maths31415926
Nov3-10, 02:36 PM
1. The problem statement, all variables and given/known data
A cylinder of radius a is placed in a uniform stream of speed U. Fluid is blown steadily outwards across the surface of the cylinder so that the normal component of velocity on the surface is V.
a, find the velocity potential for the flow
b, show that if V = U4(2^(1/2)) then there is a stagnation point at a distance (a(3+(2^(1/2))) upstream of the centre of the cylinder.
2. Relevant equations
I did a, and got:
phi(velocity potential) = cos(theta)(r+((a^2)/r)) + Valog(r)
3. The attempt at a solution
I'm not sure what to do next. I know we can use the stagnation point they give us as this is a show that question, but i'm not sure how. Also, at stagnation points, the total velocity is zero so gradphi = 0.
A cylinder of radius a is placed in a uniform stream of speed U. Fluid is blown steadily outwards across the surface of the cylinder so that the normal component of velocity on the surface is V.
a, find the velocity potential for the flow
b, show that if V = U4(2^(1/2)) then there is a stagnation point at a distance (a(3+(2^(1/2))) upstream of the centre of the cylinder.
2. Relevant equations
I did a, and got:
phi(velocity potential) = cos(theta)(r+((a^2)/r)) + Valog(r)
3. The attempt at a solution
I'm not sure what to do next. I know we can use the stagnation point they give us as this is a show that question, but i'm not sure how. Also, at stagnation points, the total velocity is zero so gradphi = 0.