A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X10-5 N.s/m². Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). 0= b. Flow shear stress is governed by the following equation du t=μ= Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in terms of the pressure gradient when the shear stress at the bottom plate is zero.

A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X10-5 N.s/m². Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). 0= b. Flow shear stress is governed by the following equation du t=μ= Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in terms of the pressure gradient when the shear stress at the bottom plate is zero.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

1.
A fluid is bounded by two parallel plates of infinite width and length as shown
in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is
fixed. The fluid's dynamic viscosity is 1.85X105 N.s/m?. Assume Couette
flow with pressure gradient, = 0.1 N/m³.
a. Propose the discretization method to solve Couette flow equation with
pressure gradient below. Let the number of nodes, n = 9, the distance
between the nodes is 0.05 m. Obtain the velocity of all the internal nodes
using the matrix inversion method and the iterative method. Compare
the results and the effectiveness of both methods (in terms of calculation
effort and ease of setting up the problem).
+
b. Flow shear stress is governed by the following equation
ôu
Propose the discretization method to solve the above equation and
calculate the shear stress at node 1. Describe the condition in tems of
the pressure gradient when the shear stress at the bottom plate is zero.
Moving plate at Um/s
N=
N-1
`Fixed plate
FIGURE Q1

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