An incompressible fluid flows between two flat plates, driven by a constant pressure gradient, dP/dx, and the constant motion of one of the plates, with speed, U. The spacing between the plates is b and the viscosity of the fluid is u. Define a coordinate system where -b/2

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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An incompressible fluid flows between two flat plates, driven by a constant pressure
gradient, dP/dx, and the constant motion of one of the plates, with speed, U. The spacing
between the plates is b and the viscosity of the fluid is µu. Define a coordinate system
where -b/2 < y< b/2 (y = 0 midway between the plates).
a. What is the Navier-Stokes equation for x-direction momentum for parallel flow.
b. What are the boundary conditions for this case?
c. Solve for the x-direction velocity profile between the plates, u(y).
d. Integrate to show that the relationship between the volume flow rate (per unit
width of the plate), the speed of the plate and the pressure gradient is given by:
dP
b3
+ U
12µ
2
b
Transcribed Image Text:An incompressible fluid flows between two flat plates, driven by a constant pressure gradient, dP/dx, and the constant motion of one of the plates, with speed, U. The spacing between the plates is b and the viscosity of the fluid is µu. Define a coordinate system where -b/2 < y< b/2 (y = 0 midway between the plates). a. What is the Navier-Stokes equation for x-direction momentum for parallel flow. b. What are the boundary conditions for this case? c. Solve for the x-direction velocity profile between the plates, u(y). d. Integrate to show that the relationship between the volume flow rate (per unit width of the plate), the speed of the plate and the pressure gradient is given by: dP b3 + U 12µ 2 b
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