An approximation that can be used to determine how swirl affects the choking constraint on flow through the throat of a nozzle is obtained. The flow model is consistent with an experimentally observed flow pattern that contains a recirculating internal cell upstream of the throat. Results of the approximation are applied to three different flow situations. First, it is found that the choking constraint imposes a limit on the maximum tangential Mach number that can be achieved in a vortex tube even when an infinite pressure ratio is available. Next, analytic expressions are derived for the variation of rocket mass flow in a spinning rocket. The last application is the prediction of a performance curve for a fluidic vortex valve that is consistent with limited experimental data.