Chapter 5, Problem 61P

Consider the velocity field given by $\stackrel{\to }{V}=A{x}^2\hat{i}+Bxy\hat{j},$ where A = 1 ft⁻¹·s^−l, B = − 2 ft⁻¹·s^−l, and the coordinates are measured in feet.

1. (a) Determine the fluid rotation.
2. (b) Evaluate the circulation about the “curve” bounded by y = 0, x = 1, y = 1 and x = 0.
3. (c) Obtain an expression for the stream function.
4. (d) Plot several streamlines in the first quadrant.