Problem 4.58 - Problem 4.58 Given Data on flow through a...

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Problem 4.58 [Difficulty: 3] Given: Data on flow through a control surface Find: Net rate of momentum flux Solution: CS dA V V r r ρ Basic equation: We need to evaluate Assumptions: 1) Uniform flow at each section From Problem 4.24 V 1 10 ft s = A 1 0.5 ft 2 = V 2 20 ft s = A 2 0.1 ft 2 = A 3 0.6 ft 2 = V 3 5 ft s = It is an outlet ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) [ ] ( ) [ ] ( ) [ ] j A V A V i A V A V A V j V i V A V j V A V i V A V j V i V A V j V A V i V A V V A V V A V V dA V V CS ˆ 60 cos ˆ 60 sin ˆ 60 cos ˆ 60 sin ˆ ˆ ˆ 60 cos ˆ 60 sin ˆ ˆ 3 2 3 2 2 2 3 2 3 1 2 1 3 3 3 3 2 2 2 1 1 1 3 3 3 3 2 2 2 1 1 1 3 3 3 2 2 2 1 1 1 + + = + + = + + = + + = ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ r r r r r r r r r r r r r r r r r Then for the control surface ( ) [ ] = + 60 sin 3 2 3 1 2 1 A V A V ρ
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