For the velocity field of Prob. 958, plot streamlines = 0, 1, 2, 3, 4, 5,

For the velocity field of Prob. 9–58, plot streamlines ψ = 0, 1, 2, 3, 4, 5, and 6 m²/s. Let constants a, b, and c have the following values: a = 0.50 s^–1, b = –1.3 s^–1, and c = 0.50 s^–1. For consistency, plot streamlines between x = –2 and 2 m, and y = –4 and 4 m. Indicate the direction of flow with arrows.

Data from Problem 58

A steady, two-dimensional, incompressible flow field in the xy-plane has the following stream function: ψ = ax² + bxy + cy², where a, b, and c are constants. 

Obtain expressions for velocity components u and v. 

Verify that the flow field satisfies the incompressible continuity equation.