The area of cross-section of a large tank is 0 . 5 m 2 . It has a narrow opening near the bottom having area of cross-section 1 cm 2 . A load of 25 kg is applied on the water at the top in the tank. N

Question

The area of cross-section of a large tank is $0.5 m^{2}$ . It has a narrow opening near the bottom having area of cross-section $1 {cm}^{2}$ . A load of $25 kg$ is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is $40 cm$ above the bottom, will be _____ $cm s^{- 1}$ .

[Take $g = 10 {m s}^{- 2}$ ]

TestHub · Accepted Answer

Pressure at point 1 is P 1 = P 0 , Pressure at point 2 is P 2 = P 0 + m g A Applying Bernoulli's equation at top and bottom P 1 + 1 2 ρ v 1 2 + ρ g h 1 = P 2 + 1 2 ρ v 2 2 + ρ g h 2 ⇒ P 0 + 1 2 ρ v 2 + 0 = P 0 + m g A + 0 + ρ g h ⇒ 250 5 + 10 3 × 10 × 0 . 4 = 1 2 × 10 3 × v 2 v = 3 m s - 1 = 300 cm s - 1

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