Problem G8.1

Given the stream function psi = 3x^2 + 2y^2, calculate the velocity field and draw the streamlines psi = 0, psi = 1, and psi = -1.

Work:

u = d(psi)/dy = 4y
v = -d(psi)/dx = -6x
Continuity equation: du/dx + dv/dy = 0
v/u = dy/dx
Streamline: dx/u = dy/v
dx = 4y*dy/-6X
dy = -6x*dx/4y
equation of a streamline: (d(psi)/dx)*dx + (d(psi)/dy)*dy = 0

psi(0) = 3x^2 + 2y^2 = 0
2y^2 = -3x^2
y^2 = -(3/2)*x^2
y = SQRT[(-3/2)*x^2]
non-real answer??

Solution

non-real answer

Problem posted 08/02/05 -- LAL