The document introduces some fundamental concepts in aerodynamics. It defines aerodynamics as the study of forces on objects in air and discusses the key physical quantities involved - pressure, density, temperature, compressibility, and viscosity. It also describes flow velocity, streamlines, and how aerodynamic forces like lift and drag arise from pressure and shear stress distributions on surfaces.

1. Chapter 2
Fundamental Thoughts
• The flow of air over the surface of an airplane is
the basic source of the lifting force that allows a
heavier-than-air machine to fly
• The science that deals with the flow of air/flow of
any gas is called aerodynamics
• What is aerodynamics?
• The word comes from the Greek words: aeros,
concerning the air, and dynamics, which means
force
1 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

2. ● Aerodynamics is the study of forces and the
resulting motion of objects through the air.
■Physical Quantities of a Flowing Gas
Physical quantities in the language of
aerodynamics are:
1- Pressure 2- Density
3- Temperature 4- Compressibility
5- Viscosity 6- Flow velocity
and streamlines
2 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

3. 1-Pressure
“Pressure is the normal force due to the time rate of
change of momentum of the gas molecules impacting on
that surface”
3 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

4. • Mathematically F
Mean pressure P = F/ A
Pressure at point p = dp/ dA A
where p is the pressure
F is the normal force
A is the area
2-Density
Density is defined as the mass of gas divided by its
volume
• Mean density : ρ=m/V
• Density at point : ρ = dm / dV
• Specific volume : v = 1/ ρ
4 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

5. 5 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

6. 3- Temperature
6 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

7. 4- Compressibility
● Compressibility is a measure of the relative
change of a fluid as a response to a pressure
change
● By definition, the compressibility of a fluid β :
β = - (1/V)(dV/dp)
where V is the volume and p is the pressure
p V p+dp V+dV
7 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

8. • If the temperature of the fluid element in the
Figure is held constant, then β is called
isothermal compressibility βT = - (1/V)(∂V/∂p)T
• If no heat is added to or taken away from the
fluid element, and if friction is ignored, the
compression of the fluid element takes place
isentropically and β is called isentropic
compressibility βs = - (1/V)(∂V/∂p)s
• Since m = ρ V then dm = ρ dV + V dρ
But dm = 0 because m = constant
8 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

9. ρ dV = - V dρ dV/V = - dρ/ρ
Then β = (1/ρ) (dρ/dp)
• Thus, whenever the fluid experience a change in
pressure, dp, the corresponding change in
density, dρ, is : dρ = ρ β dp
• In general, the flow of a gas is a compressible
flow. The exception to this is the low-speed flow
of a gas ( at sea-level v ≤ 100 m/s )
9 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

10. 5- Viscosity
● Viscosity is a measure of the resistance of a
fluid to flow.
Velocity profile
Boundary Layer
10 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

11. Newton’s Theory
● In general, in any fluid flow, layers move at different
velocities and the shear stress between the layers, which
opposes any applied force, arises from the fluid’s
viscosity
●Newton postulated that, for straight parallel flow, the
shear stress, between layers is proportional to the
velocity gradient, ∂v/∂y, in the direction perpendicular to
the layers
• ∂v/∂y)
The constant µ is known as the coefficient of viscosity/the
absolute viscosity/the dynamic viscosity
N.B. Kinematic viscosity υ =
11 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

12. 6-Flow velocity and streamlines
● The flow velocity, or velocity field, of a fluid is a vector
field which is used to mathematically describe the motion
of the fluid.
● The flow velocity of a fluid is a vector field:
v = v(x,y,z,t)
which gives the velocity of an element of fluid at a
position (x,y,z) and time t .
A
12 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

13. Velocity field over airfoil
13 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

14. • Streamline: The path taken by a moving fluid
element ,in steady flow, is called a streamline of
the flow.
• Drawing the streamlines of the flow field is an
important way of visualizing the motion of the
air/gas flow.
Air flow over airfoil
14 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

15. Air flow about a house
15 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

16. ■Source of Aerodynamic Forces
● The four basic aerodynamic flow quantities : p, ρ, T, and v
● A knowledge of p, ρ, T, and v at each point of a flow fully
defines the flow field
● For steady flow:
p = p(x,y,z)
ρ = ρ(x,y,z)
Flow Field
T = T(x,y,z)
v = v(x,y,z)
● The primary function of the aerodynamics (theoretical
and or experimental) is to calculate or measure the flow
field quantities around an aircraft or any flying vehicle
16 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

17. • The aerodynamic force exerted by the airflow on
the surface of an airplane, missile, etc, results
from only two simple natural sources:
1- Pressure (p) distribution on the surface
2- Shear stress or friction ( distribution on the
surface
Pressure and shear stress distribution
17 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

18. 18 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

19. Aerodynamic Forces, Moments and Coefficients
• Lift Force L: L = q∞ S CL
• Drag Force D: D = q∞ S CD
• Pitching Moment: M = q∞ S C CM
• Where q∞ is the dynamic pressure
• q∞ = (1/2) ρ∞ v∞2
• S is the planform area of wing
• C is the mean chord of wing
• CL is the lift coefficient
• CD is the drag coefficient
• CM is the moment coefficient
19 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

20. Equation Of State For A Perfect Gas
• A perfect gas is one in which intermolecular forces are
negligible
• Air at standard conditions can be approximated by a
perfect gas
• Therefore, we will always deal with a perfect gas for
aerodynamic calculations
• Equation of state: The relation between p, ρ, and T for a
gas is called the equation of state
• For a perfect gas, the equation of state is:
• P=ρRT
• Where R is the specific gas constant, the values of which
varies from one type of gas to another
• For normal air R = 287 J/(kg)(K)
20 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

21. Units
• Two system of units are commonly used:
• 1- (SI) system is a metric system based on the meter,
kilogram, second, and Kelvin as basic units of length,
mass, time, and temperature
• 2- English Engineering System of units based on the
foot, slug, second, and Rankine as basic units of length,
mass, time, and temperature
• Force = mass x acceleration
• F = m x a
• In SI units : 1 Newton = (1 kilogram)(1 meter/second2)
• In English Engineering system:
• 1 pound = ( 1 slug )(1 foot/second2)
21 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University

22. Conversion Factors
• 1 ft = 0.3048 m
• 1 slug = 14.594 kg
• 1 Ib = 4.448 N
• 1 oK = 1.8 oR
22 Prof. Galal Bahgat Salem
Aerospace Dept., Cairo University