A square hole of side length l is made at a d | vedclass

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

Question

(A) The rate of flow of water (volume flow rate) is given by $Q = A 	imes v$,where $A$ is the area of the hole and $v$ is the velocity of efflux.Acco

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The rate of flow of water (volume flow rate) is given by $Q = A 	imes v$,where $A$ is the area of the hole and $v$ is the velocity of efflux.According to Torricelli's law,the velocity of efflux at a depth $d$ is $v = \sqrt{2gd}$.For the square hole at depth $h$: Area $A_1 = l^2$,velocity $v_1 = \sqrt{2gh}$. Thus,$Q_1 = l^2 \sqrt{2gh}$.For the circular hole at depth $4h$: Area $A_2 = \pi r^2$,velocity $v_2 = \sqrt{2g(4h)} = 2\sqrt{2gh}$. Thus,$Q_2 = \pi r^2 (2\sqrt{2gh})$.Given that the rates of flow are equal,$Q_1 = Q_2$:$l^2 \sqrt{2gh} = 2\pi r^2 \sqrt{2gh}$$l^2 = 2\pi r^2$$r^2 = \frac{l^2}{2\pi}$$r = \frac{l}{\sqrt{2\pi}}$

$A$ square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4h$ from the surface of water in a water tank kept on a horizontal surface. If $l << h$ and $r << h$,and the rate of water flow from the holes is the same,then $r$ is equal to:

Similar Questions

Water is filled in a tank up to a height of $3 \,m$. The base of the tank is at a height of $1 \,m$ above the ground. What should be the height of a hole made in the side of the tank so that water can be sprayed up to the maximum horizontal distance on the ground?

$A$ 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:

If in a stationary lift,a man is standing with a bucket full of water,having a hole at its bottom. The rate of flow of water through this hole is $R_0$. If the lift starts to move up and down with the same acceleration $a$,and the rates of flow of water are $R_u$ and $R_d$ respectively,then:

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 $; m$)?

$A$ tank filled with fresh water has a hole in its bottom and water is flowing out of it. If the size of the hole is increased,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module