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Determine the third velocity component such that continuity equation is satisfied if two components are u=2y2, w=2xyz.
- a)-2xy+x2y+f(y,z)
- b)4xy-x2y+f(y,z)
- c)-4xy-x2y+f(y,z)
- d)-2xy-x2y+f(y,z)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Determine the third velocity component such that continuity equation i...
The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.
Here du/dx=0 and w=2xy.
On solving by integrating, we get v = -4xy-x2y+f(y,z).
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Determine the third velocity component such that continuity equation i...
Solution:
Given,
u = 2y^2
w = 2xyz
Let's assume the third velocity component as v.
Continuity equation for incompressible fluid is given by:
∂u/∂x + ∂v/∂y + ∂w/∂z = 0
Substituting the given values in the above equation, we get:
∂(2y^2)/∂x + ∂v/∂y + ∂(2xyz)/∂z = 0
0 + ∂v/∂y + 2xy = 0
∂v/∂y = -2xy
Integrating with respect to y, we get:
v = -2xy^2 + f(z)
where f(z) is an arbitrary function of z.
Hence, the third velocity component is given by:
v = -2xy^2 - x^2y + f(z)
Comparing the given options with the above equation, we get that option 'C' is the correct answer:
v = -4xy - x^2y + f(z)
Given,
u = 2y^2
w = 2xyz
Let's assume the third velocity component as v.
Continuity equation for incompressible fluid is given by:
∂u/∂x + ∂v/∂y + ∂w/∂z = 0
Substituting the given values in the above equation, we get:
∂(2y^2)/∂x + ∂v/∂y + ∂(2xyz)/∂z = 0
0 + ∂v/∂y + 2xy = 0
∂v/∂y = -2xy
Integrating with respect to y, we get:
v = -2xy^2 + f(z)
where f(z) is an arbitrary function of z.
Hence, the third velocity component is given by:
v = -2xy^2 - x^2y + f(z)
Comparing the given options with the above equation, we get that option 'C' is the correct answer:
v = -4xy - x^2y + f(z)
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Community Answer
Determine the third velocity component such that continuity equation i...
Even the answer selection seems wrong.
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