Explanation Given: Velocity of water flowing into the bend fitting ( V A ) is 6 m / s . Calculations: The flow of the fluid is assumed to be steady, incompressible, and inviscid. So, the density of ideal fluid water is constant. Consider the fixed control volume consists of bend fitting, fixed support and the water it contains. Draw the free body diagram for the control volume as in Figure (1). Determine the discharge of water from the pipe ( Q ) . Q = V C A C = ( 6 m / s ) [ π ( 0.075 m ) 2 ] = 0.03375 π m 3 / s The flow of water is exposed to atmosphere at B . Thus pressure at B is p B = p atm = 0 The diameter of the pipe fitting remains constant. Thus, the velocity at sections B and C remains same. V B = V C = 6 m / s From the Bernoulli’s equation, the pressure at C ( p C ) can be determined as p C = p B = 0 For the steady and incompressible flow, the linear momentum equation in x direction can be applied as ∑ F = ∂ ∂ t ∫ cv V ρ d V + ∫ es V ρ V ⋅ d A ∑ F x = 0 + ( V C ) x ρ w ( − V C A C ) + ( V B ) x ρ w ( V B A B ) − C x = ( V C ) x ρ w ( − Q ) + ( V B ) x ρ w ( Q ) − C x = [ ( 6 m / s ) ( 1000 kg / m 3 ) ( − 0.03375 π m 3 / s ) + ( − 6 sin 30 ° m / s ) ( 1000 kg / m 3 ) ( 0.03375 π m 3 / s ) ] C x = 954.26 N Thus, horizontal component developed at support C is 954.26 N _

2nd Edition

ISBN: 9780134626055

Author: HIBBELER

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 6, Problem 53P

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The horizontal and vertical force components, and the moment developed at support C to hold the fitting.

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Chapter 6, Problem 52P

Chapter 6, Problem 54P

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