Question

Exhaust gases entering a convergent nozzle have a total pressure (Pt) of 200 kPa and total temperature (Tt) of 800 K. The gases exit the nozzle into ambient air at a static pressure (Po) of 101.3 kPa. Assuming that y 1.33 and R-287 J/(kg.K), determine the critical pressure ratio.

Answer 1

critical pressure ratio = 108.07 k pa

Step-by-step explanation:

Pt = 200 k Pa

Tt = 800 k

Po = 101.3 k Pa

y = 1.33

R = 287 J/(kg.k)

critical pressure ratio ( Pc )

`(Pc)/(Pt)` =
`((2)/(y+1))^{(y)/(y-1) }` ------- equation 1

Pt given as 200 k Pa

Y = 1.33

back to equation 1

`(Pc)/(Pt)` =
`((2)/(1.33 + 1))^{(1.33)/(1.33 - 1) }`

Pc = 200 * 0.5404 = 108.07 k pa

Answer 2

0.351

Step-by-step explanation:

n=1/(γ−1) = 1/ (1.33-1)= 3.03

critical pressure ratio

`p_2/p_1 = (2)/(n+1) ^{((n)/(n-1) )}\\\\= (2)/(3.03+1) ^{((3.03)/(3.03-1) )}\\\\= 0.496^(1.493)\\\\= 0.351`