Newton's Second Law of Motion

Newton's second law is the next one to be imposed upon fluid motion. It is known that the rate of change of momentum is proportional to the applied force. If F is the force upon a system,

$$F~=~{{dM} \over {dt}}$$ (3.9)

where M is the linear momentum. Further,

$$M~=~\int_{system} V dm~=~\int_{system} V \rho d \forall$$ (3.10)

It is to be realised that momentum M and velocity V are vectors and each of a component in each of the coordinate directions. Accordingly, Eq. 3.10 represents three equations.

The form of this equation holds good for angular momentum. If a torque T acts upon the system. We have,

$$T~ =~{{dH} \over {dt}}$$ (3.11)

$$~~H~=~\int_{system} (r\times V)\delta m = \int_{system} (r \times V) \rho d \forall$$

which again is a vector equation. Torque T can be due to body forces and/or surface forces. In addition there can also be torque directly introduced into the system such as that through a mechanical shaft connected to the system.