(D) In steady state,the volume flow rate of water entering the vessel must be equal to the volume flow rate of water leaving the vessel through the ho

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

(D) In steady state,the volume flow rate of water entering the vessel must be equal to the volume flow rate of water leaving the vessel through the hole.Let $Q$ be the rate of inflow,$a$ be the area of the hole,and $h$ be the height of the water level.The rate of outflow is given by Torricelli's law: $Q_{out} = a v = a \sqrt{2gh}$.Equating inflow and outflow: $Q = a \sqrt{2gh}$.Rearranging for $h$: $h = \frac{Q^2}{2 g a^2}$.Given $Q = 100 \ cm^3 s^{-1}$,$a = 1 \ cm^2$,and $g = 1000 \ cm s^{-2}$.Substituting the values: $h = \frac{(100)^2}{2 \times 1000 \times (1)^2} = \frac{10000}{2000} = 5 \ cm$.

Class 11 Physics Mechanical Properties of Fluids Velocity of Efflux and Torricelli's law

Medium

$A$ cylindrical vessel open at the top is $20 \ cm$ high and $10 \ cm$ in diameter. $A$ circular hole whose cross-sectional area is $1 \ cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of $100 \ cm^3 s^{-1}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g = 1000 \ cm s^{-2}$)

A
$20$
B
$15$
C
$10$
D
$5$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Mechanical Properties of Fluids

Subtopic

Velocity of Efflux and Torricelli's law

The water is filled up to a height of $12\, \text{m}$ in a tank having vertical sidewalls. $A$ hole is made in one of the walls at a depth $h$ below the water level. The value of $h$ for which the emerging stream of water strikes the ground at the maximum range is $.....\, \text{m}$.

MediumJEE MAIN 2021

View Solution

$A$ container has a hole of cross-sectional area $1 \, cm^2$ at its bottom. If water is poured into the container at a rate of $70 \, cm^3/s$, what is the maximum height (in $cm$) to which the water can be filled?

Medium

View Solution

$A$ cylinder containing water stands on a table of height $H$. $A$ small hole is punched in the side of the cylinder at its base. The stream of water strikes the ground at a horizontal distance $R$ from the table. Then the depth of water in the cylinder is ............

Medium

View Solution

$A$ 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

DifficultAP EAMCET 2002

View Solution

Water is filled in a cylindrical vessel of height $H$. $A$ hole is made at height $z$ from the bottom, as shown in the figure. The value of $z$ for which the range $(R)$ of the emerging water through the hole will be maximum is:

MediumWBJEE 2024

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

The water is filled up to a height of $12\, \text{m}$ in a tank having vertical sidewalls. $A$ hole is made in one of the walls at a depth $h$ below the water level. The value of $h$ for which the emerging stream of water strikes the ground at the maximum range is $.....\, \text{m}$.

$A$ container has a hole of cross-sectional area $1 \, cm^2$ at its bottom. If water is poured into the container at a rate of $70 \, cm^3/s$, what is the maximum height (in $cm$) to which the water can be filled?

$A$ cylinder containing water stands on a table of height $H$. $A$ small hole is punched in the side of the cylinder at its base. The stream of water strikes the ground at a horizontal distance $R$ from the table. Then the depth of water in the cylinder 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

Water is filled in a cylindrical vessel of height $H$. $A$ hole is made at height $z$ from the bottom, as shown in the figure. The value of $z$ for which the range $(R)$ of the emerging water through the hole will be maximum is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module