Explanation Given: The velocity at A ( V A ) is 6 m/s . The diameter at A ( d A ) is 300 mm. The diameter at B ( d B ) is 100 mm. Calculation: The assumption made in the problem is given as follows: The Point B is in open to atmosphere so the pressure at B ( p B ) is zero. The Datum A and B is coincide with same horizontal streamline so the datum energy z A = z B = z . Consider that the control volume to be the water in the pipeline. Refer Appendix A, “Properties of air at standard atmospheric pressure 101.3 kPa vs. temperature” in the textbook. The density of air (at A ) is 1.127 kg/m 3 for corresponding temperature 40 ° C . The density of air (at B ) is 1.292 kg/m 3 for corresponding temperature 0 ° C . Calculate the velocity at A using continuity Equation. ∂ ∂ t ∫ c v e d V + ∫ c s e V ⋅ d A = 0 0 − ( ρ a ) A V A A A + ( ρ a ) B V B A B = 0 − ( ρ a ) A V A A A + ( ρ a ) B V B A B = 0 − ( ρ a ) A V A × ( π 4 × d A 2 ) + ( ρ a ) B V B ( π 4 × d B 2 ) = 0 [ − 1.127 × 6 × ( π 4 × ( 300 mm × 1 m 1 , 000 mm ) 2 ) + 1

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 5, Problem 34P

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