Fundmental thoughts

Prof. Galal Bahgat Salem

Aerospace Dept., Cairo University

1

2Chapter

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



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



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”



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



5



6

3- Temperature



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 p+dp V V+dV



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



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 flowof a gas ( at sea-level v ≤ 100 m/s )



10

5- Viscosity

● Viscosity is a measure of the resistance of a

fluid to flow.Velocity profile

Boundary Layer



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 =



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



13

Velocity field over airfoil



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



15

Air flow about a house



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)

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

Flow Field



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



18



19

Forces, Moments and CoefficientsAerodynamic

• 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



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 = ρ R T

• 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)



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)



22

Conversion Factors

• 1 ft = 0.3048 m

• 1 slug = 14.594 kg

• 1 Ib = 4.448 N

• 1 oK = 1.8 oR

Fundmental thoughts

Documents

Transcript of Fundmental thoughts