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Consider the three-dimensional function þ(x,y,z) = Axy (4.a) Compute the velocity of a fluid given by grad(4). (4.b) Is this result a plausible velocity field for an incompressible fluid? (4.c) What is the vorticity of the fluid with this velocity field?

Consider the three-dimensional function þ(x,y,z) = Axy (4.a) Compute the velocity of a fluid given by grad(4). (4.b) Is this result a plausible velocity field for an incompressible fluid? (4.c) What is the vorticity of the fluid with this velocity field?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
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Consider the three-dimensional function φ(x, y, z) = Axy (4.a) Compute the velocity of a fluid given by grad(φ). (4.b) Is this result a plausible velocity field for an incompressible fluid? (4.c) What is the vorticity of the fluid with this velocity field?
Transcribed Image Text:Consider the three-dimensional function φ(x, y, z) = Axy (4.a) Compute the velocity of a fluid given by grad(φ). (4.b) Is this result a plausible velocity field for an incompressible fluid? (4.c) What is the vorticity of the fluid with this velocity field?
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Answer

ϕ(x,y,z)= Axy

4.a  The velocity of a fluid 

u= -∂ϕ∂x

v = -∂ϕ∂y

Where u and v are components of velocity in x and y-direction.

u= -Ay

v= -Ax

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