Chapter 3, Problem 3.1P

To determine

By discussing three different forms of Newton’s second law (the linear momentum relation).

Answer to Problem 3.1P

All the equations are valid and equivalent for constant mass systems.

Explanation of Solution

Given information:

Three forms of Newton’s second law i.e.

1. ${\displaystyle \sum F=ma}$
2. ${\displaystyle \sum F=\frac{d}{dt}}\left(mv\right)$
3. ${\displaystyle \sum F=\frac{d}{dt}\left({\displaystyle \underset{system}{\int }v\rho {\text{d}}^{\circ }v}\right)}$

For a constant mass system, all the three forms of the equation are valid and equivalent. All the given forms of equation can be used in certain fluid problems. The first form can be used for small elements and mostly used in solid mechanics. The second form can be used in rocket propulsion. The third form is most suitable for fluid mechanics as opposed to solid mechanics and can be used in control volume analysis such as force analysis in the pipe bend, impact of the jet on a plane surface and force due to flow around a curved vane.

Conclusion:

Thus, all the three forms of the equation are valid and equivalent for a constant mass system.