Question

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

u = 3x+c1y
v= x + c2y

Where c1 and c2 are coffients.
Required:

a. Determine all stagnation points.
b. Determine the coefficients C1, C2 such that the flow is a potential flow.
c. For the values of the coefficients calculated at point (b), determine the expression of the stream function.
d. For the values of the coefficients calculated at point (b), considering a temperature field T = 2x + 3y, determine the value of (v.v)T at the point (x,y) = (1,2)

Answer 1

a) C1 = 3C2

b) C1 = 1 , C2 = -3

c)
`w = (-x^2)/(2) + (y^2)/(2) + 3xy + C`

d) (v.v)T = 0

Step-by-step 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 = (-x^2)/(2) +(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