Equation Of Continuity - Practice Questions & MCQ

It is applied when fluid is an ideal fluid. (means fluid is Incompressible and Non-viscous)

The equation of continuity is derived from the principle of conservation of mass.

Have a look at the flow of ideal fluid through the tube AB.

For the above figure 

Let Mass of the liquid entering per second at $\mathrm{A}=\dot{M}_A$
And Mass of the liquid leaving per second at $\mathrm{B}=\dot{M}_B$
From Mass conservation law we can write

$$
\dot{M}_A=\dot{M}_B
$$

If the cross-sectional area of the pipe at points $A$ and $B$ be $a_1$ and $a_2$ respectively.
And let the liquid enter with normal velocity $\mathrm{v}_1$ at A and leave with velocity $\mathrm{v}_2$ at B .
And $\rho_1$ and $\rho_2$ be the densities of the liquid at point A and B respectively.
Then $\dot{M}_A=\rho_1 a_1 v_1$ and $\dot{M}_B=\rho_2 a_2 v_2$
But $\dot{M}_A=\dot{M}_B$
And Since flow is incompressible so $\rho_1=\rho_2$
So Equation of Continuity for the liquid flow in tube AB is given by

$$
\begin{gathered}
a_1 v_1=a_2 v_2 \\
\text { or } \quad \text { av }=\text { constant }
\end{gathered}
$$
 

Or the Equation of Continuity states that for the liquid flow in the tube, the product of cross-section area and velocity remains the same at all points in the tube.

From the  Equation of Continuity, we can say that

• The velocity of flow will increase if cross-section decreases and vice-versa.