(A) The mass of the liquid passing through the pipe per unit time is given by the rate of mass flow: $\frac{dm}{dt} = \rho A V$,where $\rho = d$ is th

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(A) The mass of the liquid passing through the pipe per unit time is given by the rate of mass flow: $\frac{dm}{dt} = \rho A V$,where $\rho = d$ is the density.Thus,$\frac{dm}{dt} = dAV$.The kinetic energy $K$ of a mass $m$ moving with speed $V$ is $K = \frac{1}{2} m V^2$.The kinetic energy imparted per unit time is $\frac{dK}{dt} = \frac{1}{2} V^2 \frac{dm}{dt}$.Substituting the value of $\frac{dm}{dt}$,we get $\frac{dK}{dt} = \frac{1}{2} V^2 (dAV) = \frac{1}{2} AdV^3$.

Class 11 Physics Fluid Mechanics and Surface Tension Types of Flow, Equation of Continuity and Flow Rate

Difficult

An engine pumps a liquid of density $d$ continuously through a pipe of cross-sectional area $A$. If the speed of the liquid passing through the pipe is $V$,what is the kinetic energy per unit time imparted to the liquid?

A
$\frac{1}{2} AdV^3$
B
$\frac{1}{2} AdV^2$
C
$\frac{1}{2} AdV$
D
$AdV^2$

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Fluid Mechanics and Surface Tension

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Types of Flow, Equation of Continuity and Flow Rate

Select the incorrect statement regarding turbulent flow.

Easy

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The cylindrical tube of a spray pump has radius $R,$ one end of which has $n$ fine holes,each of radius $r.$ If the speed of the liquid in the tube is $v,$ the speed of the ejection of the liquid through the holes is

MediumAIPMT 2015

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Water is flowing in a pipe of diameter $4 \text{ cm}$ with a velocity $3 \text{ m/s}$. The water then enters into a tube of diameter $2 \text{ cm}$. The velocity of water in the other pipe is .......... $\text{m/s}$.

Medium

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$A$ pipe having an internal diameter $D$ is connected to another pipe of the same size. Water flows into the second pipe through $n$ holes, each of diameter $d$. If the water in the first pipe has speed $v$, what is the speed of water leaving the second pipe?

DifficultAP EAMCET 2012

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In a streamline flow,

Easy

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An engine pumps a liquid of density $d$ continuously through a pipe of cross-sectional area $A$. If the speed of the liquid passing through the pipe is $V$,what is the kinetic energy per unit time imparted to the liquid?

Similar Questions

Select the incorrect statement regarding turbulent flow.

The cylindrical tube of a spray pump has radius $R,$ one end of which has $n$ fine holes,each of radius $r.$ If the speed of the liquid in the tube is $v,$ the speed of the ejection of the liquid through the holes is

Water is flowing in a pipe of diameter $4 \text{ cm}$ with a velocity $3 \text{ m/s}$. The water then enters into a tube of diameter $2 \text{ cm}$. The velocity of water in the other pipe is .......... $\text{m/s}$.

$A$ pipe having an internal diameter $D$ is connected to another pipe of the same size. Water flows into the second pipe through $n$ holes, each of diameter $d$. If the water in the first pipe has speed $v$, what is the speed of water leaving the second pipe?

In a streamline flow,

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