Question

A liquid is under streamline flow through a horizontal pipe of non uniform cross-sectional area. If the volume rate of flow at a cross-section of area $a$ is $V$, then volume rate of flow at a different cross-section of area $\frac{a}{2}$ is

• A. $\frac{V}{2}$
• B. $2V$
• C. $\frac{V}{4}$
• D. $V$

Answer 1

The correct option is D $V$

Applying continuity equation at the two cross-sections for the given streamline flow,
$A\times v=\text{constant}...\left(i\right)$
Now, for a given time interval $\Delta t$, the volume flow rate is, $A\times v\times \Delta t$
So, volume flow rate at any cross-section will remain constant.$V_i=V_f=V$
Hence, volume flow rate at second cross-section of area $\frac{a}{2}=V$