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 1 ${cm}^2$ at its bottom. If the height of the water in the tank remains steady, then this height is :

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

Answer 1

The correct option is A 2.9 cm

Since height of water column is constant

therefore, water inflow rate (Qin​) = water outflow rate

${10}^{-4}={10}^{-4}v$

${10}^{-4}={10}^{-4}\sqrt{2gh}$

$h=\frac{1}{2g}$

$h=\frac{1}{2\times 9.8}=5.1cm$

Hence option B is correct