(A) The force exerted by the water jet exiting the hole is given by $F = \rho A v^2$,where $A$ is the area of the hole and $v$ is the velocity of the

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$\sqrt{\frac{2\mu M}{\pi \rho H}}$

(A) The force exerted by the water jet exiting the hole is given by $F = \rho A v^2$,where $A$ is the area of the hole and $v$ is the velocity of the water.Using Torricelli's Law,the velocity of the water at the bottom is $v = \sqrt{2gH}$.Thus,the force is $F = \rho A (2gH)$.For the vessel to begin moving,this force must overcome the limiting friction force,$f_s = \mu Mg$.Equating the two: $\rho A (2gH) = \mu Mg$.Substituting $A = \frac{\pi D^2}{4}$,we get $\rho \left( \frac{\pi D^2}{4} \right) (2gH) = \mu Mg$.Simplifying the equation: $\frac{\rho \pi D^2 g H}{2} = \mu Mg$.Solving for $D$: $D^2 = \frac{2\mu M}{\pi \rho H}$.Therefore,$D = \sqrt{\frac{2\mu M}{\pi \rho H}}$.

Class 11 Physics Fluid Mechanics and Surface Tension Velocity of Efflux and Torricelli's law

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$A$ cylindrical vessel filled with water up to a height of $H$ stands on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of the vessel and the plane is $\mu$ and the total mass of the water plus the vessel is $M$. What should be the minimum diameter of the hole so that the vessel begins to move on the floor if the plug is removed? (Here,the density of water is $\rho$)

A
$\sqrt{\frac{2\mu M}{\pi \rho H}}$
B
$\sqrt{\frac{\mu M}{2\pi \rho H}}$
C
$\sqrt{\frac{\mu M}{\rho H}}$
D
none

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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There is a hole in the bottom of a tank containing water. If the total pressure at the bottom is $3 \ atm$,then the velocity of water flowing from the hole is $(1 \ atm = 10^5 \ Pa)$ :-

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