Assume an $80\%$ bell nozzle with a parabolic approximation to the thrust$-$optimized nozzle contour $($see Lecture $14,$ Slide $31).$ Determine nozzle length Ln$.$ Provide a scaled sketch of the nozzle, including the curvatures of radii upstream and downstream of the throat, and the angles theta$\_$i and theta$\_$e at the start and end of the parabolic nozzle, respectively. Calculate the divergence loss.

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NASA$-$GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA$2,$ FEBRUARY $5,2004$

BY BONNIE MCBRIDE AND SANFORD GORDON

REFS: NASA RP$-1311,$ PART I, $1994$ AND NASA RP$-1311,$ PART II$,1996$

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### CEA analysis performed on Sat $09-$Mar$-202423$:$33$:$19$

# Problem Type: "Rocket" $($Infinite Area Combustor$)$

prob case$=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_9372$ ro equilibrium

# Pressure $(1$ value$)$:

p$,$bar$=78\mathrm{.}9539$

# Chamber$/$Exit Pressure Ratio $(1$ value$)$:

pi$/$p$=396\mathrm{.}04$

# Oxidizer$/$Fuel Wt$.$ ratio $(1$ value$)$:

o$/$f$=2\mathrm{.}8$

# You selected the following fuels and oxidizers:

reac

fuel RP$-1$ wt$\%=100\mathrm{.}0000$

oxid O$2($L$)$ wt$\%=100\mathrm{.}0000$

# You selected these options for output:

# short version of output

output short

# Proportions of any products will be expressed as Mass Fractions.

output massf

# Heat will be expressed as siunits

output siunits

# Input prepared by this script:$/$var$/$www$/$sites$/$cearun$.$grc$.$nasa.gov$/$cgi$-$bin$/$CEARU

N$/$prepareInputFile$.$cgi

### IMPORTANT: The following line is the end of your CEA input file!

end

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM

COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR

Pin $=1145\mathrm{.}1$ PSIA

CASE $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

REACTANT WT FRACTION ENERGY TEMP

$($SEE NOTE$)$ KJ$/$KG$-$MOL K

FUEL RP$-11\mathrm{.}0000000-24717\mathrm{.}700298\mathrm{.}150$

OXIDANT O$2($L$)1\mathrm{.}0000000-12979\mathrm{.}00090\mathrm{.}170$

O$/$F$=2\mathrm{.}80000\%$FUEL$=26\mathrm{.}315789$ R$,$EQ$.$RATIO$=1\mathrm{.}216309$ PHI,EQ$.$RATIO$=1\mathrm{.}216309$

CHAMBER THROAT EXIT

Pinf$/$P $1\mathrm{.}00001\mathrm{.}7284396\mathrm{.}04$

P$,$ BAR $78\mathrm{.}95445\mathrm{.}6800\mathrm{.}19936$

T$,$ K $3714\mathrm{.}443535\mathrm{.}242023\mathrm{.}75$

RHO, KG$/$CU M $6\mathrm{.}182703\mathrm{.}812903\mathrm{.}1828-2$

H$,$ KJ$/$KG $-764\mathrm{.}28-1441\mathrm{.}13-6311\mathrm{.}72$

U$,$ KJ$/$KG $-2041\mathrm{.}29-2639\mathrm{.}17-6938\mathrm{.}08$

G$,$ KJ$/$KG $-41739\mathrm{.}9-40439\mathrm{.}9-28636\mathrm{.}6$

S$,$ KJ$/($KG$)($K$)11\mathrm{.}031411\mathrm{.}031411\mathrm{.}0314$

M$,(1/$n$)24\mathrm{.}18524\mathrm{.}53526\mathrm{.}864$

$($dLV$/$dLP$)$t $-1\mathrm{.}04740-1\mathrm{.}04301-1\mathrm{.}00052$

$($dLV$/$dLT$)$p $1\mathrm{.}80771\mathrm{.}77281\mathrm{.}0158$

Cp$,$ KJ$/($KG$)($K$)6\mathrm{.}77716\mathrm{.}74082\mathrm{.}0454$

GAMMAs $1\mathrm{.}13431\mathrm{.}12991\mathrm{.}1843$

SON VEL,M$/$SEC $1203\mathrm{.}51163\mathrm{.}5861\mathrm{.}3$

MACH NUMBER $0\mathrm{.}0001\mathrm{.}0003\mathrm{.}867$

PERFORMANCE PARAMETERS

Ae$/$At $1\mathrm{.}000041\mathrm{.}845$

CSTAR, M$/$SEC $1779\mathrm{.}81779\mathrm{.}8$

CF $0\mathrm{.}65371\mathrm{.}8715$

Ivac, M$/$SEC $2193\mathrm{.}23518\mathrm{.}9$

Isp, M$/$SEC $1163\mathrm{.}53330\mathrm{.}9$

MASS FRACTIONS

$*$CO $0\mathrm{.}329240\mathrm{.}315520\mathrm{.}21365$

$*$CO$20\mathrm{.}311250\mathrm{.}332860\mathrm{.}49297$

COOH $0\mathrm{.}000040\mathrm{.}000030\mathrm{.}00000$

$*$H $0\mathrm{.}001110\mathrm{.}000960\mathrm{.}00004$

HCO $0\mathrm{.}000030\mathrm{.}000020\mathrm{.}00000$

HO$20\mathrm{.}000230\mathrm{.}000150\mathrm{.}00000$

$*$H$20\mathrm{.}005320\mathrm{.}005050\mathrm{.}00470$

HCOOH $0\mathrm{.}000010\mathrm{.}000000\mathrm{.}00000$

H$2$O $0\mathrm{.}245190\mathrm{.}252650\mathrm{.}28805$

H$2$O$20\mathrm{.}000030\mathrm{.}000020\mathrm{.}00000$

$*$O $0\mathrm{.}011090\mathrm{.}008880\mathrm{.}00001$

$*$OH $0\mathrm{.}052910\mathrm{.}045740\mathrm{.}00055$

$*$O