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In a two-dimensional incompressible steady flow, the velocity component u = !ex is obtained. What is the other component v of velocity?
  • a)
    v = Aexy
  • b)
    v = Aey
  • c)
    v = −Aex y + f(x)
  • d)
    v = −Aey x + f(y)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a two-dimensional incompressible steady flow, the velocity compone...
For a 2D incompressible flow
∂u/ ∂x + ∂v / ∂y = 0 ⋯ ①
Given u = Aex Therefore ∂u / ∂x = Aex
Substituting the same in equation ①
Aex + ∂v / ∂y = 0
⇒∂v / ∂y = −Aex
⇒ v = −Aex y + g(x)
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Most Upvoted Answer
In a two-dimensional incompressible steady flow, the velocity compone...
Solution:

Given, u = !ex

To find: v

We know that the flow is incompressible, i.e., ∂u/∂x + ∂v/∂y = 0

Differentiating u w.r.t. x, we get:

∂u/∂x = ∂/∂x (Aex) = Aex

Differentiating v w.r.t. y, we get:

∂v/∂y = ∂/∂y (-Aexy) = -Aex

Now, using the continuity equation, we have:

∂u/∂x + ∂v/∂y = 0

Substituting the values of ∂u/∂x and ∂v/∂y, we get:

Aex - Aex = 0

Therefore, the other component of velocity is:

v = -Aexy

Hence, option C is the correct answer.
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In a two-dimensional incompressible steady flow, the velocity component u = !ex is obtained. What is the other component v of velocity?a) v = Aexyb) v = Aeyc) v = −Aex y + f(x)d) v = −Aey x + f(y)Correct answer is option 'C'. Can you explain this answer?
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