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Consider a steady two-dimensional steady viscous incompressible flow between two infinitely large parallel plates (Figure QA2). Assume the top plate is moving to the right at a constant speed U₁ +h -h YA U U₁ Top Plate X -(1+ 1- 2 h Fluid (P. μ) Bottom Plate Figure QA2 a) If the pressure gradient in the direction of flow is dp By making reasonal assumptions, solve the dx conservation equations and show that the velocity distribution between the two plate can be expressed as: h² dp Uιμ dx 2h -(1-²) b) Assume U₁ =10m/s, h=200 mm, u=1.0x 10-³Ns/m², the wall shear stress at y =th. What is the power requirement to drag the top plate at this speed? dP dx = 0.50 N/m² m Calculate d) Do you expect to have a flow reversal in any part of the flow? If yes, would it occur close to the top plate or bottom plate? Explain.

Consider a steady two-dimensional steady viscous incompressible flow between two infinitely large parallel plates (Figure QA2). Assume the top plate is moving to the right at a constant speed U₁ +h -h YA U U₁ Top Plate X -(1+ 1- 2 h Fluid (P. μ) Bottom Plate Figure QA2 a) If the pressure gradient in the direction of flow is dp By making reasonal assumptions, solve the dx conservation equations and show that the velocity distribution between the two plate can be expressed as: h² dp Uιμ dx 2h -(1-²) b) Assume U₁ =10m/s, h=200 mm, u=1.0x 10-³Ns/m², the wall shear stress at y =th. What is the power requirement to drag the top plate at this speed? dP dx = 0.50 N/m² m Calculate d) Do you expect to have a flow reversal in any part of the flow? If yes, would it occur close to the top plate or bottom plate? Explain.

Elements Of Electromagnetics
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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Question A2 Consider a steady two-dimensional steady viscous incompressible flow between two infinitely large parallel plates (Figure QA2). Assume the top plate is moving to the right at a constant speed U₁. +h -h YA U1 1 Top Plate (1+ X dp a) If the pressure gradient in the direction of flow is h² Fluid (P.) Bottom Plate dp h Uιμ dx Figure QA2 conservation equations and show that the velocity distribution between the two plate can be expressed as: -2) dx 2h By making reasonal assumptions, solve the b) Assume U₁ =10m/s, h=200 mm, μ = 1.0x 10-3³ Ns/m², dP dx the wall shear stress at y = th. U₁ What is the power requirement to drag the top plate at this speed? = 0.50 N/m² m Calculate (d) Do you expect to have a flow reversal in any part of the flow? If yes, would it occur close to the top plate or bottom plate? Explain.
Transcribed Image Text:Question A2 Consider a steady two-dimensional steady viscous incompressible flow between two infinitely large parallel plates (Figure QA2). Assume the top plate is moving to the right at a constant speed U₁. +h -h YA U1 1 Top Plate (1+ X dp a) If the pressure gradient in the direction of flow is h² Fluid (P.) Bottom Plate dp h Uιμ dx Figure QA2 conservation equations and show that the velocity distribution between the two plate can be expressed as: -2) dx 2h By making reasonal assumptions, solve the b) Assume U₁ =10m/s, h=200 mm, μ = 1.0x 10-3³ Ns/m², dP dx the wall shear stress at y = th. U₁ What is the power requirement to drag the top plate at this speed? = 0.50 N/m² m Calculate (d) Do you expect to have a flow reversal in any part of the flow? If yes, would it occur close to the top plate or bottom plate? Explain.
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