A large tank filled with water to a height h | vedclass

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

Question

(C) The time $t$ taken for the water level to fall from an initial height $H_1$ to a final height $H_2$ in a tank with cross-sectional area $A$ and or

Vedclass · Accepted Answer

$\sqrt{2} - 1$

Vedclass · Answer

(C) The time $t$ taken for the water level to fall from an initial height $H_1$ to a final height $H_2$ in a tank with cross-sectional area $A$ and orifice area $A_0$ is given by $t = \frac{A}{A_0} \sqrt{\frac{2}{g}} (\sqrt{H_1} - \sqrt{H_2})$.For the first interval,the level falls from $h$ to $\frac{h}{2}$. Thus,$t_1 = \frac{A}{A_0} \sqrt{\frac{2}{g}} (\sqrt{h} - \sqrt{\frac{h}{2}}) = \frac{A}{A_0} \sqrt{\frac{2h}{g}} (1 - \frac{1}{\sqrt{2}})$.For the second interval,the level falls from $\frac{h}{2}$ to $0$. Thus,$t_2 = \frac{A}{A_0} \sqrt{\frac{2}{g}} (\sqrt{\frac{h}{2}} - 0) = \frac{A}{A_0} \sqrt{\frac{2h}{g}} (\frac{1}{\sqrt{2}})$.The ratio is $\frac{t_1}{t_2} = \frac{1 - \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}} = \sqrt{2} - 1$.

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of the time taken for the level of water to fall from $h$ to $\frac{h}{2}$ and from $\frac{h}{2}$ to zero is:

Similar Questions

Which one of the following is not a biopolymer?

$A$ square of side $3\;cm$ is placed at a distance of $25\;cm$ from a concave mirror of focal length $10\;cm$. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is $......\;cm^2$.

Which of the following characteristics is false for $Bryophytes$?

The major product of the following reaction is:

You are given a tissue with its potential for differentiation in an artificial culture. Which of the following pairs of hormones would you add to the medium to secure shoots as well as roots?

Vedclass Test Series

Exam Paper Generator

Online Exam Module