Wave Action following Sudden Release of Compressed Gas from a Cylinder

Abstract

The limitations of sound wave theory, and the work of Earnshaw and Riemann are first examined in relation to the propagation, under frictionless conditions, of waves of finite amplitude. The theory of pressure equalization in a semi-infinite pipe, due to Aschenbrenner, is extended to cover discharge from a cylinder into a pipe of the same bore, or to atmosphere. The effects of friction are examined and the accepted mathematical solution of the analogous electrical transmission-line problem is applied to the case of small-amplitude waves. Friction in relation to waves of finite amplitude is examined, and a hyperbolic law defining the effects of friction is deduced. The arguments developed are applied to discharge from a cylinder through an orifice of smaller diameter. The experimental apparatus consisted of a number of cylinders of 2-inch bore, and of lengths from 1 foot to 40 ft. 6 in., from which air, at gauge pressures from 140 lb. per sq. in. to minus 25 inches of mercury, was discharged either directly to atmosphere or through a pipe of 2-inch bore and up to 81 feet in length. Indicator diagrams were recorded at points spaced along the cylinder and pipe, and corresponding diagrams were also obtained, using a cylinder 4 feet long and 4 inches in diameter in conjunction with a pipe of 2-inch bore. From the general agreement between the experimental and the theoretical investigation, it is concluded that the processes of discharge, under the conditions considered, are capable of full explanation on the basis of accepted physical laws. Experimental confirmation is obtained for the theoretical treatment put forward by Giffen for discharge from a cylinder through an orifice of smaller diameter, and quantitative data are given in regard to velocities of propagation, pressure amplitudes, attenuation, etc., for the range of conditions covered.