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The velocity distribution for flow between two fixed parallel plates:
- a)Is constant over the cross-section
- b)Is zero at the plates and increases linearly to the midplane
- c)Varies parabolically across the section
- d)Is zero in the middle and increase linearly towards the plates
Correct answer is option 'C'. Can you explain this answer?
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The velocity distribution for flow between two fixed parallel plates:...
The velocity distribution across a section of two fixed parallel plates is parabolically given by
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Where ∂P/∂x = pressure gradient along the length of the plate
y = point of consideration from the lower fixed plate
t = distance between the two fixed parallel plates
Velocity distribution and Shear stress distribution
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The velocity distribution for flow between two fixed parallel plates:...
Explanation:
The velocity distribution for flow between two fixed parallel plates is known as the Hagen-Poiseuille flow. It is a laminar flow in which the fluid moves in parallel layers, with no disruption between the layers.
Parabolic Velocity Distribution:
The correct answer is option 'C' which states that the velocity distribution varies parabolically across the section. This is because the velocity of the fluid at any point between the two plates is proportional to the distance from the center of the channel. This means that the velocity is highest at the center of the channel and decreases towards the walls. The velocity distribution can be represented mathematically as:
u(y) = (P/2μL) * [(h^2/4) - y^2]
Where u(y) is the velocity at a distance y from the center of the channel, P is the pressure difference between the two ends of the channel, μ is the viscosity of the fluid, L is the length of the channel, and h is the height of the channel.
The velocity distribution follows a parabolic curve because the fluid is incompressible and its velocity must be zero at the walls of the channel. This is known as the "no-slip" condition, which states that the fluid in contact with a solid surface will have zero velocity relative to that surface.
Conclusion:
In conclusion, the velocity distribution for flow between two fixed parallel plates varies parabolically across the section. This is due to the no-slip condition at the walls of the channel, which causes the velocity to be highest at the center and decrease towards the walls.
The velocity distribution for flow between two fixed parallel plates is known as the Hagen-Poiseuille flow. It is a laminar flow in which the fluid moves in parallel layers, with no disruption between the layers.
Parabolic Velocity Distribution:
The correct answer is option 'C' which states that the velocity distribution varies parabolically across the section. This is because the velocity of the fluid at any point between the two plates is proportional to the distance from the center of the channel. This means that the velocity is highest at the center of the channel and decreases towards the walls. The velocity distribution can be represented mathematically as:
u(y) = (P/2μL) * [(h^2/4) - y^2]
Where u(y) is the velocity at a distance y from the center of the channel, P is the pressure difference between the two ends of the channel, μ is the viscosity of the fluid, L is the length of the channel, and h is the height of the channel.
The velocity distribution follows a parabolic curve because the fluid is incompressible and its velocity must be zero at the walls of the channel. This is known as the "no-slip" condition, which states that the fluid in contact with a solid surface will have zero velocity relative to that surface.
Conclusion:
In conclusion, the velocity distribution for flow between two fixed parallel plates varies parabolically across the section. This is due to the no-slip condition at the walls of the channel, which causes the velocity to be highest at the center and decrease towards the walls.
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The velocity distribution for flow between two fixed parallel plates:a)Is constant over the cross-sectionb)Is zero at the plates and increases linearly to the midplanec)Varies parabolically across the sectiond)Is zero in the middle and increase linearly towards the platesCorrect answer is option 'C'. Can you explain this answer?
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