I need help on this question: Q. As a means of measuring the viscosity, a liquid is forced to flow through two very large parallel plates by applying a pressure gradient, dp/dx. You can assume that the velocity between the plates is given by (Figure1). Where μ is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates. a) Derive an expression for the shear stress acting on the top plate, τW. b) Q' is the flow rate per unit width (i.e. has units of m2/s). Express Q' in terms of τW. c) When the flow rate per unit width is Q' = 1.2 x 10-4 m2/s, the gap between the plates is 5 mm, the device estimates the shear stress at the top wall to be -0.05 Pa. Estimate the viscosity of the fluid.
I need help on this question: Q. As a means of measuring the viscosity, a liquid is forced to flow through two very large parallel plates by applying a pressure gradient, dp/dx. You can assume that the velocity between the plates is given by (Figure1). Where μ is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates. a) Derive an expression for the shear stress acting on the top plate, τW. b) Q' is the flow rate per unit width (i.e. has units of m2/s). Express Q' in terms of τW. c) When the flow rate per unit width is Q' = 1.2 x 10-4 m2/s, the gap between the plates is 5 mm, the device estimates the shear stress at the top wall to be -0.05 Pa. Estimate the viscosity of the fluid.
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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I need help on this question:
Q. As a means of measuring the viscosity, a liquid is forced to flow through two very large parallel plates by applying a pressure gradient, dp/dx. You can assume that the velocity between the plates is given by (Figure1).
Where μ is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates.
a) Derive an expression for the shear stress acting on the top plate, τW.
b) Q' is the flow rate per unit width (i.e. has units of m2/s). Express Q' in terms of τW.
c) When the flow rate per unit width is Q' = 1.2 x 10-4 m2/s, the gap between the plates is 5 mm, the device estimates the shear stress at the top wall to be -0.05 Pa. Estimate the viscosity of the fluid.
Transcribed Image Text:1 dp
-y(h-y)
2µ dx
u(y):
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