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For a 2D incompressible steady flow of fluid velocity V = (x2 – 2xy) i + v j. the velocity in y direction at (1, 1) is 2 m/s. find total acceleration at (1, 1) in m/s2.
  • a)
    4.5
  • b)
    4
  • c)
    5
  • d)
    0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
For a 2D incompressible steady flow of fluid velocity V = (x2 – 2xy) ...
Here, velocity field V = (x2 – 2xy) i + v j
u = x2-2xy v = ?
Given, 2D incompressible steady flow so du/dx + dv/dy = 0
& du/dx = 2x-2y
So, ∫ dv = -∫ (2x-2y) dy
V = y2-2xy+C
Then, ax = u du/dx + v du/dy and ay = u dv/dx + v dv/dy
At (1, 1) u = -1 m/s & v = 2 m/s
Now, ax = (-1 × 0) + (2 × -2) = -4 m/s2
& ay = (-1×-2) + (2×0) = 2 m/s2
Now, aT = √(-4)2 + 22 = 4.5 m/s2
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For a 2D incompressible steady flow of fluid velocity V = (x2 – 2xy) i + v j. the velocity in y direction at (1, 1) is 2 m/s. find total acceleration at (1, 1) in m/s2.a)4.5b)4c)5d)0Correct answer is option 'A'. Can you explain this answer?
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