MAE305_pset02s - M&AE 3050 Problem Set 2 Solution Fa 2009...

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M&AE 3050 Problem Set 2 Fa 2009 Solution 1. The Standard Sea Level values of temperature T and pressure p are T SL = 288 . 15 K and p SL = 101 , 325 Pa. Using the formulae derived in class and the temperature proFle given in ±ig. 3.4 in Anderson, calculate the pressure and density of air at (a) 10,000 m in the Standard Atmosphere (b) 20,000 m in the Standard Atmosphere ±or each altitude, compare your values with the tabulated values in Appendix A of Anderson and comment on any di²erences. Solution (a) The temperature at 10,000 m is given by T (10 , 000) = T SL + a (10 , 000 0) = 288 . 15 6 . 5 × 10 - 3 × 10 4 = 223 . 15 K , where a = dT /dh is the so-called adiabatic lapse rate . We can use the relationship for the pressure variation for the linear temperature proFle p = ± T T SL ² - g 0 / ( aR ) p SL The exponent g 0 / ( aR )isg ivenby 9 . 81 / ( 0 . 0065 × 287 . 05) = 5 . 258. Substi- tuting this above yields p (10 , 000) = ± 223 . 15 288 . 15 ² 5 . 258 101 , 325 = 0 . 2608 × 101 , 325 = 26 , 422 Pa , The density is given by ρ = ± T T SL ² - g 0 / ( aR ) - 1 ρ SL , where ρ SL = p SL /RT SL = (101 , 325) / (287 . 05 × 288 . 15) = 1 . 225 kg/m 3 . Substitut- ingintotheexpress ionfor ρ yields ρ = ± 223 . 15 288 . 15 ² (5 . 258 - 1) =0 . 3367 × 1 . 225 = 0 . 4125 kg / m 3 . The tabulated values for h G =10 , 000 m are p =26 , 500 Pa and ρ . 41351 kg/m 3 , which are very close to our calculations. The error is due in part to the fact that we are solving for h , 000 m, not h G , 000 m. Nevertheless, the error is acceptably small.
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This note was uploaded on 10/02/2010 for the course MAE 3050 taught by Professor Caughey during the Fall '08 term at Cornell University (Engineering School).

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MAE305_pset02s - M&AE 3050 Problem Set 2 Solution Fa 2009...

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