Water flows into a large tank with flat bottom at the rate of . Water is also

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 $0.5 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height is $g = 10 m / s^{2}$

Smart Achievers · Accepted Answer

(3)

Since height of water column is constant therefore,

Water inflow rate $(Q_{m})$ = water outflow rate

$0.5 c m^{2}$

$Q_{o u t} = A u = 10^{- 4} \times \sqrt{2 g h}$

$10^{- 4} = 10^{- 4} \sqrt{20 \times h}$

$h = \frac{1}{20} m = 5 c m$

Solution

Q.
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 $0.5 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height is $g = 10 m / s^{2}$

1 25 cm

2 15 cm

3 20 cm

4 5 cm

Ans.
(3)

Since height of water column is constant therefore,

Water inflow rate $(Q_{m})$ = water outflow rate

$Q_{i n} = 10^{- 4} m^{3} s^{- 1}$

$Q_{o u t} = A u = 10^{- 4} \times \sqrt{2 g h}$

$10^{- 4} = 10^{- 4} \sqrt{20 \times h}$

$h = \frac{1}{20} m = 5 c m$

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