Chapter 5, Problem 1CP

Does the amount of mass entering a control volume have to be equal to the amount of mass leaving during an unsteady-flow process?

To determine

Whether the amount of mass entering a control volume have to be equal to the amount of mass leaving during an unsteady-flow process or not.

Explanation of Solution

Write the equation for mass balance

  ${\dot{m}}_{in}-{\dot{m}}_{out}=\frac{d{m}_{cv}}{dt}$  .......(I)

Here, mass entering the control volume is ${\dot{m}}_{in}$, mass leaving the control volume is ${\dot{m}}_{out},$ and rate of change of mass contained in the control volume is $\frac{d{m}_{cv}}{dt}$.

For unsteady flow process rate of change of mass of control volume is zero.

  $\frac{d{m}_{cv}}{dt}\ne 0\text{kg}/\text{sec}$

Substitute 0 for $\frac{d{m}_{cv}}{dt}$ in Equation (I).

  $\begin{array}{l}{\dot{m}}_{in}-{\dot{m}}_{out}\ne 0\\ {\dot{m}}_{in}\ne {\dot{m}}_{out}\end{array}$

Thus the mass entering the control volume is not equal to the mass leaving the control volume for unsteady flow process.