Question

Problem #5 Consider a steady, incompressible, inviscid two-dimensional flow in a corner, the stream function is given by, -xy a) Obtain expressions for the velocity components u and v b) If the pressure at the origin, O, is equal to p o obtain an expression for the pressure field Sketch lines of constant pressure c)

Answer 1

I) partial differential phi/ partial differential y = 4 partial differential/ partial differential y (xy) = 4 u = x - partial differential phi/partial differential x = v v = -y ii) check continuity partial differential u/ partial differential x + partial differential v/ partial differential y = 0 1 - 1 = 0 N - S (Navier - Stoke eq^n) rho (partial differential u/ partial differential t + u partial differential u/ partial differential x + v partial differential v/ partial differential y + w partial differential u/ partial differential z) = -partial differential p/ partial differential x + rho dx + mu (partial differential^2 u/ partial differential x^2 + partial differential^2/ partial differential y^2 \r\n rho (x(1) + (-y) (0)) = -partial differential p/ partial differential x + mu (0 + 0) partial differential p/ partial differential x = -3 x (1) (For x component similar thing for y - component partial differential y/ partial differential y = -rho y (2) check partial differential^2 p/ partial differential x partial differential y = partial differential/partial differential x (partial differential p/ partial differential y) = 0

Dear,

If you have any doubt regarding answer please ask in comment section.

Thanks