Substituting Eqs 3 78 And 3 80 Into 3 79 2 2 T2 T Gm 3 1 Y M 1 Yn M2 M 3 81 Since 22 01 P2 Pi T1 T2 1 (116.43 KiB) Viewed 32 times
please derive these 4 equations.
Substituting Eqs 3 78 And 3 80 Into 3 79 2 2 T2 T Gm 3 1 Y M 1 Yn M2 M 3 81 Since 22 01 P2 Pi T1 T2 2 (35.28 KiB) Viewed 32 times
Substituting Eqs. (3.78) and (3.80) into (3.79), 2 2 T2 T Gm (3) 1 + y M 1+yN M2 M (3.81) Since 22/01 = (p2/pı)(T1/T2), Eqs. (3.78) and (3.81) yield 2 P2 C)) 1 + y M 1 + y M M M2 (3.82) P1 The ratio of total pressures is obtained directly from Eqs. (3.30) and (3.78), 1 y/(y-1) -M2 Po2 1+ y M 1+ y M 1 + 2 V 1 + 2 Ροι (3.83) M The ratio of total temperatures is obtained directly from Eqs. (3.28) and (3.81), y - 1 2 1+ M? TO Το, = 6+ 1+yM 1 + YM M2 M 2 (3.84) y - 1 1+ M] 2
From Eq. (3.20) and the definition of Mach number, U2 1/2 M₂ (T2 M2 42 M1 di CD ) 11 M1 (3.80) c
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