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

$$\begin{array}{c}{a}_1{v}_1=a_2{v}_2\\ \text{ or }\text{ av }=\text{ constant }\end{array}$$
 

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.