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The shear stress between two fixed parallel plates with a laminar flow between them
- a)varies directly as distance from the mid-plane
- b)varies inversely as distance from the midplane
- c)varies parabolically across the gap
- d)remains constant across the gap
Correct answer is option 'A'. Can you explain this answer?
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The shear stress between two fixed parallel plates with a laminar flow...
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The shear stress between two fixed parallel plates with a laminar flow...
The shear stress between two fixed parallel plates with a laminar flow between them
Explanation:
When a fluid flows between two fixed parallel plates, it is called a laminar flow. In this flow, the layers of fluid slide over each other in an orderly manner, and there is no mixing or turbulence. The shear stress is the force per unit area that acts tangentially to the flow direction, causing the fluid layers to slide over each other.
Shear stress variation
The shear stress between two fixed parallel plates with a laminar flow between them varies directly as the distance from the mid-plane. This means that as we move away from the mid-plane towards the top or bottom plate, the shear stress increases or decreases proportionally.
Reasoning:
1. In a laminar flow, the velocity of fluid near the mid-plane is maximum, and it decreases towards the top and bottom plates due to the no-slip condition at the walls.
2. According to Newton's law of viscosity, the shear stress is directly proportional to the velocity gradient.
3. The velocity gradient is the change in velocity with respect to the distance from the mid-plane.
4. As we move away from the mid-plane towards the top or bottom plate, the velocity gradient increases, resulting in a higher shear stress.
5. Conversely, as we move closer to the mid-plane, the velocity gradient decreases, leading to a lower shear stress.
Conclusion:
Therefore, the shear stress between two fixed parallel plates with a laminar flow between them varies directly as the distance from the mid-plane. This variation is a result of the velocity gradient in the flow, where the shear stress is higher near the top and bottom plates and lower near the mid-plane.
Explanation:
When a fluid flows between two fixed parallel plates, it is called a laminar flow. In this flow, the layers of fluid slide over each other in an orderly manner, and there is no mixing or turbulence. The shear stress is the force per unit area that acts tangentially to the flow direction, causing the fluid layers to slide over each other.
Shear stress variation
The shear stress between two fixed parallel plates with a laminar flow between them varies directly as the distance from the mid-plane. This means that as we move away from the mid-plane towards the top or bottom plate, the shear stress increases or decreases proportionally.
Reasoning:
1. In a laminar flow, the velocity of fluid near the mid-plane is maximum, and it decreases towards the top and bottom plates due to the no-slip condition at the walls.
2. According to Newton's law of viscosity, the shear stress is directly proportional to the velocity gradient.
3. The velocity gradient is the change in velocity with respect to the distance from the mid-plane.
4. As we move away from the mid-plane towards the top or bottom plate, the velocity gradient increases, resulting in a higher shear stress.
5. Conversely, as we move closer to the mid-plane, the velocity gradient decreases, leading to a lower shear stress.
Conclusion:
Therefore, the shear stress between two fixed parallel plates with a laminar flow between them varies directly as the distance from the mid-plane. This variation is a result of the velocity gradient in the flow, where the shear stress is higher near the top and bottom plates and lower near the mid-plane.
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The shear stress between two fixed parallel plates with a laminar flow between thema)varies directly as distance from the mid-planeb)varies inversely as distance from the midplanec)varies parabolically across the gapd)remains constant across the gapCorrect answer is option 'A'. Can you explain this answer?
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