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

Answer:

critical pressure ratio = 108.07 k pa

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 )

$\frac{Pc}{Pt}$ = $(\frac{2}{y+1})^{\frac{y}{y-1} }$  ------- equation 1

Pt given as 200 k Pa

Y = 1.33

back to equation 1

$\frac{Pc}{Pt}$ = $(\frac{2}{1.33 + 1})^{\frac{1.33}{1.33 - 1} }$

Pc = 200 * 0.5404 = 108.07 k pa

Answer 2

Answer:

0.351

Explanation:

n=1/(γ−1) = 1/ (1.33-1)= 3.03

critical pressure ratio

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