Example Problem - Flow between parallel plates (a cell-culture flow chamber?) Consider a steady viscous flow between two stationary plates separated by a height H, and with ar ӘР applied pressure gradient, = A. Assume that the plates have a width b. Əx Neglect the effect of gravity. a) b) c) ди Assume fully developed flow, i.e. the velocity profile is independent of x ( əx Assume incompressibility. Determine the velocity profile in the system. y=+H/₂ ////// ди b) Determine the shear stress t = μ on the bottom wall as a function of Q. Əy 2) Complete the Couette Flow problem at the end of notes 14, = 0) // 1) Using the example problem from Notes 14: a) Derive a formula for the flow rate Q for a channel of height H, width W, length L and a pressure difference AP U=O
Example Problem - Flow between parallel plates (a cell-culture flow chamber?) Consider a steady viscous flow between two stationary plates separated by a height H, and with ar ӘР applied pressure gradient, = A. Assume that the plates have a width b. Əx Neglect the effect of gravity. a) b) c) ди Assume fully developed flow, i.e. the velocity profile is independent of x ( əx Assume incompressibility. Determine the velocity profile in the system. y=+H/₂ ////// ди b) Determine the shear stress t = μ on the bottom wall as a function of Q. Əy 2) Complete the Couette Flow problem at the end of notes 14, = 0) // 1) Using the example problem from Notes 14: a) Derive a formula for the flow rate Q for a channel of height H, width W, length L and a pressure difference AP U=O
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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Transcribed Image Text:Example Problem - Flow between parallel plates (a cell-culture flow chamber?)
Consider a steady viscous flow between two stationary plates separated by a height H, and with ar
ӘР
applied pressure gradient, -= A. Assume that the plates have a width b.
əx
Neglect the effect of gravity.
a)
b)
ди
Assume fully developed flow, i.e. the velocity profile is independent of x (
Əx
Assume incompressibility.
Determine the velocity profile in the system.
y=+H/₂2
//
du
b) Determine the shear stress T = μ on the bottom wall as a function of Q.
ду
2) Complete the Couette Flow problem at the end of notes 14,
= 0)
1) Using the example problem from Notes 14:
a) Derive a formula for the flow rate Q for a channel of height H, width W, length L and a
pressure difference AP
=
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Step 1: Determine the velocity profile in the system, Example problem, and the Couette flow problem.
VIEWStep 2: find the velocity profile in the system.
VIEWStep 3: find the formula for the flow rate Q and, the shear stress on the bottom wall as a function of Q.
VIEWStep 4: find the Couette flow problem
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