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The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible is
- a)k1 = k2
- b)k1 = -k,2
- c)k1 = 3k2/2
- d)4k1 = 5k2
Correct answer is option 'A'. Can you explain this answer?
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The velocity components of a plane flow are x/k1 - y/k2 , 0 in the dir...
Understanding Incompressible Flow
Incompressible flow is characterized by a constant density throughout the fluid. For a flow to be classified as incompressible, the divergence of the velocity field must equal zero.
Velocity Components of the Flow
The given velocity components in the flow are:
- u = x/k1 - y/k2 (in the x-direction)
- v = 0 (in the y-direction)
- w = 0 (in the z-direction)
Divergence of the Velocity Field
To determine if the flow is incompressible, we calculate the divergence of the velocity field (∇·V):
- ∇·V = ∂u/∂x + ∂v/∂y + ∂w/∂z
Since v and w are both zero, this simplifies to:
- ∇·V = ∂(x/k1 - y/k2)/∂x + 0 + 0
Calculating the partial derivative:
- ∂u/∂x = 1/k1
- ∂u/∂y = -1/k2
Thus, the divergence becomes:
- ∇·V = 1/k1 - 1/k2
Condition for Incompressibility
For the flow to be incompressible, we set the divergence to zero:
- 1/k1 - 1/k2 = 0
This implies:
- 1/k1 = 1/k2
Consequently, we can derive:
- k1 = k2
Conclusion
Thus, the correct condition for the flow to be incompressible is:
- Option A: k1 = k2
This means that for the flow to maintain constant density, the coefficients k1 and k2 must be equal.
Incompressible flow is characterized by a constant density throughout the fluid. For a flow to be classified as incompressible, the divergence of the velocity field must equal zero.
Velocity Components of the Flow
The given velocity components in the flow are:
- u = x/k1 - y/k2 (in the x-direction)
- v = 0 (in the y-direction)
- w = 0 (in the z-direction)
Divergence of the Velocity Field
To determine if the flow is incompressible, we calculate the divergence of the velocity field (∇·V):
- ∇·V = ∂u/∂x + ∂v/∂y + ∂w/∂z
Since v and w are both zero, this simplifies to:
- ∇·V = ∂(x/k1 - y/k2)/∂x + 0 + 0
Calculating the partial derivative:
- ∂u/∂x = 1/k1
- ∂u/∂y = -1/k2
Thus, the divergence becomes:
- ∇·V = 1/k1 - 1/k2
Condition for Incompressibility
For the flow to be incompressible, we set the divergence to zero:
- 1/k1 - 1/k2 = 0
This implies:
- 1/k1 = 1/k2
Consequently, we can derive:
- k1 = k2
Conclusion
Thus, the correct condition for the flow to be incompressible is:
- Option A: k1 = k2
This means that for the flow to maintain constant density, the coefficients k1 and k2 must be equal.
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The velocity components of a plane flow are x/k1 - y/k2 , 0 in the dir...
Consider the expression for the incompressible flow.
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The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer?.
The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer?.
Solutions for The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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ample number of questions to practice The velocity components of a plane flow are x/k1 - y/k2 , 0 in the directions x, y, z, respectively. If k1 , k2 ≠ 0 are constant times, the correct expression for the flow to be incompressible isa)k1 = k2b)k1 = -k,2c)k1 = 3k2/2d)4k1 = 5k2Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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