Question

An engine pumps a liquid of density $d$ continuously through a pipe of area of cross-section $A$. If the speed with which the liquid passes through a pipe is $v$, then the rate of liquid flow is

• A. $Ad{v}^3/2$
• B. $\left(1/2\right)adv$
• C. $Ad{v}^2/2$
• D. $Adv$

Answer 1

The correct option is D $Adv$

Area of the cross-section of the pipe is $A$
Speed of flow of liquid is $v$
Thus volume rate of liquid flow $\frac{dV}{dt}=Av$
Density of the liquid is $d$
So, rate of mass of liquid flow $\frac{dm}{dt}=d\frac{dV}{dt}=Avd$