Choke Angle in Supercritical Contractions

Abstract

Open channels carrying supercritical flow may have changes in cross section or alignment. Where the geometric transition causes a channel wall to deflect into the tangent of the approaching streamlines, a positive standing oblique wave is generated. While such waves are not simple hydraulic jumps, their fundamental basis is the same as that of jumps and their physical aspect is similar. Under certain conditions, an oblique wave may choke discharge and the flow regime must reestablish itself in the subcritical state. From mass, velocity, and momentum balances and differentiation, an explicit expression is determined for the limiting channel-wall deflection at which choked flow must occur. It is seen that while rules of thumb for choke angle may be reasonable for many applications, the analytic value varies significantly with Froude number and criteria of wave stability.