Fluid Dynamics Homework Question 2?

2. If the velocity field is �'⃗ = (�, �, �), with u, v, w being the velocity component in x, y, and z

directions, respectively, show that the term ∇ ∙ �'⃗ indicates the volumetric dilatation rate, that is

the fraction of volume increase per unit time. (hint: use the divergence theorem)



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