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HW_20_Soln

# HW_20_Soln - From Buckingham Π the pertinent variables are...

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ME 309 Fall 2008 Section 2 (Merkle) Homework # 20 Due Fri 17 Oct 2008 Problem 20-1 . A water pump with impeller diameter of 600 mm is to be designed to move 0.4 m3/ s when running at 800 rpm. Testing is performed on a ½ scale model running at 2000 rpm using air at 300 K as the working fluid. For similar conditions (neglecting Reynolds number effects), what will be the model flow rate? If the model draws 75 W what will be the power requirement of the prototype. Pump performance parameters depend upon seven quantities: the head rise, h [ m ], the volumetric flow rate, Q [ m 3 /s ], the rotor speed , N [ rpm ], the impeller diameter, D [ m ], the fluid density, ρ [ kg/m 3 ], the fluid viscosity, μ [ kg/ ( m s )] and the power required, P [ W ]. (See pg 290 in text, but note I have used a different definition for head rise. You may use either one, but be consistent.) Solution: Given: List of pi terms from Buckingham, class or text. Assumptions: Dynamic similarity (including geometric and kinematic similarity)

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Unformatted text preview: From Buckingham Π , the pertinent variables are: 3 1 ND Q = Π , 5 3 2 D N P = Π Density of water = 997 kg/m 3 Air used in model testing is incompressible: 3 177 . 1 300 * 3 . 8314 97 . 28 * 101325 m kg air = = Analysis: For dynamic similarity, PI groups are same for model and prototype. Flow rate: 3 3 1 P M D N Q D N Q P P M M = = Π Solve for model flow rate: s m s m D N D N Q Q P M P M P M 3 3 3 3 3 3 125 . 600 800 300 2000 4 . = • • = = (Note, can use ratios of rpm or of frequency—no need to convert for a ratio) Power Required: 5 3 5 3 2 P P P P M M M M D N P D N P = = Π Solve for power required by prototype: kW W D N D N P P M M M P P P M P 130 000 , 130 300 2000 177 . 1 600 800 997 75 5 3 5 3 5 3 5 3 = = • • • • = = Comment: Note it takes more power to pump water than air. Problem 20-2 . Work Problem 7.58 in text/ Problem 20-3 Work Problem 7.61 in text....
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HW_20_Soln - From Buckingham Π the pertinent variables are...

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