Calculating rates of strain, vorticity, and rate of dilatation for 3 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

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...Omega2 = dv/dx - du/dy = 0
DilRate = Sii = S11 + S22 + S33 = c + c - 2c = 0

b)
S11 = du/dx = 0
S22 = dv/dy = 0
S33 = dw/dz = 0
S12 = 1/2(du/dy + dv/dx) = 0
S13 = 1/2(du/dz + dw/dx) = 0
S23 = ...