written 3.0 years ago by |
Derivation
Expression for Stagnation Pressure (Ps)
PsP1=[(1+k−12M21)KK−1]..(i)
Expression for Stagnation Density (ρs)
For Adiabatic process
(ρ1ρs)=(p1ps)1Kor(ρsρ1)=(psp1)1k
(Taking reciprocal)
ρs=ρ1[psp1]1K
Substituting the value of (psp1) from equation (i),
ρs=ρ1[(1+K−12M21)KK−1]1Kρs=ρ1[1+K−12M21]1K−1..(ii)
Above equation gives value of Stagnation Density.
Expression for Stagnation Temperature Ts
as Psρs=RT
For the stagnation point, we have equation of state as Psρs=RTs
∴Ts=1RPsρs
Substituting the value of Ps and ρs from equations (ii), we have
Ts=1RP1[1+(K−12)M21](KK−1)ρ1[1+(K−12)M21]1K−1=1RP1ρ1[1+(K−12)M21](KK−1)−(1K−1)=1RP1ρ1[1+(K−12)M21](K−1K−1)=P1ρ1R[1+(K−12)M21]=T1[1+(K−12)M21]
(∵P1ρ1=RT1)
Ts=T1[1+(K−12)M21]
Above equation gives value of Stagnation Temperature.