Question

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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. = 20 (1-PIR) 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-r IR) density, P. velocity, U. incoming area, A density, P mounting stand

Answer 1

mass flow rate (m) = 1; U; A; 1 X 100 X m = = lokg/s do 10 Now, in exhaust jet dostos discharge (0) - s de de=uda AZXR² dA= 2a8dr 2ardr & Foo =*/2011) jord R Yau Yau. R² 82 YTU ४ 4R² 2 0 & 6= TR²U Vaug But considering uniform average relocity Hang 8 = Vary XA XaR² – (11) from ůl und ) larg - U = 600 ml

s pouda 2 ) P2 = 1.333 m larg (6) Thrust of turbojet engine final monentum (P2) - initial momentum 28.) B = SdP = Sam. dm.co dm = To Yoda, dA=2ardr 2ardr +th 212 rar R² 8 10 Fook 1.333 fo (7R²) u² 6 1.333 (so Ao Harg) Harg (Larg=u) (f: A; U; = Po Allung = n) continuity equation Thrust of turbojet engive P2-P, (1-333 mx600) - in (100) Toom - 7000 N 284 8x Up ( 2 + 2 + 6R4

(6) It jet had uniform velocity, u then final momentum (12) = nu Thrust = mu m (U-U;) 10 (600 - 100) mui 11 sooo N.