First slide

Fluid dynamics

Question

A tank has a hole at its bottom. The time needed to empty the tank from level $h_{1} to h_{2}$ will be proportional to

Moderate

A

$h_{1} - h_{2}$
B

$h_{1} + h_{2}$
C

$\sqrt{h_{1}} - \sqrt{h_{2}}$
D

$\sqrt{h_{1}} + \sqrt{h_{2}}$

Solution

Let $- \frac{dh}{dt}$ represent the rate of descent of water level. Let A and a represent the cross-sectional areas of the container and hole respectively
Then, $- A \frac{dh}{dt} = a \sqrt{2 gh}$
or dt = -k $\frac{dh}{\sqrt{n}} dt$
or $\int_{0}^{t} dt = - k \int_{h_{1}}^{h_{2}} \frac{1}{\sqrt{h}} dh$
or $t = - k | \frac{h^{\frac{1}{2} + 1}}{- \frac{1}{2} + 1} {|^{h_{2}}}_{h_{1}}$
or t = -2k[ $\sqrt{h_{2}} - \sqrt{h_{1}}$ ]
t is directly proportioanl to ( $\sqrt{h_{1}} - \sqrt{h_{2}}$ )

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App