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Unformatted text preview: Spring 2006 1 ME 201 Thermodynamics Exam #1 Solution Problem 1 As shown in the drawing below, two pipes merge into one. Determine the velocity (in m/s) of water in the merged pipe under the following conditions: Pipe #1: diameter: 0.03 m, water flow rate: 0.75 kg/s Pipe #2: diameter: 0.06 m, water flow rate: 1.07 x 103 m 3 /s Pipe #3: diameter: 0.04 m Density of water: 996 kg/m 3 Flow area of pipe: π D 2 /4 Solution: We begin by writing our continuity relation for pipe #3. 3 3 3 v A m & ¡ ρ = Solving for the velocity in pipe #3 gives 3 3 3 A m v ρ = ¡ & We are given ρ = 996 kg/m 3 and 2 3 2 2 3 3 m 10 x 2566 . 1 4 ) 04 . ( 4 D A = π = π = For the mass flow rate in pipe #3, we use the conservation of mass equation, which gives 2 1 3 m m m ¡ ¡ ¡ + = Pipe #1 Pipe #2 Pipe #3 ME 201 Thermodynamics Spring 1998 2 where s / kg 75 . m 1 = & kg/s 1.0657 ) 10 x 07 . 1 )( 996 ( V m3 2 2 = = ρ = & & Then s / kg 8157 . 1 0657 . 1 75 . m 3 = + = & So that m/s 1.45 ) 10 x 66 (996)(1.25(996)(1....
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This note was uploaded on 07/25/2008 for the course ME 201 taught by Professor Somerton during the Spring '06 term at Michigan State University.
 Spring '06
 SOMERTON

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