Explanation Given information: The volumetric flow rate ( Q ) is 500 gal/min. The magnitude of velocity ( v ) is 48 ft/s. The constant speed ( v 1 ) is 12 ft/s. Calculation: Find the mass flow rate ( d m d t ) using the relation: d m d t = ρ Q = γ g × Q Here, γ is density of the fluid and g is acceleration due to gravity. Substitute 62.4 lb/ft 3 for γ , 32.2 ft/s 2 for g , and 500 gal/min for Q . d m d t = 62.4 lb/ft 3 32.2 ft/s 2 × ( 500 gal/min × 0 .002228 ) ft 3 /s = 2.159 slug/s Write the expression for upstream velocity vector. u = v i − ( − v 1 i ) Substitute 48 ft/s for v and 12 ft/s for v 1 . u = 48 i − ( − 12 i ) = 60 i For the moving frame: Find the reference mass flow rate ( d m ′ d t ) using the relation: d m ′ d t = u v d m d t Substitute 48 ft/s for v , 2.159 slug/s for d m d t , and 60 ft/s for u . d m ′ d t = 60 48 × 2.159 = 2.6987 slug/s Write the expression for velocity vectors: u = u i u 1 = u ( cos 30 ° i + sin 30 ° j ) u 2 = v ( cos 45 ° i − sin 45 ° j ) Draw the free body diagram of the nozzle using impulse momentum principle as in Figure (1).

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

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