certain distance from the end, the standard taper being such that the pipe surface inclines toward the axis of the pipe by 1 in 32. This makes the total taper, as measured by the variation in outside diameter, equal to 1 in 16, or in. to the ft. The proportions of standard pipe threads and the standard dimensions of wrought-iron steam, gas, and water pipes are given in the accompanying tables Pipe Measurements. When taking measurements for piping, the center-to-center distances of the different pipe lines are measured first, and then allowance is made for the fittings. In measuring for 45° fittings, as where offsets are required, place the fittings in position and measure between them, using try pieces that point straight toward each other. In case it is inconvenient to do this, the measurement representing the exact distance from center to center between the parallel pipe lines con. nected by the offset may be taken, and the length of the diagonal line from center to center of 45° fittings is found by multiplying the distance by 1.4142, and of 60° fittings by 1.1547. From the lengths thus found must be subtracted the distance between the ends of the diagonal pipe and the center of the fittings. EXAMPLE. What length of pipe is required at b, Fig. 1, assuming that 1 in. is allowed between each end of the pipe and the center of each fitting, the distance c being 4 ft. 9 in., and 45° fittings being used? a FIG. 1. a SOLUTION.-Multiplying 4 ft. 9 in., or 57 in., by 1.4142 and subtracting the sum of the distances from the end of the pipe to the center of the fittings at each end, we have 57 X 1.4142 — (1 + 1) = 78.6 in., or a trifle over 6 ft. 6 in. Ans. A simple method for finding the diagonal length with 45° fittings is as follows: Strike two parallel chalk lines on the floor to represent the center lines of the pipes to be joined by the diagonal piece, as a b and c d, Fig. 2. Lay a steel square against one of these lines, as shown, and draw a perpendic h d FIG. 2. ular line ef. From the intersection at ƒ on cd lay off a point g, making f g equal to ef. Draw a line through e and g. Then lay a 45° fitting over each of these intersections and measure with a rod h the length of pipe required. SIZES OF PIPING. General Rales.-The size of steam pipes for heating purposes depends on several factors, among which are the pressure, length of the pipe, and frictional resistance of the pipe and fittings. All these factors, including also the diameter of the pipe, influence the velocity of flow and hence the amount of steam delivered in a given time. Steam-heating mains should be proportioned according to the desired drop in pressure and the amount of radiating surface to be supplied. As branches are taken off, the piping is commonly reduced in size toward the end of the main. Some pipe fitters reduce the size of mains in proportion to the decrease in the combined area of the branches to be supplied, but this is not correct. The reduction should be more gradual. The frictional resistance to the flow of steam increases with the length of the pipe, the quantity of steam delivered being correspondingly diminished. Approximately, the resistance varies inversely as the square of the velocity; that is, taking a velocity of 100 ft. per sec. for example, and assuming the reduction in pressure in 100 ft. of main to be about 1 lb., with 50 ft. velocity per sec. the reduction in pressure would be only one-fourth, or lb. In the design of large heating systems, it is essential that the length of the various pipes be considered in determining their diameter. Empirical Rule for Ordinary Residence Mains.-Under the conditions ordinarily found in low-pressure, gravity, resi dence-heating systems, an adequate supply of steam can be obtained by allowing .8 sq. in. in sectional area of the main for each 100 sq. ft. of radiation to be supplied. This factor applies to mains larger than 2 in. and makes allowance for loss by condensation. For smaller mains, 1 sq. in. of sectional area should be allowed for each 100 sq. ft. of direct radiation. Sizes of Mains for Two-Pipe Systems and Direct Radiation.-In the following table, prepared by Mr. A. R. Wolff, is given, for a two-pipe system, the amount of radiation that mains of different sizes and 100 ft. long will supply under different steam pressures. The values given are based on the assumption that 1 sq. ft. of radiating surface will transmit 250 B. T. U. per hr.; hence, the values in the columns headed "Total Heat Transmitted, B. T. U.," are obtained by multiplying by 250 the values in the columns headed "Direct Radiating Surface, Square Feet." The amount of radiation supplied by a pipe more than 100 ft. long may be found by multiplying the number of square feet of radiation given in the table, as corresponding to the size of the pipe, by the square root of the quotient obtained by dividing 100 by the length of the main, in feet. To avoid the necessity for calculating this factor, its value for mains of different lengths is given in table "Factors for Mains." To the actual length of the pipe must be added an allowance for the resistance of fittings, etc.; the corrected length is called the equivalent length. In low-pressure heating the resistance of bends and fittings is approximately equivalent to increasing the length of the main by the following amounts: Right-angle elbow, 40 diameters; globe valve, 125 diameters; entrance to T, 60 diameters. Thus, if a main 3 in. in diameter has an actual length of 124 ft., and three elbows, two globe valves, and one T, its equivalent length is 124 + 3 X 40 X + 2 × 125 ×+ 1 × 60 × 1 231.5 ft. SIZES OF MAINS, DIRECT RADIATION, TWO-PIPE SYSTEM. Factor FACTORS FOR MAINS. Length of Pipe, Ft. 200 300 400 500 600 700 800 900 1,000 500 600 .71 .58 .5 .45 .41 .38 .35 .33 .32 Sizes of Mains for Indirect Radiation.-One square foot of indirect radiation will under natural draft condense as much steam as 2 sq. ft. of direct radiation. Therefore, the table, "Sizes of Mains, Direct Radiation, Two-Pipe System," may be used for determining the size of pipe required. To use the table for indirect radiation, multiply the given number of square feet of indirect radiation by 2; look for the number nearest to the product in the column headed "Direct Radiating Surface, Square Feet" and at the left the pipe sizes will be found. Sizes of Mains for Direct-Indirect Radiation.-The sizes of mains for direct-indirect, also called semidirect, radiators can be found in the table headed "Sizes of Mains, Direct Radiation, Two-Pipe System," multiplying the given radiating surface by 1.5 before entering the column headed "Direct Radiating Surface, Square Feet." Size of Main for One-Pipe Systems.-The pipe sizes given in the following table are such as will insure satisfactory results with single-pipe systems in which the distance of the water level in the return above the boiler water-line is from 6 to 12 in., the steam pressure varying from to 2 lb. per sq. in. Since in single-pipe work the steam and water of condensation flow through the same pipe, and frequently in opposite directions, it is necessary to use larger pipes than with twopipe systems, so as to insure as free a flow of the opposing currents as practicable. The pipe sizes given in the table "Size of Main, Direct Radiation, One-Pipe System," may be multiplied by .8 to obtain the diameter of supply mains for a two-pipe system. The corresponding diameter of return main may then be taken from the table "Sizes of Mains, Direct Radiation, Two |