(B) Consider a point $A$ at the center of the liquid surface and a point $B$ at the side of the container at the same horizontal level as $A$ in the r

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(B) Consider a point $A$ at the center of the liquid surface and a point $B$ at the side of the container at the same horizontal level as $A$ in the rotating frame.Using Bernoulli's principle in the rotating frame,the pressure difference between the center and the side is given by the hydrostatic pressure difference due to the height $h$:$P_B - P_A = h \rho g$In the rotating frame,the effective pressure difference due to centrifugal force is:$P_B - P_A = \int_0^r \rho \omega^2 x \, dx = \frac{1}{2} \rho \omega^2 r^2$Equating the two expressions for pressure difference:$h \rho g = \frac{1}{2} \rho \omega^2 r^2$$h = \frac{r^2 \omega^2}{2g}$

Class 11 Physics Fluid Mechanics and Surface Tension Mix Examples-Fluid Mechanics and Surface Tension

Difficult

$A$ cylindrical container is filled with liquid. When the container is rotated about its axis,the liquid rises along its sides. If the radius of the container is $r$ and the angular velocity of the container is $\omega$ rad/s,what will be the difference in the height of the liquid at the center and at the sides?

A
$\frac{r\omega}{2g}$
B
$\frac{r^2\omega^2}{2g}$
C
$\sqrt{2gr\omega}$
D
$\frac{\omega^2}{2gr^2}$

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Class 11

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Fluid Mechanics and Surface Tension

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Mix Examples-Fluid Mechanics and Surface Tension

$STATEMENT-1$: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up,but tends to narrow down when held vertically down.
$STATEMENT-2$: In any steady flow of an incompressible fluid,the volume flow rate of the fluid remains constant.

DifficultIIT 2008

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$A$ ball is made of a material of density $\rho$ where $\rho_{\text{oil}} < \rho < \rho_{\text{water}}$,with $\rho_{\text{oil}}$ and $\rho_{\text{water}}$ representing the densities of oil and water,respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water,which of the following pictures represents its equilibrium position?

MediumAIEEE 2010

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$A$ bucket contains water filled up to a height $h = 15 \ cm$. The bucket is tied to a rope which is passed over a frictionless light pulley,and the other end of the rope is tied to a weight of mass which is half of that of the (bucket $+$ water). The water pressure above atmospheric pressure at the bottom is ....... $kPa$.

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$A$ large number of water drops,each of radius $r$,combine to form a single drop of radius $R$. If the surface tension is $T$ and the mechanical equivalent of heat is $J$,then the rise in temperature will be:

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$A$ liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides. If the radius of the vessel is $0.05\,m$ and the speed of rotation is $2\,rev/s$,the difference in the height of the liquid at the center of the vessel and its sides will be .............. $cm$ $(\pi^2 = 10)$.

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$A$ large number of water drops,each of radius $r$,combine to form a single drop of radius $R$. If the surface tension is $T$ and the mechanical equivalent of heat is $J$,then the rise in temperature will be:

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