Explanation Given information: The mass ( m ) of the engine is 3000 kg . The density ( ρ ) of air is 1.21 kg / m 3 . The diameter ( d ) of slipstream is 2.2 m . Calculation: Consider F is the force exerted on the slipstream of one engine. Sketch the free body diagram of airplane as shown in figure 1. Refer to Figure 1. The force exerted on the airplane is − 2 F shown above diagram. Find the force ( F ) exerted on slipstream as shown below: ∑ M B = 0 0.3 m g − ( 1.6 ) ( 2 F ) = 0 (1) Substitute 3 , 000 kg for m 9.81 m / s 2 for g in Equation (1). 0.3 ( 3000 × 9.81 ) − ( 1.6 ) ( 2 F ) = 0 8 , 829 − 3.2 F = 0 3.2 F = 8 , 829 F = 2 , 759.06 × 10 3 N Sketch the free body diagram of slipstream as shown in figure 2. Refer to Figure 2. Find the mass flow rate ( d m d t ) using the Equation as follows: mass = density × volume = density × ( area × length ) Δ m = ρ A B ( Δ l ) (2) Substitute ( v B × Δ t ) for Δ l in Equation (2). Δ m = ρ A B v B ( Δ t ) Δ m Δ t = ρ A B v B Δ m Δ t = d m d t = ρ A B v B Express the force exerted on the slipstream to find the velocity of the air using as follows: F = d m d t ( v B − v A ) (3) Consider the speed v A far upstream

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

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Chapter 14.3, Problem 14.73P

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Find the velocity of the air.

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Find the velocity of the air.

Solution Summary: The author calculates the force exerted on the slipstream of one engine by sketching the free body diagram of airplane.

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