HW 5 - ASE 362KI Assignment 5 Thursday, February 14I 2007...

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Unformatted text preview: ASE 362KI Assignment 5 Thursday, February 14I 2007 We are not quite ready to move on to questions on oblique shocks so here are some problems on topics we have covered — all are from old mid-semester exams. 1) 2) 3) in many engineering flow problems there is a transfer of heat from the flowing gas to its surroundings (or vice-verse). An example would be a heat exchanger. The velocity of the gas is affected by the heat interaction. We find in practice that when the gas velocity is “small”, the flow is accelerated by heat addition, but when the flow velocity is ‘large’ heat addition decelerates the gas. The transition point between the flow acceleration and flow deceleration occurs when 6q/dv is zero (oq is the heat added, v is the velocity). At this transition point (when 6q/dv=0) we find that v=,/yRT = 3 (Le. M=1). Assuming 1-D, steady flow, prove this result. [Hintz start with the energy equation in differential form and assume a perfect gas.] An aircraft flies supersonically at 10km altitude on a “standard” day. (Static pressure and temperature at that altitude are 26.5kPa and 223.3K respectively). The true air speed of the aircraft is 659 m/s. A pitot tube attached to the aircraft is used to sense stagnation pressure which is then converted to flight Mach number by an onboard computer. However the computer programmer has made an error -‘he (not a UT graduate) has assumed that the gas deceleration to zero velocity at the probe face occurs isentropically rather than via a normal shock. What is the difference between the true airspeed and the airspeed calculated by the computer program? The slab shown is moving at 270 m/s into still ambient air whose static temperature and pressure are 293K and 105 Nm'2 respectively. The slab is at zero angle of attack so face ABCD is normal to the oncoming flow. Assuming that the drag only comes from pressure forces calculate the drag (you can take the pressure on face EFGH as being the undisturbed ambient value). If you had assumed that the flow had been incompressible how much in error would your drag estimate have been? Now assume that the slab velocity increases to 540 m/s. By what factor does the drag increase over its value when the slab is moving at 270 m/s? 4) 2 kg/s of airflow through a convergent duct. You are told that P1=150kPa, T1=35OK, P2=101.3kPa, T2=320K and that A1=0.1m2. Calculation of the entropy change between stations 1 and 2 reveals that the flow is non-isentropic. Calculate the axial force on the duct. a z [(I-~\j(2k}> (223-'3>3h2 6§°t “‘- H1 ‘ ___. 2301.51 1-20 90L —‘ (O '62.Cg>(26§00> [l0 ‘6 ’11} 6-315“ ?01'P\ v: H ,s (M‘MWe/f ism/M‘s Tw- AkocA m. 6915‘ = [ti-(~Z>sz>] 1?}CIH-K/265‘oo ’- 3.: 4.) . P VJ I u I N u .‘ f1 7— V.'.' ,. ., 1;; , . 7 ,, 7 ., . )r/Yfim , SuLsam'c -‘ . .USt. “Pow: ,.Poo ,.. 2 Pa. («4 A 8CD. ’. . a, meat * Ur we km W, as, ,, ,_ ab. 4" _‘ E: ,, ,_ , M..-“ A. A,” ,. a 2' RTE” 22—14! 50 SHEETS 22442 100 SHEETS 225! KM 2200 SHEETS 9 \. \M_,/ 9%. AW! [IA : § i x . . v i i E . 1 ‘ i . 1 1 a 3 E c E 3 m 3 5 E. x i E l I g i g i E ° Wists WV" Wt Mow.» P|.Md 0,} and A; > Fwd- ‘Pmfl; AL: Vlamo‘ V\ 0‘0 gflv‘m . . :- ,V|A\ ’2. = (ISoxw3) (V0 (04) (2%f>(zsé> .. v, -_ 8-301 M]; E (loo§>(3§o —- 12°. «a W2 - (Ilia): . 1 1 “3/(Divz Fz/QT'Z :. _Qm3oo)/(ze})(szo> ; |-\o’$ kblufl A2 = C2>/-(‘-i03>(w§-°D = _ F +- ( .S‘OJOOO god) — (Magoo x 04303-3?) -_ z(z»r§'°\- ia-sfi) >- I: 1" [pl-253+!- " H'ég’oz' F = ‘l117-0N ...
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This note was uploaded on 02/14/2012 for the course ASE 362K taught by Professor Dolling,d during the Spring '07 term at University of Texas at Austin.

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HW 5 - ASE 362KI Assignment 5 Thursday, February 14I 2007...

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