Chapter 14.4, Problem 66E

Channel flow The flow in a long shallow channel is modeled by the velocity field F = (0, 1 – x²), where R = {(x, y): |x| ≤ 1 and |y| = 5}.

a.    Sketch R and several streamlines of F.

b.    Evaluate the curl of F on the lines x = 0, x = $\frac{1}{4}$, x = $\frac{1}{2}$, and x = 1.

c.    Compute the circulation on the boundary of R.

d.    How do you explain the fact that the curl of F is nonzero at points of R, but the circulation is zero?