Problem #1 Solution
Given:
M = 5.1
Alt = 21.3 km
air = 1.4, Mw = 28.965 kg/kmol
!"# =
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!".!"#
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= 287.05 !"!
(a) I used the following: http:/aero.stanford.edu/std
ASSIGNED:
DUE:
18 September 2014
30 September 2014
NOTES
Show all work! A significant portion of the credit will be given for steps shown even if the final
answer is wrong. Likewise, giving a correct answer without showing intermediate steps will
NOT rece
MAE 422 Fall 2016: Homework Assignment #2
ASSIGNED:
DUE:
22 September 2016
04 October 2016
NOTES
Reminder: Please follow the homework guidelines as listed in the syllabus and the homework
suggestions document posted to UB Learns. When using the VT calcula
MAE 422 Fall 2016: Exam #2, Take-home Project
ASSIGNED:
DUE:
16 November 2016
8 December 2016
EXAM INSTRUCTIONS
This take-home project counts as an exam (15-25% course credit). To complete these problems, feel free to use whatever
tools or methods you wis
Interactions and Reflections of Oblique Shocks and Prandtl-Meyer Expansions
PRANDTL-MEYER
EXPANSION FAN
OBLIQUE SHOCK
upstream velocity
direction,
M1 > 1
upstream velocity
direction,
M1 > 1
Now, we know how to analyze these two basic supersonic problem
One Dimensional, Steady, Compressible Flow
Our first use of the equations of motion and thermodynamics will
be the simplest possible geometry.
Assume:
1D flow (all variables are a function of X only!)
Steady Flow
No body forces
No heat addition (for no
MAE 422 Fall 2016: Homework Assignment #3
ASSIGNED:
DUE:
6 October 2016
18 October 2016
NOTES
Reminder: Please follow the homework guidelines as listed in the syllabus and the homework
suggestions document posted to UBlearns. When using the VT calculator,
MAE 422 Homework Guidelines
This document details what is expected of you on homework assignments. Please refer to it if you need
clarification on any topic. Points will be deducted if you do not follow these guidelines.
You may use a cover sheet, but it
MAE 422 Fall 2016: Homework Assignment #4
ASSIGNED:
DUE:
18 October 2016
27 October 2016
NOTES
Reminder: Please follow the homework guidelines as listed in the syllabus and the homework
suggestions document posted to UBlearns.
PROBLEMS
1. Consider a scena
MAE 422 Fall 2016: Homework Assignment #6
ASSIGNED:
DUE:
29 November 2016
8 December 2016
Because it is the end of the semester, late credit for this assignment will only be granted for
assignments turned in until Tuesday, December 13th (75% maximum). Any
Quasi One Dimensional, Steady, Compressible Flow
In pure 1-D Flow, all variables were considered to be a function of
x only and were considered independent of area.
Quasi 1-D Flow also assumes all variables are functions of x, but
we also allow area t
Method of Characteristics
Method of Characteristics (MOC)
A mathematical technique for solving certain types of partial
differential equations (those considered hyperbolic).
Supersonic inviscid flow has such a character (subsonic flow is
elliptic)
M
2D Steady, Compressible Flow Motivation
We wish to study two very basic problems in which we turn a supersonic, moving gas.
By our Tangency Boundary Condition, flow must become parallel to the inclined surfaces.
This analysis will result in a mathematical
What makes a uid compressible?
A compressible uid is one that undergoes changes in its density.
Consider an element of uid of xed mass, m, and a volume, V:
m
V
density
V
m
P
specic volume
Pressure places uniform
Deni&ons, part 1
Local Thermodynamic Equilibrium (LTE)
Thermodynamic equilibrium is the condi&on which maximizes the
balance of a molecular system for a given state.
In other words, a system in equilibrium will re
Equa%ons of Fluid Mo%on
Conserva%on Laws
A series of conserva%on laws can be dened for con0uum uids
that track mass, momentum, and energy of the uid.
Can be derived in a number of ways (you should have seen thes
MAE 422 Fall 2016: Homework Assignment #5
ASSIGNED:
DUE:
3 November 2016
29 November 2016
NOTES
Reminder: Please follow the homework guidelines as listed in the syllabus and the homework
suggestions document posted to UB Learns.
PROBLEMS
1. The Space Shut
MAE 422 Fall 2016: Final Exam Review Sheet
NOTES ABOUT THE EXAM
The final exam will be from 3:30 6:30 on Thursday, December 15TH in the usual classroom
(Cooke 121).
The exam will be four parts: (A) 14 questions (2pts each) requiring you to either answer
t
Question 1 c
Question 2 (a)
Pr=1.0:0.01:1.9;
gamma=1.4;
Mb=sqrt(2/gamma*(Pr)-1);
plot1=plot(Mb,Pr,'*');
grid on
legend('machnumber vs benoulli pressure ratio ')
xlabel('machnumber')
ylabel('pressure ratio')
hold on
Pr=1.0:0.01:1.9;
gamma=1.4;
MT=sqrt(2/(g
Question 5
T=240;
M=0:0.1:10;
Gamma=1.4
To=(1+(2*(gamma)/(gamma+1)*(M.^2-1)*(2+(gamma-1)*M.^2)/(gamma+1)*M.^2)*T;
plot(To,M)
grid on
legend('totaltemperature vs machnumber')
xlabel('totaltemperature')
ylabel('mach_number')
b) From seeing this plot, engine
MAE 422 - Gas Dynamics
FALL SEMESTER 2016
Course Outcome:
To develop an understanding of the theory of compressible gases at appreciable
subsonic and supersonic speeds with application to high-speed aerodynamics and
propulsion.
Course Overview:
Explores f
Equations of Fluid Motion
Conservation Laws
A series of conservation laws can be defined for continuum fluids
that track mass, momentum, and energy of the fluid.
Can be derived in a number of ways (you should have seen these
at least once already).
H
Definitions, part 1
Local Thermodynamic Equilibrium (LTE)
Thermodynamic equilibrium is the condition which maximizes the
balance of a molecular system for a given state.
In other words, a system in equilibrium will remain unchanged no
matter how much
Basic Notion of Compressible Flow
We will see that, in compressible flows, fluid momentum and energy are
intrinsically coupled and thermodynamics will be our set of tools for
coupling the math together.
A significant outcome of the course will be to obs
ASSIGNED:
DUE:
2 September 2014
16 September 2014
NOTES
Show all work! A significant portion of the credit will be given for steps shown even if the final
answer is wrong. Likewise, giving a correct answer without showing intermediate steps will
NOT recei