Fluid II-solutions

Fluid II-solutions - le (txl65) Fluid II mohanty (81440)...

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le (txl65) – Fluid II – mohanty – (81440) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. 001 10.0 points A ±ountain sends a stream o± water 23 . 8 m up into the air. I± the base o± the stream is 8 . 9 cm in diame- ter, what power is required to send the water to this height? The acceleration o± gravity is 9 . 8 m / s 2 . Correct answer: 31339 . 3 W. Explanation: Let : h 1 = 23 . 8 m , d = 8 . 9 cm = 0 . 089 m , r = 4 . 45 cm = 0 . 0445 m , and g = 9 . 8 m / s 2 . Using conservation o± energy, 1 2 mv 2 = mg h v = r 2 g h = R 2 (9 . 8 m / s 2 ) (23 . 8 m) = 21 . 5981 m / s is the velocity o± the stream at its base. The ²ow rate at the base is π r 2 v = π (0 . 0445 m) 2 (21 . 5981 m / s) = 0 . 134365 m 3 / s . Using the density o± water as 1000 kg / m 3 , we see that 134 . 365 kg o± water emerges ±rom the ±ountain each second. m t = ρπ r 2 v = (1000 kg / m 3 ) π (0 . 0445 m) 2 × (21 . 5981 m / s) = 134 . 365 kg . Thus, each second, su³cient work is done to raise 134 . 365 kg to a height o± 23 . 8 m or P = W t = mg h t = ρπ r 2 v g h t = (1000 kg / m 3 ) π (0 . 0445 m) 2 × (21 . 5981 m / s) (9 . 8 m / s 2 ) 23 . 8 m 1 s = 31339 . 3 W . 002 10.0 points A styro±oam slab has a thickness o± 10 . 3 cm and a density o± 319 kg / m 3 . What is the area o± the slab i± it ²oats just awash (top o± slab is even with the water sur- ±ace) in ±resh water when a 65 . 1 kg swimmer is aboard? The density o± water is 1000 kg / m 3 . Correct answer: 0 . 928104 m 2 . Explanation: Let : d = 10 . 3 cm , ρ s = 319 kg / m 3 , and m = 65 . 1 kg . Since the slab ²oats awash, the buoyant ±orce is B = ρ w V g = ρ w dAg , and is equal in magnitude to the weight o± the slab and the swimmer: ρ w dAg = ρ s dAg + mg A = m d ( ρ w - ρ s ) = 65 . 1 kg
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This note was uploaded on 04/05/2011 for the course SD ds taught by Professor Sdsd during the Spring '11 term at Tarrant County.

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Fluid II-solutions - le (txl65) Fluid II mohanty (81440)...

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