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A fluid motion is given by V=(y+z)i+(z+x)j+(x+y)k. Is this motion irrotational? If the velocity potential is and V =Vo, then prove that c= yz +a %3D

A fluid motion is given by V=(y+z)i+(z+x)j+(x+y)k. Is this motion irrotational? If the velocity potential is and V =Vo, then prove that c= yz +a %3D

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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a) A fluid motion is given by ▼=(y+z)i+(z+x)j+(x+y)k. Is this motion irrotational? If the velocity potential is ø and V=Vø, then prove that c= yz+a where a is a constant.
Transcribed Image Text:a) A fluid motion is given by ▼=(y+z)i+(z+x)j+(x+y)k. Is this motion irrotational? If the velocity potential is ø and V=Vø, then prove that c= yz+a where a is a constant.
b) Evaluate the surface integral of the vector field F(x, y,z)=(2ry, 8xz, 4yz) using Divergence Theorem. Given S is the surface of tetrahedron with vertices 0(0,0,0), A(1,0,0), B(0,1,0) and C(0,0,1).
Transcribed Image Text:b) Evaluate the surface integral of the vector field F(x, y,z)=(2ry, 8xz, 4yz) using Divergence Theorem. Given S is the surface of tetrahedron with vertices 0(0,0,0), A(1,0,0), B(0,1,0) and C(0,0,1).
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