A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20 . 0 m below the water level. If the rate of flow from the hole is 3 . 08 × 10 - 5 m 3 s - 1 , then the diameter of the hole is [Take g = 10 m s - 2 ]

Question

A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20 . 0 m below the water level. If the rate of flow from the hole is 3 . 08 × 10 - 5 m 3 s - 1 , then the diameter of the hole is [Take g = 10 m s - 2 ], 1 . 0 mm, 1 . 2 mm, 1 . 4 mm, 1 . 6 mm

MARKS App · Accepted Answer

Velocity of the efflux for an orifice at depth h can be written as, v = 2 g h = 2 × 10 × 20 = 20 m s - 1 Now, volume flow rate can be written as, area of orifice × velocity of efflux ⇒ 3 . 08 × 10 - 5 = π d 2 4 × 20 ⇒ d = 4 × 3 . 08 × 10 - 5 π × 20 = 1 . 4 mm

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