Problem 5: A small circular hole 6.00 mm in diameter is cut in the side of a large water tank, 14.0 m below the water level in the tank. The top of the tank is open to the air. Find (a) the speed of efflux of the water and (b) the volume discharged per second.

Solution

Given Dia of the hole = d = 6 mm = 6 × 10^{-3} m Height of the water cloumn above the hole = 14 m

Required

(a) Speed of efflux

(b) Volume (V) discharge rate

Required

(a) Speed of efflux

(b) Volume flow rate

Formulae

(1) Torricelli’s Theorem,

(2) Volume flow rate

(3)

Comprehension: In Torricelli’s theorem, ‘h’ is the height of water level from the hole. Similarly, it is given that the top of the tank is open, therefore, pressure on water is constant which atmospheric pressure.

Calculation: (a) Apply formuls (1) to find ‘v’, velocity of efflux.

(b) Apply formula (2) to find the volume flow rate by putting the value of ‘A’ from formula (3) and ‘v’ from equation (1),

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