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Calculating Rates of Strain, Vorticity and Dilation of Flows

Calculate the rates of strain, vorticity, and rates of dilatation for 3 flows.

a) u=cx, v=cy, w=-2cz

b) u=c, v=w=0

c) u=2cy, v=w=0

Solution Preview

a)
S11 = du/dx = c
S22 = dv/dy = c
S33 = dw/dz = -2c
S12 = 1/2(du/dy + dv/dx) = 0
S13 = 1/2(du/dz + dw/dx) = 0
S23 = 1/2(dv/dz + dw/dy) = 0
Omega1 = dw/dy - dv/dz = 0
Omega2 = du/dz - dw/dx = ...

Solution Summary

The answer includes several finished equations for each part of the question.

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