Question

Water flows into a large tank with flat bottom at the rate of ${10}^{-4}{m}^3{s}^{-1}$. Water is also leaking out of a hole of area $1c{m}^2$ at its bottom. If the height of the water in the tank remains steady, then this height is__?

• A. $4cm$
• B. $2.9cm$
• C. $1.7cm$
• D. $5.1cm$

Answer 1

Answer: (D)

$5.1cm$

Since height of water column is constant therefor, water inflow rate $\left(Q_{in}\right)$
$=$ water outflow rate
$Q_{in}={10}^{-4}{m}^3{s}^{-1}$
$Q_{out}=Au={10}^{-4}\times \sqrt{2gh}$
${10}^{-4}={10}^{-4}=\sqrt{20\times h}$
$h=\frac{1}{20}m$
$h=5cm$
$\therefore$ correct answer is $\left(4\right)$.