Question

Consider the following two-dimensional velocity field V = (u,v)

Answer 1

Answer:

a) C1 = 3C2

b) C1 = 1 , C2 = -3  

c) $w = \frac{-x^2}{2} + \frac{y^2}{2} + 3xy + C$

d) (v.v)T = 0

Explanation:

u = 3x + C1y

v = x + C2y

A) determining all  stagnation points

At The stagnation points : u = 0, v = 0

for all  values of C1 and C2 , C1 = 3C2

B) The coefficients of C1 and C2 so that the flow is potential

C1 = 1 , C2 = -3  

C) Determine the expression of the stream function

$w = \frac{-x^2}{2} +\frac{y^2}{2} +3xy+ C$

D) The value of (v.v)T at the point (x,y) = (1,2)

(v.v)T = 0

Attached is the detailed solution