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For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation is
- a)linear with zero value at the plates
- b)linear with zero value at the center
- c)quadratic with zero value at the plates
- d)quadratic with zero value at the center
Correct answer is option 'B'. Can you explain this answer?
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The shear stress variation in a steady incompressible laminar flow between two infinite parallel stationary plates is linear with zero value at the center.
Explanation:
In a steady incompressible laminar flow between two infinite parallel stationary plates, the fluid moves in layers parallel to the plates. This type of flow is also known as a Couette flow.
Shear Stress:
Shear stress is the force per unit area acting tangentially to the surface of the fluid. In the case of a flow between parallel plates, the shear stress is caused by the relative motion of the fluid layers.
Shear Stress Variation:
The shear stress varies across the fluid layer from the bottom plate to the top plate. The variation of shear stress can be determined using the velocity distribution of the fluid.
Linear Variation:
In a Couette flow, the velocity of the fluid varies linearly from the bottom plate to the top plate. This means that the velocity gradient, which is directly proportional to the shear stress, also varies linearly.
So, the shear stress variation is linear with zero value at the center. This means that the shear stress is maximum at the plates and decreases linearly towards the center of the fluid layer.
Zero Value at the Center:
At the center of the fluid layer, the velocity is maximum and the velocity gradient is zero. This results in zero shear stress at the center of the fluid layer.
Conclusion:
In summary, the shear stress variation in a steady incompressible laminar flow between two infinite parallel stationary plates is linear with zero value at the center. This is because the velocity varies linearly across the fluid layer, resulting in a linear variation of shear stress.
Explanation:
In a steady incompressible laminar flow between two infinite parallel stationary plates, the fluid moves in layers parallel to the plates. This type of flow is also known as a Couette flow.
Shear Stress:
Shear stress is the force per unit area acting tangentially to the surface of the fluid. In the case of a flow between parallel plates, the shear stress is caused by the relative motion of the fluid layers.
Shear Stress Variation:
The shear stress varies across the fluid layer from the bottom plate to the top plate. The variation of shear stress can be determined using the velocity distribution of the fluid.
Linear Variation:
In a Couette flow, the velocity of the fluid varies linearly from the bottom plate to the top plate. This means that the velocity gradient, which is directly proportional to the shear stress, also varies linearly.
So, the shear stress variation is linear with zero value at the center. This means that the shear stress is maximum at the plates and decreases linearly towards the center of the fluid layer.
Zero Value at the Center:
At the center of the fluid layer, the velocity is maximum and the velocity gradient is zero. This results in zero shear stress at the center of the fluid layer.
Conclusion:
In summary, the shear stress variation in a steady incompressible laminar flow between two infinite parallel stationary plates is linear with zero value at the center. This is because the velocity varies linearly across the fluid layer, resulting in a linear variation of shear stress.
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For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation isa)linear with zero value at the platesb)linear with zero value at the centerc)quadratic with zero value at the platesd)quadratic with zero value at the centerCorrect answer is option 'B'. Can you explain this answer?
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