(B) The volume flow rate is given by $Q = A \cdot v$,where $v = \sqrt{2gh}$ is the velocity of efflux.Given: $Q = 0.74\,m^3/min = \frac{0.74}{60}\,m^3

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(B) The volume flow rate is given by $Q = A \cdot v$,where $v = \sqrt{2gh}$ is the velocity of efflux.Given: $Q = 0.74\,m^3/min = \frac{0.74}{60}\,m^3/s$,radius $r = 2\,cm = 0.02\,m$,and $g = 9.8\,m/s^2$.The area of the opening is $A = \pi r^2 = 3.14 \times (0.02)^2 = 3.14 \times 4 \times 10^{-4}\,m^2$.Substituting these into the equation $Q = A\sqrt{2gh}$:$\frac{0.74}{60} = (3.14 \times 4 \times 10^{-4}) \sqrt{2 \times 9.8 \times h}$.$\frac{0.01233}{1.256 \times 10^{-3}} = \sqrt{19.6h}$.$9.816 = \sqrt{19.6h}$.Squaring both sides: $96.36 = 19.6h$.$h = \frac{96.36}{19.6} \approx 4.92\,m$.Thus,the depth is close to $4.8\,m$.

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

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The top of a water tank is open to air and its water level is maintained. It is discharging $0.74\,m^3$ of water per minute through a circular opening of $2\,cm$ radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ $m$

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A
$6.0$
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$4.8$
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$9.6$
D
$2.9$

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Class 11

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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The top of a water tank is open to air and its water level is maintained. It is discharging $0.74\,m^3$ of water per minute through a circular opening of $2\,cm$ radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ $m$

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$A$ container is filled with water up to a height $h$. $A$ small hole is made at the bottom. What is the ratio of the time taken for the water level to fall from $h$ to $\frac{h}{2}$ to the time taken for it to fall from $\frac{h}{2}$ to $0$?

$A$ cylindrical vessel filled with water up to the height $H$ becomes empty in time $t_0$ due to a small hole at the bottom of the vessel. If water is filled to a height $4H$,it will flow out in time:

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Equal volumes of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in the figure. Two small holes are punched at depths $h/2$ and $3h/2$ from the surface of the lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes,then $v_1/v_2$ is:

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