Question 10.23: Find and plot the velocity field for the flow in the corner. T...

This exercise can be solved by using Eqs. 10.73: u = ∂\psi/∂y and v = −∂\psi/∂x. For the streamfunction of interest we find

u=\frac{\partial \psi }{\partial y}=\frac{\partial}{\partial y}(Axy)=Ax         and          v=\frac{-\partial \psi }{\partial x}=\frac{-\partial}{\partial x}(Axy)=-Ay

A vector plot of this velocity field is shown in Figure 10.66. Note that this plot is entirely consistent with the streamlines for this flow shown in Figure 10.65.