High Velocity Flow with Free Boundary in Open Channels

Abstract

The method of calculation of high velocity flow with free boundary is developed by means of the method of characteristics. The basic equations used here are the plane two-dimensional flow equations in the steady state. These equations are transformed into the characteristic form. It is shown that the position of free boundary is determined as the intersection of stream line (λ1-line) and another characteristic line λ2 or λ3. The hydraulic variables along the free boundary are also calculated by using the relation satisfied along λ1- and λ2-line or λ1- and λ3-line. The numerical method shown here is applied for some typical high velocity flows with free boundaries studied by Rouse and Knapp. The calculated results are compared with the previous experimental results in order to verify the method of calculation.