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 it will take to empty the tank through a hole of radius $5 \times 10^{-3}\,m$ in its bottom .......... $\sec$
Diffcult
Download our app for free and get started
$A_{1} v_{1}=A_{2} v_{2}$
$\pi \mathrm{R}^{2} \mathrm{dh} / \mathrm{dt}=\pi \mathrm{r}^{2} \mathrm{v}$ $...(i)$
$\mathrm{v}=\sqrt{2 \mathrm{gh}}$ $...(ii)$
from equation $(ii)$ put the value of $v$ in equation $( i)$
$-\pi \mathrm{R}^{2} \mathrm{dh} / \mathrm{dt}=\pi \mathrm{r}^{2} \sqrt{2 \mathrm{gh}}$
$\Rightarrow-\int \frac{\mathrm{R}^{2} \mathrm{dh}}{\mathrm{r}^{2} \sqrt{2 \mathrm{gh}}}=\int \mathrm{dt} \Rightarrow-\frac{\mathrm{R}^{2}}{\mathrm{r}^{2} \sqrt{2 \mathrm{g}}} \int_{\mathrm{h}}^{0} \frac{\mathrm{dh}}{\sqrt{\mathrm{h}}}=\int_{0}^{\mathrm{t}} \mathrm{dt}$
on solving $t=46.26$ second
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionIn a streamline flow
- 2View SolutionA block of ice floats in an oil in a vessel when the ice melts, the level of oil will ..............
- 3View SolutionCorrect Bernoulli's equation is (symbols have their usual meaning) :
- 4Water is flowing with a velocity of $2\,m/s$ in a horizontal pipe where cross-sectional area is $2 \times 10^{-2}\, m^2$ at pressure $4 \times 10^4\, pascal$. The pressure at cross-section of area $0.01\, m^2$ in pascal will beView Solution
- 5The diameter of an air bubble which was initially $2\,mm$, rises steadily through a solution of density $1750\,kg\,m\,m ^{-3}$ at the rate of $0.35\,cms ^{-1}$. The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible).View Solution
- 6A large vessel of height $H$, is filled with a liquid of density $\rho$, upto the brim. A small hole of radius $r$ is made at the side vertical face, close to the base. The horizontal force is required to stop the gushing of liquid is ...........View Solution
- 7Water $\left(\rho=1000 \,kg / m ^3\right)$ and kerosene $\left(\sigma=800 \,kg / m ^3\right)$ are filled in two identical cylindrical vessels. Both vessels have small holes at their bottom. The speed of the water and kerosene coming out of their holes are $v_1$ and $v_2$ respectively. Select the correct alternativeView Solution
- 8The limbs of a $U$ -tube glass are lowered into vessels $A$ and $B, A$ containing water. Some air is pumped out through the top of the tube $C$. The liquids in the left hand limb $A$ and the right hand limb $B$ rise to heights of $10\, cm$ and $12\, cm$ respectively. The density of liquid $B$ is ........ $g/cm^3$View Solution
- 9A container of height $10\, cm$ is filled with water. There is a hole at bottom. Find the pressure difference between points at top and bottom.View Solution
- 10A wooden cube just floats inside water with a $200 \,gm$ mass placed on it. When the mass is removed, the cube floats with its top surface $2 \,cm$ above the water level. the side of the cube is ......... $cm$View Solution