CXLV. The quasi-cylindrical shock tube

Summary The disturbance produced behind a shock wave of arbitrary strength, travelling along a tube of varying cross section, is investigated. The shape of the cross section is arbitrary and the problem is linearized on the basis of small variations in area along the length of the tube. It is found that if the initial cross sectional area is S, and there is a net change in area of amount [AN], then the consequent change in pressure behind the shock is where (p 1−p 0) is the initial pressure discontinuity across the shock. The parameter K decreases monotonically with the shock strength and 0·5⩾K>0·394. More generally it is shown that the pressure is affected by two distinct perturbations superimposed on the initial flow, namely a permanent modification arising directly from the variations in cross section, and a transient disturbance reflected from the shock and propagated with sonic velocity relative to the main flow. Expressions for both these contributions are obtained.