Question

A turbojet engine in a wind tunnel receives air at a velocity of U;= 100 m/s and a density of p.= 1 kg/m'. The velocity is uniform and the cross-sectional area of the approaching stream which enters the engine is A = 0.1 m². The velocity of the exhaust jet from the engine, however, is not uniform but has a velocity which varies over the cross-section according to: u. = 2U (I-YIR) where the constant U= 600 m/s and R is the radius of the jet cross-section. Radial position with the axi-symmetric jet is denoted by r. The density of the exhaust jet is uniformly p=0.5 kg/m a. Determine the average velocity of the exhaust jet. b. Find the thrust of the turbojet engine. c. Find what the thrust would be if the exhaust jet had a uniform velocity, U. Assume the pressures in both the inlet and exhaust jets are the same as the surrounding air and that mass is conserved in the flow through the engine (roughly true in practice) R velocity, U. - 20(1-PIR) density, P. velocity, U. incoming area, A density, P. mounting stand

Answer 1

(a) first will calculate n = 1; U; Aj 10 kgls mass flow rate (in) (1) (100) (0.1) du exhaust jet cross section. Area (4) = R² da. aardo dm = PoudA 83 20 zardo m sam (- 8 ) R im zul. 20 8284 2 4R2 do to UaR² for average xelozity (uav) in = to Yan 'A Pou a R² Po uar (8R²) = you are Uow - u = 600 mls

(6) For thrust (E) F = Pf - Pi Pf s find morenten. Þ; initial morentum B im nav For Pipe shape, momentum correction factor Pf = 9 Bllo A. Marg). You (n = Po Ao You - P; 4; 4;) PE 4 m lau 3 F = 4 (10) 1600) – (10) (1000) F = 7000 N of For uniform velocity there is no need morentum correction factor mu 10X 6000 6000 at F = Pf- Pi 6000 - 10 (100) 5000 N Fr