Chapter 7, Problem 21P

In Chap. 4, we defined the material acceleration, which is the acceleration following a fluid particle,
$\stackrel{\to }{a}\left(x,y,z,t\right)=\frac{\partial \stackrel{\to }{V}}{\partial t}+\left(\stackrel{\to }{V}.\stackrel{\to }{\nabla }\right)\stackrel{\to }{V}$

(a) That are the primary dimensions of the gradient operator $\stackrel{\to }{\nabla }$ ? (b) Verify that each additive term in the equation has the same dimensions.

Answers: (a) $\left\{{\text{L}}^{-1}\right\}$ ; (b) $\left\{{\text{L}}^{\text{1}}{\text{t}}^{\text{-2}}\right\}$