The height of the water level in a tank of un | vedclass

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

Question

(B) The velocity of efflux $(v)$ from a hole at the bottom of a tank is given by Torricelli's law: $v = \sqrt{2gh}$.Given:Height of water level, $h =

Vedclass · Accepted Answer

$120 	imes 10^{-6} \,m^3$

Vedclass · Answer

(B) The velocity of efflux $(v)$ from a hole at the bottom of a tank is given by Torricelli's law: $v = \sqrt{2gh}$.Given:Height of water level, $h = 5 \,m$.Area of the hole, $A = 2.4 \,mm^2 = 2.4 	imes 10^{-6} \,m^2$.Time, $t = 5 \,s$.Acceleration due to gravity, $g = 10 \,ms^{-2}$.The volume of water leaked $(V)$ is given by the product of the area of the hole, the velocity of efflux, and the time:$V = A 	imes v 	imes t = A \sqrt{2gh} 	imes t$.Substituting the values:$V = (2.4 	imes 10^{-6} \,m^2) 	imes \sqrt{2 	imes 10 \,ms^{-2} 	imes 5 \,m} 	imes 5 \,s$.$V = 2.4 	imes 10^{-6} 	imes \sqrt{100} 	imes 5$.$V = 2.4 	imes 10^{-6} 	imes 10 	imes 5$.$V = 2.4 	imes 50 	imes 10^{-6} \,m^3$.$V = 120 	imes 10^{-6} \,m^3$.

The height of the water level in a tank of uniform cross-section is $5 \,m$. The volume of water leaked in $5 \,s$ through a hole of area $2.4 \,mm^2$ made at the bottom of the tank is (Assume the level of the water in the tank remains constant and acceleration due to gravity $= 10 \,ms^{-2}$).

Similar Questions

$A$ cylindrical tank has a hole of $1 \ cm^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70 \ cm^3/s$,then the maximum height up to which water can rise in the tank is: $(g = 9.8 \ m/s^2)$ (in $cm$)

The height of water in a tank is $H$. The range of the liquid emerging out from a hole in the wall of the tank at a depth $\frac{3H}{4}$ from the upper surface of water will be:

$A$ cylindrical tank of height $0.4\,m$ is open at the top and has a diameter $0.16\,m$. Water is filled in it up to a height of $0.16\,m$. How long will it take to empty the tank through a hole of radius $5 \times 10^{-3}\,m$ in its bottom? (in seconds)

$A$ closed pipe containing liquid showed a pressure $P_{1}$ by gauge. When the valve is opened,the pressure was reduced to $P_{2}$. The speed of water flowing out of the pipe is $[\rho = \text{density of water}]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module