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2Chapter

The flow of air over the surface of an airplane is

heavier-than-air machine to fly

any gas is called aerodynamics

What is aerod namics?

The word comes from the Greek words: aeros,

concernin the air, and d namics, which means

force

Prof. Galal Bahgat SalemAerospace Dept., Cairo University

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ero ynam cs s e s u y o orces an e

resulting motion of objects through the air.

aerodynamics are:

1- Pressure 2- Density3- Temperature 4- Compressibility

5- Viscosity 6- Flow velocity


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1-Pressure

Pressure is the normal force due to the time rate of

that surface


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Mathematically F

Mean pressure P = F/ A

ressure a po n p = p

where p is the pressure

A is the area

2-Densit

Density is defined as the mass of gas divided by its

volume

Mean density : = m / V Density at point : = dm / dV


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3- Tem erature


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- Compressibility is a measure of the relative

change

= - (1/V)(dV/dp)

p p+dpV V+dV


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If the tem erature of the fluid element in theFigure is held constant, then is called

isothermal compressibility T = - (1/V)(V/p)T

If no heat is added to or taken away from thefluid element, and if friction is ignored, the

compress on o e u e emen a es p ace

isentropically and is called isentropic

= -s s

Since m = V then dm = dV + V d


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dV = - V d dV/V = - d/

=

Thus, whenever the fluid experience a change in, ,

density, d, is : d = dp

In eneral the flow of a as is a com ressibleflow. The exception to this is the low-speed flow

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


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-

Viscosity is a measure of the resistance of a

.Velocity profile

Boundary Layer


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Newtons Theor 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 fluids

viscosity

, ,

shear stress,, between layers is proportional to the

velocity gradient, v/y, in the direction perpendicular toe ayers

= (v/y)

absolute viscosity/the dynamic viscosity

N.B. Kinematic viscosity = /


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6-Flow velocity and streamlines

The flow velocity, or velocity field, of a fluid is a vector

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 apos on x,y,z an me .

A


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Velocity field over airfoil


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element ,in steady flow, is called a streamline of

the flow.

Drawing the streamlines of the flow field is animportant way of visualizing the motion of the

air/gas flow.


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Air flow about a house


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The four basic aerodynamic flow quantities : p, , T, and v

A knowledge of p, , T, and v at each point of a flow fullydefines the flow field

For steady flow:

= , ,

= (x,y,z)

T = T(x,y,z)

Flow Field

v = v(x,y,z)

The primary function of the aerodynamics (theoretical

field quantities around an aircraft or any flying vehicle


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the surface of an airplane, missile, etc, results

1- Pressure (p) distribution on the surface

surface


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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 = v

S is the planform area of wing

CL is the lift coefficient

C is the drag coefficient

CM is the moment coefficient


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Equation Of State For A Perfect Gas

A perfect gas is one in which intermolecular forces arenegligible

Air at standard conditions can be approximated by aperfect gas

,aerodynamic calculations

Equation of state: The relation between p, , and T for a

For a perfect gas, the equation of state is:

P = R T

Where R is the specific gas constant, the values of whichvaries from one type of gas to another


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Conversion Factors

= .

1 slug = 14.594 kg

= .

1 oK = 1.8 oR


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