Consider the following three-dimensional velocity vector: V = 4xy² i + fj- z²y² k a) Find the appropriate form of the function f such that the velocity vector represents a physical incompressible flow. b) What is the stream function for this flow? c) Write down the expression for the velocity potential along the plane z = 0.

Consider the following three-dimensional velocity vector: V = 4xy² i + fj- z²y² k a) Find the appropriate form of the function f such that the velocity vector represents a physical incompressible flow. b) What is the stream function for this flow? c) Write down the expression for the velocity potential along the plane z = 0.

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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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

Consider the following three-dimensional velocity vector:
V = 4xy² i + fj- z²y² k
a) Find the appropriate form of the function f such that the velocity vector
represents a physical incompressible flow.
b) What is the stream function for this flow?
c) Write down the expression for the velocity potential along the plane z = 0.

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