- #1
Quinn Pochekailo
- 13
- 1
Homework Statement
The velocity components in a steady, incompressible, 2-D flow field are
u = 2y
v = 4x
Find the corresponding stream function.
Homework Equations
u = ∂Ψ/∂y
v = -∂Ψ/∂x
The Attempt at a Solution
I can verify that a stream function exists for this problem because conservation of mass is satisfied. (∂u/∂x + ∂v/∂y = 0)
After plugging in my values for u and v, I get that Ψ = y2 + f(x) and Ψ = -2x2 + f(y).
I then equate the 2 equations to give me f(x) + y2 = -2x2 + f(y).
I then set f(y) to 0, to give me that f(x) = -2x2 - y2.
I then put f(x) back into my original Ψ equation to give me that Ψ = -2x2 and this is the function that I get for my stream function.
However, my book is telling me that Ψ = -2x2 + y2 should be my stream function.
Am I doing something wrong?
Thanks in advance.