(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

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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?

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

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Class 11 Questions

Class 11

Physics Questions

Chapter

Fluid Mechanics and Surface Tension

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Types of Flow, Equation of Continuity and Flow Rate

An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A$ and radius $r$ at point $B$ further along the flow direction. If the velocity at point $A$ is $v$,what is its velocity at point $B$?

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Give an example of steady flow.

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$A$ laminar stream is flowing vertically down from a tap of cross-section area $1 \ cm^2$. At a distance $10 \ cm$ below the tap,the cross-section area of the stream has reduced to $0.5 \ cm^2$. The volumetric flow rate of water from the tap is about ........ $litre/min$.

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What is steady flow?

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An incompressible fluid flows steadily through a horizontal cylindrical pipe. The pipe has radius $3R$ at point $A$ and $1.5R$ at point $B$, further along the flow direction at the same level. If the velocity at point $A$ is $v$, then the velocity at point $B$ is:

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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

An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A$ and radius $r$ at point $B$ further along the flow direction. If the velocity at point $A$ is $v$,what is its velocity at point $B$?

Give an example of steady flow.

$A$ laminar stream is flowing vertically down from a tap of cross-section area $1 \ cm^2$. At a distance $10 \ cm$ below the tap,the cross-section area of the stream has reduced to $0.5 \ cm^2$. The volumetric flow rate of water from the tap is about ........ $litre/min$.

What is steady flow?

An incompressible fluid flows steadily through a horizontal cylindrical pipe. The pipe has radius $3R$ at point $A$ and $1.5R$ at point $B$, further along the flow direction at the same level. If the velocity at point $A$ is $v$, then the velocity at point $B$ is:

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