(A) According to Torricelli's Law, the velocity of efflux $v$ is given by $v = \sqrt{2gh}$, where $h$ is the height of the water level above the openi

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(A) According to Torricelli's Law, the velocity of efflux $v$ is given by $v = \sqrt{2gh}$, where $h$ is the height of the water level above the opening.As water drains out, the height $h$ decreases over time.Since the velocity of efflux $v$ is proportional to $\sqrt{h}$, the velocity decreases as the water level drops.Because the velocity is lower when the water level is lower, it takes more time to drain the same volume of water as the height decreases.Therefore, the time taken to drain the first $5 \text{ litres}$ $(t_1)$ is the smallest, and the time taken to drain the last $5 \text{ litres}$ $(t_3)$ is the largest.Thus, $t_1 < t_2 < t_3$.

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

Easy

$A$ cylindrical vessel, open at the top, contains $15 \text{ litres}$ of water. Water drains out through a small opening at the bottom. $5 \text{ litres}$ of water comes out in time $t_1$, the next $5 \text{ litres}$ in further time $t_2$, and the last $5 \text{ litres}$ in further time $t_3$. Then,

TS EAMCET 2023 All TS EAMCET

A
$t_1 < t_2 < t_3$
B
$t_1 > t_2 > t_3$
C
$t_1 = t_2 = t_3$
D
$t_2 > t_1 = t_3$

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

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Water flows into a cylindrical vessel of large cross-sectional area at a rate of $10^{-4} \; m^3/s$. It flows out from a hole of area $10^{-4} \; m^2$, which has been punched through the base. How high does the water rise in the vessel (in $; m$)?

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