Question

A long cylindrical tank of radius $1m$ is being filled by a pipe of radius $2cm$. The incoming water has a velocity of $1m/s$. The tank has a hole of radius $1cm$ at the bottom. What is the height of water in the tank in steady state?

• A. The level will continue to rise.
  
• B. $0.6m$
  
• C. $0.8m$
  
• D. $0.4m$
  

Answer 1

The correct option is C $0.8m$


In steady state,
$A_1{v}_1=A_2{v}_2$

Here,
$v_1=1m/s,v_2=\sqrt{2gh}$,

$r_1=2cm,r_2=1cm$

$\pi \times {\left(\frac{2}{100}\right)}^2\times 1=\pi \times {\left(\frac{1}{100}\right)}^2\times \sqrt{2gh}$

$\Rightarrow h=\frac{16}{20}=0.8m$

Final Answer: $\left(c\right)$