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Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates (Figure 4). The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is h, and gravity acts in the negative z-direction. There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. a) Find the velocity distribution, b) Draw the velocity profile for fully developed region of flow, c) Calculate the maximum velocity and the average velocity, d) Estimate the shear force per unit area acting on the bottom plate. Note: You can solve this question either by writing shell momentum balance or by using the Navier Stokes equations.

Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates (Figure 4). The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is h, and gravity acts in the negative z-direction. There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. a) Find the velocity distribution, b) Draw the velocity profile for fully developed region of flow, c) Calculate the maximum velocity and the average velocity, d) Estimate the shear force per unit area acting on the bottom plate. Note: You can solve this question either by writing shell momentum balance or by using the Navier Stokes equations.

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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gap between two infinite parallel plates (Figure 4). The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is h, and gravity acts in the negative z-direction. There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. a) Find the velocity distribution, b) Draw the velocity profile for fully developed region of flow, c) Calculate the maximum velocity and the average velocity, d) Estimate the shear force per unit area acting on the bottom plate. Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow Note: You can solve this question either by writing shell momentum balance or by using the Navier Stokes equations. Moving plate Fluid: p, µ Fixed plate Figure 4. Incompressible Flow Continuity Equation: др : (pv.) = 0 dy 0 = ('ad) + ("ad ne + "'ad) *e at Incompressible Flow Navier-Stokes Equations in Cartesian Coordinates: др + Vz at + Vy ax + vz az az? ax de ду + P8y az + Vz Jz + vy dx at ap + Os ax at + Vz + Oy ay + P8z az az az
Transcribed Image Text:gap between two infinite parallel plates (Figure 4). The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is h, and gravity acts in the negative z-direction. There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. a) Find the velocity distribution, b) Draw the velocity profile for fully developed region of flow, c) Calculate the maximum velocity and the average velocity, d) Estimate the shear force per unit area acting on the bottom plate. Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow Note: You can solve this question either by writing shell momentum balance or by using the Navier Stokes equations. Moving plate Fluid: p, µ Fixed plate Figure 4. Incompressible Flow Continuity Equation: др : (pv.) = 0 dy 0 = ('ad) + ("ad ne + "'ad) *e at Incompressible Flow Navier-Stokes Equations in Cartesian Coordinates: др + Vz at + Vy ax + vz az az? ax de ду + P8y az + Vz Jz + vy dx at ap + Os ax at + Vz + Oy ay + P8z az az az
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