Aerodynamics: Find Expressions for u and v

[shreddinglicks]

Homework Statement

The absolute value of the velocity and the equation of the streamlines in a velocity field are given, respectively,

|V|=sqrt(x^2+2xy+2y^2) and y^2+2xy = C

Find expressions for u and v.

Homework Equations

dy/dx = v/u
|v| = sqrt(u^2+v^2)

The Attempt at a Solution

included in attachment

 

[RUber]

Most of your steps look good. Remember that
$u^2 = f(x,y)$
implies
$u = \pm \sqrt{f(x,y)}.$
This is important because you need to be consistent and keep $\frac vu = -1$.

 

[shreddinglicks]

Thanks, my only major concern is that when I take the partial derivative, how do I know which term to take derivatives in respect to y or x. Do I have to make assumptions?