P15_047 - 2 2 47. (a) We use the Bernoulli equation: p1 + 1...

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47. (a) We use the Bernoulli equation: p 1 + 1 2 ρv 2 1 + ρgh 1 = p 2 + 1 2 ρv 2 2 + ρgh 2 ,whe re h 1 is the height of the water in the tank, p 1 is the pressure there, and v 1 is the speed of the water there; h 2 is the altitude of the hole, p 2 is the pressure there, and v 2 is the speed of the water there. ρ is the density of water. The pressure at the top of the tank and at the hole is atmospheric, so p 1 = p 2 .S incethe tank is large we may neglect the water speed at the top; it is much smaller than the speed at the hole. The Bernoulli equation then becomes ρgh 1 = 1 2 ρv 2 2 + ρgh 2 and v 2 = p 2 g ( h 1 h 2 )= p 2(9 . 8m / s 2 )(0 . 30 m) = 2 . 42 m / s . The flow rate is A 2 v 2 =(6 . 5 × 10 4 m 2 )(2 . 42 m / s) = 1 . 6 × 10 3 m 3 /
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