A large open tank has two holes in its wall. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The volume flow rate (quantity of water per second) is given by the product of the area of the hole $(A)$ and the velocity of efflux $(v)$.Accordi

Vedclass · Accepted Answer

$\frac{a}{\sqrt{2 \pi}}$

Vedclass · Answer

(C) The volume flow rate (quantity of water per second) is given by the product of the area of the hole $(A)$ and the velocity of efflux $(v)$.According to Torricelli's law,the velocity of efflux at a depth $h$ is $v = \sqrt{2gh}$.For the square hole: Area $A_1 = a^2$,depth $h_1 = x$. Velocity $v_1 = \sqrt{2gx}$.Flow rate $Q_1 = A_1 v_1 = a^2 \sqrt{2gx}$.For the circular hole: Area $A_2 = \pi r^2$,depth $h_2 = 4x$. Velocity $v_2 = \sqrt{2g(4x)} = 2\sqrt{2gx}$.Flow rate $Q_2 = A_2 v_2 = \pi r^2 (2\sqrt{2gx})$.Given $Q_1 = Q_2$,we have:$a^2 \sqrt{2gx} = 2\pi r^2 \sqrt{2gx}$.Dividing both sides by $\sqrt{2gx}$:$a^2 = 2\pi r^2$.$r^2 = \frac{a^2}{2\pi}$.$r = \frac{a}{\sqrt{2\pi}}$.

Similar Questions

$A$ cylindrical container containing water has a small hole at a height of $H = 8 \text{ cm}$ from the bottom and at a depth of $h = 2 \text{ cm}$ from the top surface of the liquid. The horizontal distance (range) travelled by the water before it hits the ground is:

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel, then the value of $d$ is

$A$ vessel of area of cross-section $A$ has liquid to a height $H$. There is a hole at the bottom of the vessel having area of cross-section $a$. The time taken to decrease the level from $H_1$ to $H_2$ will be:

$A$ wide vessel with a small hole at the bottom is filled with two liquids. The density and height of one liquid are $\rho_1$ and $h_1$ and that of the other are $\rho_2$ and $h_2$ $(\rho_1 > \rho_2)$. The velocity of the liquid coming out of the hole is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module