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The shear stress distribution for a fluid flowing in between the parallel plates, both at rest, is
- a)constant over the cross section
- b)parabolic distribution across the section
- c)zero at the mid plane and varies linearly with distance from mid plane
- d)zero at plates and increases linearly to midpoint
Correct answer is option 'C'. Can you explain this answer?
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The shear stress distribution for a fluid flowing in between the paral...
Shear stress distribution between the parallel plates is given by,
It has same maximum value at either boundary and decreases linearly to zero at the mid plane.
It has same maximum value at either boundary and decreases linearly to zero at the mid plane.
Most Upvoted Answer
The shear stress distribution for a fluid flowing in between the paral...
Shear stress is the force per unit area acting tangentially to a surface. In the case of a fluid flowing between parallel plates, both at rest, the shear stress distribution is given by the equation:
τ = μ(du/dy)
Where τ is the shear stress, μ is the dynamic viscosity of the fluid, and du/dy is the velocity gradient perpendicular to the flow direction.
Zero at the Midplane:
In this case, the fluid is flowing in a laminar flow regime, which means that the fluid layers move parallel to each other with no mixing. Since the fluid is at rest at both plates, the velocity gradient is highest at the midplane and decreases towards the plates. As a result, the shear stress is zero at the midplane.
Varying Linearly with Distance from Midplane:
As the fluid layers move away from the midplane towards the plates, the velocity gradient decreases. This means that the shear stress increases with increasing distance from the midplane. The relationship between shear stress and distance from the midplane is linear.
Explanation:
The reason for the linear variation of shear stress with distance from the midplane can be understood by considering the velocity profile of the fluid flow. The flow velocity is highest at the center of the channel (midplane) and decreases towards the plates. This velocity profile is parabolic in shape, with the highest velocity at the center and zero velocity at the plates.
Since shear stress is directly proportional to the velocity gradient, the shear stress is highest at the midplane where the velocity gradient is highest and decreases towards the plates where the velocity gradient is zero. This results in a linear variation of shear stress with distance from the midplane.
Conclusion:
In summary, the shear stress distribution for a fluid flowing between parallel plates, both at rest, is zero at the midplane and varies linearly with distance from the midplane. This is due to the parabolic velocity profile of the fluid flow, with the highest velocity at the center and zero velocity at the plates.
τ = μ(du/dy)
Where τ is the shear stress, μ is the dynamic viscosity of the fluid, and du/dy is the velocity gradient perpendicular to the flow direction.
Zero at the Midplane:
In this case, the fluid is flowing in a laminar flow regime, which means that the fluid layers move parallel to each other with no mixing. Since the fluid is at rest at both plates, the velocity gradient is highest at the midplane and decreases towards the plates. As a result, the shear stress is zero at the midplane.
Varying Linearly with Distance from Midplane:
As the fluid layers move away from the midplane towards the plates, the velocity gradient decreases. This means that the shear stress increases with increasing distance from the midplane. The relationship between shear stress and distance from the midplane is linear.
Explanation:
The reason for the linear variation of shear stress with distance from the midplane can be understood by considering the velocity profile of the fluid flow. The flow velocity is highest at the center of the channel (midplane) and decreases towards the plates. This velocity profile is parabolic in shape, with the highest velocity at the center and zero velocity at the plates.
Since shear stress is directly proportional to the velocity gradient, the shear stress is highest at the midplane where the velocity gradient is highest and decreases towards the plates where the velocity gradient is zero. This results in a linear variation of shear stress with distance from the midplane.
Conclusion:
In summary, the shear stress distribution for a fluid flowing between parallel plates, both at rest, is zero at the midplane and varies linearly with distance from the midplane. This is due to the parabolic velocity profile of the fluid flow, with the highest velocity at the center and zero velocity at the plates.
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The shear stress distribution for a fluid flowing in between the parallel plates, both at rest, isa)constant over the cross sectionb)parabolic distribution across the sectionc)zero at the mid plane and varies linearly with distance from mid planed)zero at plates and increases linearly to midpointCorrect answer is option 'C'. Can you explain this answer?
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