(D) The volume flow rate $R_v$ is given by $R_v = A \times v$, where $A$ is the area of the hole and $v$ is the velocity of efflux given by Torricelli

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

(D) The volume flow rate $R_v$ is given by $R_v = A \times v$, where $A$ is the area of the hole and $v$ is the velocity of efflux given by Torricelli's law $v = \sqrt{2gh}$.For the square hole: Area $A_1 = x^2$, depth $h_1 = 2 \,m$. Velocity $v_1 = \sqrt{2g(2)} = 2\sqrt{g}$. Flow rate $R_{v1} = x^2 \times 2\sqrt{g}$.For the triangular hole: Area $A_2 = \frac{\sqrt{3}}{4} \times (4)^2 = 4\sqrt{3} \,cm^2$, depth $h_2 = 6 \,m$. Velocity $v_2 = \sqrt{2g(6)} = \sqrt{12g} = 2\sqrt{3g}$. Flow rate $R_{v2} = 4\sqrt{3} \times 2\sqrt{3g} = 24\sqrt{g}$.Equating the flow rates: $x^2 \times 2\sqrt{g} = 24\sqrt{g}$.$x^2 = 12$.$x = \sqrt{12} = 2\sqrt{3} \approx 3.46 \,cm$.

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

Easy

$A$ fully filled open water tank has two holes on either side of its walls. One is a square hole of side $x \,cm$ at a depth of $2 \,m$ from the top, and the other hole is an equilateral triangle of side $4 \,cm$ at a depth of $6 \,m$ from the top. If the rate of flow of water is the same from both the holes, then the value of $x$ is: (in $\,cm$)

AP EAMCET 2017 All AP EAMCET

A
$1.73$
B
$12$
C
$6.92$
D
$3.46$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Fluid Mechanics and Surface Tension

Subtopic

Velocity of Efflux and Torricelli's law

Previous Year

AP EAMCET 2017 Paper All AP EAMCET years →

Tanks $A$ and $B$ open at the top contain two different liquids up to a certain height. $A$ hole is made in the wall of each tank at a depth $h$ from the surface of the liquid. The area of the hole in $B$ is twice that of in $A$. If the liquid mass flux through each hole is equal, then the ratio of the densities of the liquids respectively, is

DifficultAP EAMCET 2002

View Solution

$A$ liquid is filled in a tank up to a height of $5 \,m$ and the bottom of the tank is at $5 \,m$ height from the ground. $A$ hole is punched in the tank so that the liquid coming out touches the ground at maximum horizontal distance. Then, the maximum horizontal distance is (in $\,m$)

MediumAP EAMCET 2018

View Solution

$A$ hole is made at the bottom of a tank filled with water (density $1000 \, kg/m^3$). If the total pressure at the bottom of the tank is $3 \, atm$ $(1 \, atm = 10^5 \, N/m^2)$,then the velocity of efflux is:

MediumAIIMS 2000

View Solution

$A$ cylindrical tank is filled with water to a level of $3 \,m$. $A$ hole is opened at a height of $52.5 \,cm$ from the bottom. The ratio of the area of the hole to that of the cross-sectional area of the tank is $0.1$. The square of the speed with which water will be coming out from the orifice is $(g=10 \,ms^{-2})$.

MediumAP EAMCET 2021

View Solution

$A$ 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,

EasyTS EAMCET 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

$A$ liquid is filled in a tank up to a height of $5 \,m$ and the bottom of the tank is at $5 \,m$ height from the ground. $A$ hole is punched in the tank so that the liquid coming out touches the ground at maximum horizontal distance. Then, the maximum horizontal distance is (in $\,m$)

$A$ hole is made at the bottom of a tank filled with water (density $1000 \, kg/m^3$). If the total pressure at the bottom of the tank is $3 \, atm$ $(1 \, atm = 10^5 \, N/m^2)$,then the velocity of efflux is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module