M&AE 3050
Problem Set 6 Due Thursday, November 5, 2009
Fa 2009
1. An airplane has a wing planform area of S = 60 m2 , a wing span of b = 24 m, and a gross mass of M = 25, 000 kg. It is in level, unaccelerated ight, which implies L = Mg at a true airspeed
M&AE 3050
Problem Set 6 Solution
Fall 2009
1. An airplane has a wing planform area of S = 60 m2 , a wing span of b = 24 m, and a gross mass of M = 25, 000 kg. It is in level, unaccelerated ight, which implies L = Mg at a true airspeed of V = 225 m/s, a de
M&AE 3050 Introduction to Aeronautics
Review Sheet: Dimensional Analysis
Fall 2015
How to generate dimensionless variables for a given problem:
1. Identify the physical variables relevant to the problem: a1 to am .
2. Identify the independent fundamental
M&AE 3050 Introduction to Aeronautics
Compressible Flows - Review
Fall 2015
Steady, isentropic ows:
p
= constant
p
= constant
(1)
(2)
T 1
For isentropic ows, the compressible version of Bernoulli equation tells us that total (or
stagnation) enthalpy and
M&AE 3050 Introduction to Aeronautics
Review Sheet: The Atmosphere
Fall 2015
Standard Sea Level parameters
pSSL = 101, 325 Pa = 2116.2 lb/ft
2
3
SSL = 1.225 kg/m = 0.002377 slug/ft
3
TSSL = 288.15 K = 518.67 o R = 59 o F = 15 o C
SSL = 1.789 105 kg/m.
M&AE 3050 Introduction to Aeronautics
Review Sheet: Incompressible Flows
Fall 2015
Conservation of mass (along in a stream tube)
1 V 1 A1 = 2 V 2 A2
Always valid for steady ows, since by denition, there is no ow across stream tube surfaces.
Simplies to A
M&AE 3050 Introduction to Aeronautics
Compressibility Eects Review Sheet
Fall 2015
1
Compressibility Eects
Prandtl-Glauert rule for pressure and lift coecients
Cp =
Cl =
Cp 0
2
1 M
Cl0
2
1 M
with Cp0 provided by incompressible theory.
with Cl0 provided b
M&AE 3050 Introduction to Aeronautics
Flight Performances Review Sheet
Fall 2015
1
Level, unaccelerated ight performances
1.1
Power required
Power required to maintain level, unaccelerated ight:
1
2 (W/S)2 S
PREQ = D V = CDp V 3 S +
2
V eA
R
with CDp obt
M&AE 3050 1. Problem 5.2 in Anderson. Solution
Problem Set 5 Solution
Fa 2009
We assume a Standard Atmosphere for the gas. The problem parameters are as follows v T a M c W = = = = = = = = 2.3769 103 slugs , 100 ft/s , 518.69 R , RT = (1.4)(1716)(518.69)
M&AE 3050 1. Problem 5.2 in Anderson.
Problem Set 5 Due Thursday, October 30, 2009
Fa 2009
2. Problems 5.9 and 5.10 in Anderson. 3. Problem 5.13 in Anderson. 4. Problems 5.15 and 5.16 in Anderson.
M&AE 3050
Problem Set 4 Solution
Fa 2009
1. A large vacuum tank, held at 66,400 Pa, sucks sea-level Standard Air through a converging nozzle with a throat diameter of 4 cm. Estimate the following: (a) The Mach number at the throat. (b) The temperature of
M&AE 3050 This exam is for your practice only.
Practice Exam 1
Fa 2009
1. On a summer day, the temperature in the stratosphere above Edwards Air Force Base in southern California is constant, and equal to T1 = 236.65 K for altitudes in the range 11, 000 m
M&AE 3050 Solution This exam is for your practice only.
Practice Exam 1
Fa 2009
1. On a summer day, the temperature in the stratosphere above Edwards Air Force Base in southern California is constant, and equal to T1 = 236.65 K for altitudes in the range
M&AE 3050
Practice Exam 2
Fa 2009
This is for practice only. You do NOT need to submit. 1. We wish to consider the eect of altitude on the dierence between true airspeed and calibrated airspeed, making the following comparisons. (a) Determine the i. true
M&AE 3050
Practice Exam 2
Fa 2009
This is for practice only. You do NOT need to submit. 1. We wish to consider the eect of altitude on the dierence between true airspeed and calibrated airspeed, making the following comparisons. (a) Determine the i. true
M&AE 3050
Problem Set 1 Solution
Fa 2009
1. Redo the dimensional analysis of the force acting on an object of length in a uniform steady ow of a gas of density , viscosity and free stream velocity V taking compressibility eects into consideration. Assume
M&AE 3050
Problem Set 2 Solution
Fa 2009
1. The Standard Sea Level values of temperature T and pressure p are TSL = 288.15 K and pSL = 101, 325 Pa. Using the formulae derived in class and the temperature prole given in Fig. 3.4 in Anderson, calculate the
M&AE 3050
Problem Set 3 Fa 2009 Solution For the problems below, assume all ows can be approximated as incompressible.
1. Consider the incompressible ow of water through a divergent duct. The inlet velocity and area are 5 ft/s and 10 ft2 , respectively. (
M&AE 3050
Problem Set 4 Due Thursday, October 15, 2009
Fa 2009
1. A large vacuum tank, held at 66,400 Pa, sucks sea-level Standard Air through a converging nozzle with a throat diameter of 4 cm. Estimate the following: (a) The Mach number at the throat. (
M&AE 3050 Introduction to Aeronautics
Incompressible Lift and Drag - Review
Fall 2015
1
Potential Flows
Any irrotational velocity eld, i.e. satisfying
u = 0 , can be represented as the gradient
of a potential function ,
u=
This potential function satis