Question 10.22: The flow in a corner can be modeled with the streamfunction ψ...
The flow in a corner can be modeled with the streamfunction \psi = Axy, where A is a constant. Sketch the streamlines corresponding to constant values of \psi of 0, A, 2A, 3A. Also find the streamline that passes through the point (1, 1).
To find the streamlines for constant values of \psi, we simply substitute the known value into the streamfunction equation and solve for y. For \psi = 0, x = 0 and y = 0 are solutions that make up the walls of the corner as shown in Figure 10.65. For \psi = A, the equation for the streamline is y = 1/x. For \psi = 2A and 3A, the solutions are y = \frac{1}{2}x and \frac{1}{3}x, respectively. These streamlines are also shown in Figure 10.65. To find the streamline passing through point (1, 1) we substitute these values into the streamfunction equation to find that \psi _P = A. Thus, the desired streamline is the y = 1/x, which we have already found.
