- #1

leonida

- 10

- 0

## Homework Statement

prove that with flow in a corner, with stream function ψ=Axy, particles are accelerating per [itex]\frac{DV}{Dt}[/itex]=(A

^{2}(x

^{2}-y

^{2}))/r; A=const; r-distance from the center of the corner

## Homework Equations

Vx=U=[itex]\frac{∂ψ}{∂y}[/itex] . . Vy=V=-[itex]\frac{∂ψ}{∂x}[/itex]

a=[itex]\frac{∂V}{∂t}[/itex]+U[itex]\frac{∂V}{∂x}[/itex]+[itex]\frac{∂V}{∂y}[/itex]

## The Attempt at a Solution

As per above equations i get velocity components as

U=Ax and V=-Ay

then since local acc is 0 acceleration is:

a=Ax[itex]\frac{A(x-y)}{∂x}[/itex] - Ay[itex]\frac{A(x-y)}{∂y}[/itex]

finally, as per my calcs, accelerations is:

a=A

^{2}(x+y)

where did this r come from and also (x

^{2}-y

^{2}). i was thinking using r

^{2}=x

^{2}+y

^{2}, and using to multiply the whole acceleration expression with r

^{2}/(x

^{2}+y

^{2}), but i am getting nowhere.

help please