Stream and velocity potential functions for a two-dimensional flow field given by u = 2x and v = - 2y are (A) \Psi=2xy,ϕ=x^2-y^2 (B) \Psi=x^2-y^2 ,ϕ= 2xy (C) \Psi= x^2y^2,ϕ=x^2+y^2 (D) \Psi= x^2+y^2,ϕ=x^2 y^2

Correct Answer is : None of these

SSC JE Mechanical Engineering 2018 Set 1 Paper

Question : 167 of 200

Marks: +1, -0

Stream and velocity potential functions for a two-dimensional flow field given by

u = 2x

and

v = - 2y

are
(A)

Ψ=2xy,ϕ=x^2-y^2

(B)

Ψ=x^2-y^2 ,ϕ= 2xy

(C)

Ψ= x^2y^2,ϕ=x^2+y^2

(D)

Ψ= x^2+y^2,ϕ=x^2 y^2

Solution:

Given u = 2x, v = –2y
potential function

-∂ϕ/∂x=u,=-∂ϕ/∂y=v

-∂ϕ/∂x=2x

∫ ∂ϕ =-2x∫∂x

ϕ=-{2x^2}/2+\f(y)

ϕ=-{ x^2} +\f(y)

∵-∂ϕ/∂y=v⇒ ∂ϕ/∂y=2y=\f'(y)

⇒

\f'(y)=2y

integrate function
⇒

\f(y)={2y^2}/2+c=y^2+c

So potential function

ϕ= –x^2 + y^2 + c

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