Explanation Given information: The discharge of nozzle is 40 ft 3 / min . The velocity ( v A , v B ) of magnitude is 18 m / s . Calculation: Find the mass flow rate using the relation as follows: d m d t = γ g Q (1) Here, d m d t is mass flow rate and g is acceleration due to gravity. Substitute 40 ft 3 / min for Q , 32.2 ft / s 2 for g , and 62.4 lb / ft 3 for γ in Equation (1). d m d t = 62.4 lb / ft 3 32.2 ft / s 2 × ( 40 ft 3 min ) ( 1 min 60 s ) = 1.29193 lb ⋅ s / ft Sketch the free body diagram as shown in Figure 1. Refer to Figure 1. Find the vertical ( C y ) component of reaction as follows: Taking moment D apply the impulse momentum principle: − ( Δ m ) ( v A sin 60 ° ) ( 15 12 ) + ( Δ m ) ( v A cos 60 ° ) ( 23 12 ) − C ( Δ t ) ( 15 12 ) = Δ m v B ( 3 12 ) 15 12 C = ( Δ m Δ t ) v A [ − 15 12 sin 60 ° + 23 12 cos 60 ° − 3 12 ] (2) Substitute 1.29193 lb ⋅ s / ft for d m d t , 75 ft / s for v B , and 75 ft / s for v A , in Equation (2). 15 12 C y = ( 1.2913 ) ( 75 ) [ − 1.0825 + 0.958 − 0.25 ] 15 12 C y = 96.8475 [ − 0.3745 ] 15 12 C y = − 36

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Chapter 14.3, Problem 14.65P

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Find the component of reaction at C and D.

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Find the component of reaction at C and D .

Solution Summary: The author calculates the mass flow rate and acceleration due to gravity using the relation as follows: gammagQ.

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