A Study of Transonic Gas Dynamics by the Hydraulic Analogy

The theory governing the propagation of surface water waves is analyzed to show that an analogy with the two-dimensional flow of a perfect gas exists only if the water depth is approximately V4 in., the model is fairly large, and the shock waves or hydraulic jumps present are of the weak type having a negligible increase in entropy. Photographs of the water surface waves corresponding to shock waves in front of simple wedges and circular cylinders are presented to illustrate these restrictions. It is pointed out that the surface-wave group velocity, which could be considerably less than the so-called wave velocity, provided the only correct analogy to the speed of sound in two-dimensional gas flow over a closed body. Motion pictures were taken in order to study the effect of constant acceleration on bow shock waves. I t was found that at high rates of acceleration the location of a detached shock wave was dependent mainly on a nondimensional acceleration parameter and was practically independent of the instantaneous Mach Number.