Newton's second law is the foundation for the differential equation of conservation of linear momentum (to be discussed in Chap. 9). In terms of the material acceleration following a fluid particle (Fig. P7–23), we write Newton's second law as follows:

Or, dividing both sides by the mass m of the fluid particle, \frac{\dot{F}}{m}=\frac{\partial \dot{V}}{\partial t}+(\vec{V} \cdot \vec{V}) \vec{V} Write the primary dimensions of each additive term in the (second) equation, and verify that the equation is dimensionally homogeneous. Show all your work.