A large tank is filled with water to a height $H$. A small hole is made at the base of the tank. It takes ${T_1}$ time to decrease the height of water to $\frac{H}{\eta }\,(\eta > 1)$; and it takes ${T_2}$ time to take out the rest of water. If ${T_1} = {T_2}$, then the value of $\eta $ is
Diffcult
Download our app for free and get started
(c) $t = \frac{A}{a}\sqrt {\frac{2}{g}} \left[ {\sqrt {{H_1}} - \sqrt {{H_2}} } \right]$
Now, ${T_1} = \frac{A}{a}\sqrt {\frac{2}{g}} \left[ {\sqrt H - \sqrt {\frac{H}{\eta }} } \right]$
and ${T_2} = \frac{A}{a}\sqrt {\frac{2}{g}} \left[ {\sqrt {\frac{H}{\eta }} - \sqrt 0 } \right]$
According to problem ${T_1} = {T_2}$
$\sqrt H - \sqrt {\frac{H}{\eta }} = \sqrt {\frac{H}{\eta }} - 0$==> $\sqrt H = 2\sqrt {\frac{H}{\eta }} \Rightarrow \eta = 4$
Now, ${T_1} = \frac{A}{a}\sqrt {\frac{2}{g}} \left[ {\sqrt H - \sqrt {\frac{H}{\eta }} } \right]$
and ${T_2} = \frac{A}{a}\sqrt {\frac{2}{g}} \left[ {\sqrt {\frac{H}{\eta }} - \sqrt 0 } \right]$
According to problem ${T_1} = {T_2}$
$\sqrt H - \sqrt {\frac{H}{\eta }} = \sqrt {\frac{H}{\eta }} - 0$==> $\sqrt H = 2\sqrt {\frac{H}{\eta }} \Rightarrow \eta = 4$
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
- 1The vertical limbs of a $U$ shaped tube are filled with a liquid of density $\rho$ upto a height $h$ on each side. The horizontal portion of the $U$ tube having length $2h$ contains a liquid of density $2\rho$ . The $U$ tube is moved horizontally with an accelerator $g/2$ parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs, at steady state will beView Solution
- 2During blood transfusion the needle is inserted in a vein where the gauge pressure is $2000 \;Pa$. At what height (in $m$) must the blood container be placed so that blood may just enter the vein ?View Solution
Density of whole blood, $\rho=1.06 \times 10^{3} \;kg m ^{-3}$
- 3View SolutionPressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by
- 4View SolutionIn the case of a fluid, Bernoulli's theorem expresses the application of the principle of conservation of :
- 5A piece of gold weighs $10 \,g$ in air and $9 \,g$ in water. What is the volume of cavity is $...... cc ($Density of gold $=19.3 \,g \ cm ^{-3} )$View Solution
- 6The pressure acting on a submarine is $3 \times 10^{5}\;Pa$ at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is $1 \times 10^{5} \;Pa$ density of water is $10^{3}\, kg \,m ^{-3}, g =10 \,ms ^{-2}$ )View Solution
- 7A steady flow of water passes along a horizontal tube from a wide section $X$ to the narrower section $Y$, see figure. Manometers are placed at $P$ and $Q$ at the sections. Which of the statements $A, B, C, D, E$ is most correct?View Solution
- 8There is a $1$ $mm $ thick layer of glycerine between a flat plate of area $100$ $cm^2$ $\&$ a big fixed plate. If the coefficient of viscosity of glycerine is $1.0$ $kg/m^{-s}$ then ....... $N$ force is required to move the plate with a velocity of $7$ $cm/s$ ?View Solution
- 9A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is $5\, cm$ and the angular speed of rotation is $\omega\; rad \,s^{-1}$. The difference in the height, $h($ in $cm )$ of liquid at the centre of vessel and at the side will beView Solution
- 10View SolutionA viscous fluid is flowing through a cylindrical tube. The velocity distribution of the fluid is best represented by the diagram