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Moving wall V Interface h₂ Fluid 2 P2. H2 h₂ Fluid 1 P1.M Question 5: Consider a modified form of Couette flow in which there are two immiscible fluids sandwiched between two infinitely long and wide, parallel flat plates. The flow is steady, incompressible, parallel, and laminar. The top plate moves at velocity V to the right, and the bottom plate is stationary. Gravity acts in the z-direction (downward in the figure). There is no forced pressure gradient pushing the fluids through the channel - the flow is set up solely by viscous effects created by the moving upper plate. You may ignore surface tension effects and assume that the interface is horizontal. The pressure at the bottom of the flow (z = 0) is equal to Po. a) List all the appropriate boundary conditions on both velocity and pressure. There are six required boundary conditions. b) Solve for the velocity field. Split up the solution into two portions, one for each fluid. Generate expressions for u₁ as a function of z and u2 as a function of z. c) Solve for the pressure field. Split up the solution. Solve for P1 and P2. d) Let fluid 1 be water and let fluid 2 be unused engine oil, both at 80°C. Also let h₁ = 5 mm, h2 = 8 mm, and V = 10 m/s. Plot u as a function of z across the entire channel. =

Moving wall V Interface h₂ Fluid 2 P2. H2 h₂ Fluid 1 P1.M Question 5: Consider a modified form of Couette flow in which there are two immiscible fluids sandwiched between two infinitely long and wide, parallel flat plates. The flow is steady, incompressible, parallel, and laminar. The top plate moves at velocity V to the right, and the bottom plate is stationary. Gravity acts in the z-direction (downward in the figure). There is no forced pressure gradient pushing the fluids through the channel - the flow is set up solely by viscous effects created by the moving upper plate. You may ignore surface tension effects and assume that the interface is horizontal. The pressure at the bottom of the flow (z = 0) is equal to Po. a) List all the appropriate boundary conditions on both velocity and pressure. There are six required boundary conditions. b) Solve for the velocity field. Split up the solution into two portions, one for each fluid. Generate expressions for u₁ as a function of z and u2 as a function of z. c) Solve for the pressure field. Split up the solution. Solve for P1 and P2. d) Let fluid 1 be water and let fluid 2 be unused engine oil, both at 80°C. Also let h₁ = 5 mm, h2 = 8 mm, and V = 10 m/s. Plot u as a function of z across the entire channel. =

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
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Moving wall V Interface h₂ Fluid 2 P2. H2 h₂ Fluid 1 P1.M Question 5: Consider a modified form of Couette flow in which there are two immiscible fluids sandwiched between two infinitely long and wide, parallel flat plates. The flow is steady, incompressible, parallel, and laminar. The top plate moves at velocity V to the right, and the bottom plate is stationary. Gravity acts in the z-direction (downward in the figure). There is no forced pressure gradient pushing the fluids through the channel - the flow is set up solely by viscous effects created by the moving upper plate. You may ignore surface tension effects and assume that the interface is horizontal. The pressure at the bottom of the flow (z = 0) is equal to Po. a) List all the appropriate boundary conditions on both velocity and pressure. There are six required boundary conditions. b) Solve for the velocity field. Split up the solution into two portions, one for each fluid. Generate expressions for u₁ as a function of z and u2 as a function of z. c) Solve for the pressure field. Split up the solution. Solve for P1 and P2. d) Let fluid 1 be water and let fluid 2 be unused engine oil, both at 80°C. Also let h₁ = 5 mm, h2 = 8 mm, and V = 10 m/s. Plot u as a function of z across the entire channel. =
Transcribed Image Text:Moving wall V Interface h₂ Fluid 2 P2. H2 h₂ Fluid 1 P1.M Question 5: Consider a modified form of Couette flow in which there are two immiscible fluids sandwiched between two infinitely long and wide, parallel flat plates. The flow is steady, incompressible, parallel, and laminar. The top plate moves at velocity V to the right, and the bottom plate is stationary. Gravity acts in the z-direction (downward in the figure). There is no forced pressure gradient pushing the fluids through the channel - the flow is set up solely by viscous effects created by the moving upper plate. You may ignore surface tension effects and assume that the interface is horizontal. The pressure at the bottom of the flow (z = 0) is equal to Po. a) List all the appropriate boundary conditions on both velocity and pressure. There are six required boundary conditions. b) Solve for the velocity field. Split up the solution into two portions, one for each fluid. Generate expressions for u₁ as a function of z and u2 as a function of z. c) Solve for the pressure field. Split up the solution. Solve for P1 and P2. d) Let fluid 1 be water and let fluid 2 be unused engine oil, both at 80°C. Also let h₁ = 5 mm, h2 = 8 mm, and V = 10 m/s. Plot u as a function of z across the entire channel. =
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