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AE 422 HW 2 Solution

This document contains 5 homework problems about rocket propulsion for a flight propulsion course. Problem 1 involves calculating exhaust velocity, specific impulse, and mass flow rate for an isentropic nozzle. Problem 2 involves calculating mass values for a 3-stage rocket launching a payload into low Earth orbit. Problem 3 involves calculating performance parameters like mass flow rate and chamber pressure for a rocket booster. Problem 4 involves using EQL software to determine specific impulse for an oxygen-hydrogen rocket engine nozzle operating under equilibrium and frozen flow conditions. Problem 5 repeats the analysis for a solid propellant rocket nozzle.

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959 views7 pages

AE 422 HW 2 Solution

This document contains 5 homework problems about rocket propulsion for a flight propulsion course. Problem 1 involves calculating exhaust velocity, specific impulse, and mass flow rate for an isentropic nozzle. Problem 2 involves calculating mass values for a 3-stage rocket launching a payload into low Earth orbit. Problem 3 involves calculating performance parameters like mass flow rate and chamber pressure for a rocket booster. Problem 4 involves using EQL software to determine specific impulse for an oxygen-hydrogen rocket engine nozzle operating under equilibrium and frozen flow conditions. Problem 5 repeats the analysis for a solid propellant rocket nozzle.

Uploaded by

Hatim Alayed
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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AE 422 Flight Propulsion I - 201

Homework 2 - (Chapter 10)

Due Date: (15 October 2020)

Problem # 1
Exhaust gas with R = 0.375 kJ/kg-K and γ = 1.26 flows through an isentropic nozzle. If the gas
enters the nozzle at 100 atm and 4000 K and exits to a pressure of 1 atm, determine the following
for a choked nozzle throat:
(a) the exhaust velocity Ve
(b) The specific impulse Isp
(c) The mass flow rate and ideal thrust for a throat area At of 0.1 m2
Problem # 2
Consider a three-stage rocket of lunching 1000-kg payload on low Earth orbit. The effective
velocity is divided equally for each stage. Using a solid propulsion system (C= 2440 m/s) in each
stage, find the following:
(a) Total mass of the rocket before lunching.
(b) Total mass and payload mass for each stage.
(c) Dead weight mass for each stage.
Problem # 3
A rocket booster using H2-O2 requires an ideal thrust of 100,000 lbf at a design altitude of 80 kft.
The booster will have a chamber temperature of 4840°R and a throat area of 0.5 ft2. Assuming a
specific impulse of 400 s and a calorically perfect gas with γ = 1.26 and R = 173.6 ft-lbf/lbm-°R,
determine the following:
a) Mass flow rate
b) Characteristic velocity C*
c) Chamber pressure Pc
d) Effective exhaust velocity C at 80-kft altitude
e) Ideal thrust coefficient CFi at 80-kft altitude
f) Nozzle expansion ratio ε and exit diameter
g) Altitude that flow in the nozzle is just separated (assume separation when Pa > 3.5 Pwe)
h) Ideal thrust at sea level
Problem # 4
Determine the Isp of the oxygen-hydrogen rocket engine with a chamber temperature of 3200 K
and an oxidizer-to-fuel mixture ratio by weight of 3.0:1 using the EQL software for both
equilibrium and frozen flow through the nozzle. The rocket engine has a chamber pressure (Pc) of
100 atm and an exit pressure Pe of 1 atm. Assume isentropic flow and perfect expansion.
- In this problem, you will learn how to use software by yourself.

Oulet (2) Oulet (2)


Inlet (1)
Equilibrium Frozen

𝑽 = √𝟐(𝒉𝟏 − 𝒉𝟐)

Because Pe = Pa,
C = V = 4991.55 m/s for equilibrium nozzle and Isp=C/go = 508.8 s
C = V = 4957.70 m/s for frozen nozzle and Isp=C/go = 505.4 s
Problem # 5
Repeat the same problem for the solid propellant rocket for the convergent-divergent nozzle.

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