Question

turbojet engine in a wind tunnel receives are velocity of U - 100 m/s and a density of A-1 kg/m". The velocky is uniform and the cross-sectional area of the approaching stream which enters the engine is 0.1m. 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: - 20 (1-PIR') where the constant U- 600 m/s and Ris 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 A-05 kg/m'. Determine the average velocity of the exhaust jet Find the thrust of the turbojet engine 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 roshly true in practice) R velocity 4-2011 density HINDI ng stand

Answer 1

Given situation is as follows ir Те 2. = 20(1-2) Given that U = Loom's Pi = 1 kg/rom? U=600m/s po 2005 kg/rom Ai 2001 m2

exhaust jet, Average relocit of To = luoda Ао Izarder - ular 23 R r4 - 40 sem 703 , dar R2 - 40 R² SR3 2 -] 를 그 = 40 R² 3R² ol Х 11 R² +2u 10 lo

(4 f throust - (-10oo + 32.4 x 109 xar?)N Conservation of mass smin a mout =) Pi U; A; = P to no > Doa PU; Ai Toy

=) A = 1x100x ood 0.5X I 20 A. m2 36 Now, Efferred Mooo -1000 + 32.4 x lota Ethrust = 8 KN IN C) 2 Ai P. Conservation of mass som - shout PjA; U = PAU Pj Ajo Pos 0 ㅗ 30 m2

6 Firhoust = -1; A; ut Pau 1000 + 6oooN. thrust = 5kN throug