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

Answer 1

Answer: (D)

5.1 cm

Answer 2

Since height of water column is constant
therefore, water inflow rate $(Q_{in})$
= 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 (4)