A rectangular vessel when full of water takes $10 $ minutes to be emptied through an orifice in its bottom. ......... $\min$ will it take to be emptied when half filled with water
Medium
Download our app for free and get started
(b)Time taken to be emptied for h height, $t = \sqrt {\frac{{2h}}{g}} $
and for $\frac{h}{2}$ height, $t' = \sqrt {\frac{{2h/2}}{g}} = \sqrt {\frac{h}{g}} $$\frac{{t'}}{t} = \frac{1}{{\sqrt 2 }} \Rightarrow t' = \frac{t}{{\sqrt 2 }} = \frac{{10}}{{\sqrt 2 }} = 7\;minute$
and for $\frac{h}{2}$ height, $t' = \sqrt {\frac{{2h/2}}{g}} = \sqrt {\frac{h}{g}} $$\frac{{t'}}{t} = \frac{1}{{\sqrt 2 }} \Rightarrow t' = \frac{t}{{\sqrt 2 }} = \frac{{10}}{{\sqrt 2 }} = 7\;minute$
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
- 1A thin uniform tube is bent into a circle of radius $r$ in the virtical plane. Equal volumes of two immiscible liquids, whose densities are ${\rho _1}$ and ${\rho _2}\left( {{\rho _1} > {\rho _2}} \right)$ fill half the circle. The angle $\theta$ between the radius vector passing through the common interface and the vertical isView Solution
- 2A horizontal right angle pipe bend has crosssectional area $=$ $10 $ $cm^2$ and water flows through it at speed $=$ $20$ $m/s$. The force on the pipe bend due to the turning of water is ........ $N$View Solution
- 3A spherical solid ball of volume $V$ is made of a material of density $\rho_1$ . It is falling through a liquid of density $\rho_2 (\rho_2 < \rho_1 )$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous}= -kv^2 (k >0 )$,The terminal speed of the ball isView Solution
- 4In the diagram shown, the difference in the two tubes of the manometer is $5\, cm$, the cross section of the tube at $A$ and $B$ is $6\, mm^2$ and $10\, mm^2$ respectively. The rate at which water flows through the tube is ........ $ cc/s$ $(g\, = 10\, ms^{-2})$View Solution
- 5In an experiment, a small steel ball falls through a Iiquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? ......... $cm/s$View Solution
- 6The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $‘A’$ and top area $‘a’$ and the walls of the vessel are inclined at an angle $30^o$ with the vertical.A liquid of density $\rho$ fills both the sections upto a height $2h$. Neglecting atmospheric pressure.View Solution
- 7A tank is filled upto a height $h$ with a liquid and is placed on a platform of height h from the ground. To get maximum range ${x_m}$ a small hole is punched at a distance of $y$ from the free surface of the liquid. ThenView Solution
- 8A stone is projected vertically up from the bottom of a water tank. Assuming no water resistance it will go up and come down in same time but if water drag is present then the time it takes to go up, $t_{up}$ and the time it takes to come down, $t_{down}$ are related asView Solution
- 9In the diagram shown, the difference in the two tubes of the manometer is $5\, \ cm$, the cross section of the tube at $A$ and $B$ is $6\, mm^2$ and $10\, mm^2$ respectively. The rate at which water flows through the tube is $........ cc/s$View Solution
$(g\, = 10\, ms^{-2})$
- 10In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70 \mathrm{~ms}^{-1}$ and $65 \mathrm{~ms}^{-1}$ respectively. If the wing area is $2 \mathrm{~m}^2$ the lift of the wing is__________ $\mathrm{N}$.View Solution
(Given density of air $=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$ )