Consider the general form of the Reynolds transport theorem (RTT) given by

where is the velocity of the fluid relative to the control surface. Let Bsys be the mass m of a system of fluid particles. We know that for a system, dmldt =0 since no mass can enter or leave the system by definition. Use the given equation to derive the equation of conservation of mass for a control volume.

ANSWER:

Step 1:-

The continuity equation is,

From here we can deduce the mass flow rate from a section of area A of control volume system is,

Where is the mass flow rate.

Step 2:-

This implies,

Now,