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.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
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Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.3P: Evaluate the Nusselt number for flow over a sphere for the following conditions: D=0.15m,k=0.2W/mK,...
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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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