Question

Momentum is a conserved quantity for any general control volume. a)- True b)- False

Answer 1

Answer:

The given statement is false.

Explanation:

The basic equation of motion for a control volume is as follows

$\frac{d\overrightarrow{p}}{dt}=\int_{c.v}\frac{\partial }{\partial t}(\rho v)dV+\int_{cs}(\rho \overrightarrow{v})\cdot \overrightarrow{v_{r}}.\widehat{n}dS$

the symbols have the usual meaning as

$\rho$ is density of the fluid

$v$ is the velocity of the fluid

$\widehat{n}$ is the direction vector of area over which the integration is carried out

As we see that the terms in the right hand side of the equation is not zero if the flow is unsteady or the velocity is changing in the control volume the term in the left is non zero hence the momentum is not conserved.