(3)

Double-pipe Single-pipe

In all cases if the mains are not covered, its surface is to be estimated as a part of the radiating surface.

* This quantity is greater than the area of a 34-inch pipe, and in such case the safe proceeding is to use the next greater size.