A flow develops between two parallel plates, each of area (A). The plates are separated by a gap (H) with the lower plate always fixed. The flow can be generated by imposing a constant positive pressure drop (AP/L) and/or moving the upper plate at a constant velocity UT. The general expression of the velocity in the x-direction is: only 1 ΔΡ. -(Hy-y²) + sgn U₁ 2μ L In the above equation μ is the fluid viscosity, and sgn=+1 if the upper plate is pulled in the positive x- direction while sgn=-1 if the upper plate is pulled in the negative x-direction. (1) Determine the expression of the drag force on the lower fixed plate in each of the following cases: Case1: Flow is driven by the moving upper plate and there is no pressure drop (AP/L =0). Case2: The flow is driven by the pressure drop but the upper plate is also fixed (UT =0) Case3: Both the pressure drop and moving upper plate are responsible for the flow. (2) Which one of the above three cases leads to the largest drag force? u(y) = bart-2 y H

A flow develops between two parallel plates, each of area (A). The plates are separated by a gap (H) with the lower plate always fixed. The flow can be generated by imposing a constant positive pressure drop (AP/L) and/or moving the upper plate at a constant velocity UT. The general expression of the velocity in the x-direction is: only 1 ΔΡ. -(Hy-y²) + sgn U₁ 2μ L In the above equation μ is the fluid viscosity, and sgn=+1 if the upper plate is pulled in the positive x- direction while sgn=-1 if the upper plate is pulled in the negative x-direction. (1) Determine the expression of the drag force on the lower fixed plate in each of the following cases: Case1: Flow is driven by the moving upper plate and there is no pressure drop (AP/L =0). Case2: The flow is driven by the pressure drop but the upper plate is also fixed (UT =0) Case3: Both the pressure drop and moving upper plate are responsible for the flow. (2) Which one of the above three cases leads to the largest drag force? u(y) = bart-2 y H

Name: Problem5A flow develops between two parallel plates, each of area (A)
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Description: Problem5A flow develops between two parallel plates, each of area (A). The plates are separated by a gap(H) with the lower plate always fixed. The flow can be generated by imposing a constant positivepressure drop (AP/L) and/or moving the upper plat

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Problem5
A flow develops between two parallel plates, each of area (A). The plates are separated by a gap
(H) with the lower plate always fixed. The flow can be generated by imposing a constant positive
pressure drop (AP/L) and/or moving the upper plate at a constant velocity UT. The general
expression of the velocity in the x-direction is:
only part 2
1 ΔΡ
u(y) =
2μ L
In the above equation u is the fluid viscosity, and sgn=+1 if the upper plate is pulled in the positive x-
direction while sgn=-1 if the upper plate is pulled in the negative x-direction.
(1) Determine the expression of the drag force on the lower fixed plate in each of the following cases:
Case1: Flow is driven by the moving upper plate and there is no pressure drop (AP/L =0).
Case2: The flow is driven by the pressure drop but the upper plate is also fixed (UT =0)
Case3: Both the pressure drop and moving upper plate are responsible for the flow.
(2) Which one of the above three cases leads to the largest drag force?
(Hy-y²) + sgn U₁
y
H

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