4. Show that v= 3xi+ (t- 6xy)j is a possible fluid velocity for two-dimensionalunsteady flow of a homogeneous incompressible fluid. Hence, find the pressurep(x, y,t) at any point of the fluid using Euler's equation of motion given that the bodyforce per unit mass is F = 6 yi+18x yj.

GivenV=3x2i+t-6xyjandF=6yti+18x2yj

4. Show that v = 3xi+ (t- 6xy)j is a possible fluid velocity fo unsteady flow of a homogeneous incompressible fluid. Hence, p(x, y,t) at any point of the fluid using Euler's equation of motion force per unit mass is F = 6 yi +18x yj. %3D

4. Show that v = 3xi+ (t- 6xy)j is a possible fluid velocity fo unsteady flow of a homogeneous incompressible fluid. Hence, p(x, y,t) at any point of the fluid using Euler's equation of motion force per unit mass is F = 6 yi +18x yj. %3D

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.

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4. Show that v= 3xi+ (t- 6xy)j is a possible fluid velocity for two-dimensional
unsteady flow of a homogeneous incompressible fluid. Hence, find the pressure
p(x, y,t) at any point of the fluid using Euler's equation of motion given that the body
force per unit mass is F = 6 yi+18x yj.

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