Perfect Gases

Flow Fields

Equation of State

Airspeed

Reynolds Number

Mach Number

MAE 2

2MAE 2

Fundamental Quantities in Aerodynamics

Pressure is the normal force per unit area exerted on a surface due to gas molecules impacting that surface.

Typical units: N/m2, lb/ft2, atm

The density of a gas is its mass per unit volume.

Typical units: kg/m3, slug/ft3

Temperature is a measure of the average kinetic energy of the particles in the gas.

Typical units: K, oC, oR, oF

p= limdA0 dfdA

p=pressuredF=force acting on dA

dA=small area

= limdv0 dmdv

=densitydm=mass insidedvdv=small volume

3MAE 2

Flow Fields

The velocity of a flowing gas is the velocity of a small fluid element as it passes through a fixed point.

Velocity is vector quanitity – it has a magnitude and a direction.

A fluid particle in steady flow will trace a path (called a streamline) in space.

Pressure, density, temperature, and velocity are all point properties.

They can all vary from one point in space to another.

A flow field is defined by knowledge of each parameter for every point in space.

p= p x , x , z=x , y , zT=T x , y , zV=V x , y , z

x

y z

4MAE 2

Equation of State

A perfect gas is one in which intermolecular forces are negligible.

Air, having relatively low density, acts like a perfect gas.

The equation of state for a perfect gas is:

p=RT

R=287J

kg K =1716

ft lb

slug Ro

p=pressure=density

T=temperatureR=specific gas constant

The specific gas constant (R) for air is:

5MAE 2

Airspeed

Airspeed refers to the speed of the air relative to the airplane.

The aerodynamic forces, acting on the airplane, are produced by this relative motion.

V A/G=V A/PV P /G

V A /G=speed of air relative to ground

V P /G=speed of airplane relative to ground

VA /P=speed of air relative to airplane

V=V A/P=airspeed V A/G=VV P /G

V=V A/G−V P /G

6MAE 2

Wind Tunnels

A wind tunnel produces an airspeed that is that same as the ground speed of an airplane moving in still air.

Airplane is moving relative to groundAir is not moving relative to ground

Airplane is not moving relative to groundAir is moving relative to ground

V P /GV A /G

V=−V P /G V=V A/G

VV

V=V A/G−V P /G V=V A/G−V P /G

7MAE 2

Reynolds Number

Viscosity of a fluid measures its ability to equalize differences in momentum.

The viscosity of a liquid decreases with increasing temperature.

The viscosity of a gas increases with increasing temperature.

A high Reynolds number indicates that the viscous (friction) forces are relatively low.

Re=V l

Re=Reynolds number

=densityV=airspeed

l=length of the body or surface=viscosity coefficient

=1.7894×10−5 kgm s

=3.7373×10−7 slug ft s

The viscosity coefficient for air at sea-level is approximately:

8MAE 2

Mach Number

For a perfect gas, the speed of sound depends only on temperature.

a= RT

The Mach number (M) compares the airspeed (V) to the speed of sound (a)

Speed of sound (a) should not be confused with acceleration (a)

M=Va

M < 1, flow is subsonicM = 1, flow is sonic0.8 < M < 1.2, flow is transonicM > 1, flow is supersonicM > 5, flow is hypersonic

a=speed of soundT=temperature

= ratio of specific heats =1.4 (for air)

9MAE 2

Resources

Wind Tunnels in Action (NASA)

http://www.youtube.com/watch?v=MksHQpIzui4