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For laminar flow between two fixed parallel plates, the flow velocity
- a)is constant over the cross-section
- b)varies parabolically across the section
- c)varies as three-halves power of distance from the mid-point
- d)is maximum at the center, zero at the plates and the variation in between is linear
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
For laminar flow between two fixed parallel plates, the flow velocitya...
Explanation:
When a fluid flows between two fixed parallel plates, it is called a planar, or two-dimensional, Poiseuille flow. In this type of flow, the fluid velocity varies across the channel, and can be described by the Navier-Stokes equation.
Velocity Profile:
The velocity of the fluid varies across the channel, with the maximum velocity at the center of the channel and zero velocity at the plates. The velocity profile is parabolic in shape, with the velocity increasing linearly from the plate to the center of the channel, and then decreasing linearly to the other plate. The velocity profile can be described by the Hagen-Poiseuille equation:
u(y) = (1/2μ) * (dp/dx) * (h^2/4 - y^2)
where u(y) is the velocity at a distance y from the center of the channel, μ is the fluid viscosity, dp/dx is the pressure gradient, h is the distance between the plates, and y ranges from -h/2 to h/2.
Reynolds Number:
The flow regime in planar Poiseuille flow is laminar, meaning that the fluid flows in smooth, parallel layers. The Reynolds number, which describes the ratio of inertial forces to viscous forces in the fluid, is low in laminar flow. The critical Reynolds number for planar Poiseuille flow is approximately 2300.
Applications:
Planar Poiseuille flow is used in microfluidics for applications such as drug delivery, DNA analysis, and lab-on-a-chip devices. The parabolic velocity profile allows for precise control of fluid flow and mixing, making it useful for these types of applications.
When a fluid flows between two fixed parallel plates, it is called a planar, or two-dimensional, Poiseuille flow. In this type of flow, the fluid velocity varies across the channel, and can be described by the Navier-Stokes equation.
Velocity Profile:
The velocity of the fluid varies across the channel, with the maximum velocity at the center of the channel and zero velocity at the plates. The velocity profile is parabolic in shape, with the velocity increasing linearly from the plate to the center of the channel, and then decreasing linearly to the other plate. The velocity profile can be described by the Hagen-Poiseuille equation:
u(y) = (1/2μ) * (dp/dx) * (h^2/4 - y^2)
where u(y) is the velocity at a distance y from the center of the channel, μ is the fluid viscosity, dp/dx is the pressure gradient, h is the distance between the plates, and y ranges from -h/2 to h/2.
Reynolds Number:
The flow regime in planar Poiseuille flow is laminar, meaning that the fluid flows in smooth, parallel layers. The Reynolds number, which describes the ratio of inertial forces to viscous forces in the fluid, is low in laminar flow. The critical Reynolds number for planar Poiseuille flow is approximately 2300.
Applications:
Planar Poiseuille flow is used in microfluidics for applications such as drug delivery, DNA analysis, and lab-on-a-chip devices. The parabolic velocity profile allows for precise control of fluid flow and mixing, making it useful for these types of applications.
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Community Answer
For laminar flow between two fixed parallel plates, the flow velocitya...
B is right answer.
flow velocity profile-
v is directly proportional hota hai r square.
flow velocity profile-
v is directly proportional hota hai r square.
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For laminar flow between two fixed parallel plates, the flow velocitya)is constant over the cross-sectionb)varies parabolically across the sectionc)varies as three-halves power of distance from the mid-pointd)is maximum at the center, zero at the plates and the variation in between is linearCorrect answer is option 'B'. Can you explain this answer?
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