AERODYNAMICS-1-REVIEWER

AERODYNAMICS 1 REVIEWER
Aerodynamics – The science relating to the effects produced by air or other gases in motion. The study of the properties of
moving air, and especially of the interaction between the air and solid bodies moving through it.

Fundamental Physical Quantities of a Flowing Gas:

1. Pressure - the normal force exerted per unit area due to time rate of change of momentum of gas molecules impacting
on the surface. Common units of pressure N/m2, dyn/cm2, lb/ft2, and atm

2. Density - Defined as the mass per unit volume of a substance. Common units of density kg/m3, g/cm3, slugs/ft3, and
lbm/ft3

3. Temperature - The measure of the average kinetic energy of the particles in a gas. The measure of the hotness or
coldness of the body. Common units of temperature are: Kelvin (K), degree Celsius (C), degree Rankine (R), and
degree Fahrenheit (F).

4. Velocity - The distance travelled by some object per unit time. Velocity connotes direction as well as speed.(Vector
quantity). For a flowing gas, we must further recognize that each region of the gas does not necessarily have the
same velocity; that is, the speed and direction of the gas may vary from point to point in the flow. Hence flow velocity
is a point property.

Streamlines of the flow - the path taken by a moving fluid element.

The Two Main Sources of all Aerodynamic Forces:
1. Pressure Distribution on the surface
2. Shear Stress (friction on the surface)

* Air behaves like a perfect gas. A perfect gas is defined as one in which intermolecular forces are negligible.

Equation of State for a Perfect Gas

Where:
P  RT P = pressure in Pa or psf
ρ = density in kg/m3 or slugs/ft3
T = temperature in Kelvin or Rankine
R = specific gas constant
R for normal air:
287.08 J/kg . K
or 1716 ft .lb/slug.R or 53.342 ft.lbf/lbm.

I. THE ATMOSPHERE
 The atmosphere is defined as the whole mass of air extending at a specified height
 The atmosphere is the mechanical mixture of gases surrounding the earth

Atmospheric Constituents

Nitrogen ------------------ 78.03%
Oxygen ------------------- 20.99%
Aragon --------------------- 0.94%
Carbon Oxide ------------- 0.03%
Hydrogen ------------------ 0.01%
Helium --------------------- 0.004%
Neon ----------------------- 0.0012% and a small amount of water vapor and other gases

,Layers of the Atmosphere:

1. Troposphere - The lowest and most turbulent region where clouds, moisture, and weather are formed.
This layer contains about 75% of the total mass of the atmosphere. This is where all plants and animals live
and breathe. Characterized by decreasing temperature with increasing height. The lowest altitude from
0 – 11 km

2. Stratosphere - The calm region of the atmosphere. Ozone in this layer stops many of the sun's harmful ultraviolet rays
from reaching the earth. This layer plus the troposphere make up 99% of the total mass of the atmosphere. The
temperature in this region is constant at 216.7 or 216.5 ⁰ K or 390 or 390.15 ⁰ R or -56.5 ⁰ C

3. Mesosphere - The third layer is the mesosphere. The temperature there is around -90° C (-130° F). This is where we
see "falling stars," meteors that fall to the earth and burn up in the atmosphere. At certain times of the year, we can see
many of these "falling stars" when the earth goes through the pieces of a broken comet. The top of the mesosphere is the
coldest part of Earth's atmosphere.

4. Thermosphere - Solar activity strongly influences temperature in the thermosphere. Although the thermosphere is
considered part of Earth's atmosphere, the air density is so low in this layer that most of the thermosphere is what we
normally think of as outer space. It is also where the space shuttle orbits. The aurora (the Southern and Northern Lights)
primarily occur in the thermosphere.

5. Ionosphere - The portion of the atmosphere which is ionized and contains plasma. The part of the atmosphere that is
ionized by solar radiation. It has practical importance because among other functions, it influences radio propagation to
distant places on the Earth.

6. Exosphere - The highest layer of the atmosphere. Very high up, the Earth's atmosphere becomes very thin. The region
where atoms and molecules escape into space. It extends to 40,000 miles above the earth's surface. The thermosphere
and the exosphere together make up the upper atmosphere.

The International Standard Atmosphere (ISA) – hypothetical model of the properties of atmosphere such as pressure,
temperature, density, etc.

Purposes of ISA:
1. To provide basis for comparing the performance characteristics of airplanes.
2. To allow for the calibration of altimeters, it is desirable to have standard properties of the atmosphere which represent
“average” conditions.

NOTE: Standard properties have been established by the ICAO. The ISA is generally used by the airplane and engine
manufacturer around the world.

Basic Properties of Air:

1. Pressure (P) - The values of standard air pressures at sea level (Po) are:

Po = 14.7 lb/in2 = 2116.8 or 2116.2 lb/ft2 = 29.92 in Hg
= 76 cmHg = 760 mmHg = 101325 Pa = 1 atm

NOTE: Atmospheric pressure decreases with altitude

2. Temperature (T) - The values of standard air temperature at sea level (To) are:

To = 15 C = 59 F
= 288.2 K = 519 or 518.7 R

NOTE: Atmospheric temperature decreases with height in the troposphere region.

3. Density (ρ) - The values of standard air densities at sea level are:

,NOTE: Atmospheric density decreases with height

4. Viscosity (μ) - The ability of the fluid to resist shearing stresses. It is the sticky or adhesive characteristics of a fluid. The
values of standard air viscosities at sea level are:

μu = 3.7372 x 10-7 slug/ft.sec
= 1.7894 x 10-5 kg/m-sec

Kinematic Viscosity - The kinematic viscosity is the dynamic viscosity μ divided by the density of the fluid ρ. It is usually
denoted by the Greek letter nu (ν).




Humidity - Amount of water vapor in air (condition of moisture or dampness). Temperature influence the maximum amount
of water vapor that the air can hold . Higher air temperature  absorb more water vapour. Density of air varies with
humidity. Density on damp day (hot day) is less than density on dry day (cold day).

The Lapse Rate for the Gradient Layers of the Atmosphere:

dT Where: a = temperature lapse rate
a dT = change in temperature
dh dh = change in height

Temperature Variation with Altitude Formula

T  To  ah
Where: T = temperature at any altitude up to 11 km (troposphere)
To = 288.2 K or 519 R
h = height from sea level up to 11 km
a = lapse rate

Standard Values of Temperature Lapse Rate:
a = -0.0065 or -0.00651 K/m
= -6.5 or -6.51 K/km
= -0.003566 R/ft

General Equation for Pressure Variation with Altitude (Troposphere, 0 – 11 km)
 g o /( aR )
P T  g  9.81m / s 2
   
aR  0.0065K / m( 287.08 N .m / kg .K )
P1  T1 
 5.26


For Air:
5.26
P T  Where:

Po  To 
P = pressure at any altitude up to 11 km
Po = standard pressure at sea level
T = temperature at any altitude up to 11 km
To = standard temperature at sea level

General Equation for Density Variation with Altitude (Troposphere, 0 - 11 km)
 ([ g o /( aR )] 1 )
 T   g    9.81m / s 2 
   1    0.0065K / m( 287.08 N .m / kg .K )   1
 T 
 aR 
 

, For Air:
Where:
4.26
 T  ρ = density at any altitude up to 11 km
  ρo = standard density at sea level
 o To  T = temperature at any altitude up to 11 km
To = standard temperature at sea level

Pressure Variation with Altitude (Stratosphere, 11-25 km)

P  g 
  RT  ( h  h )
Where:
e  
1


P = pressure at any altitude above 11 km
P1 P1 = pressure at 11 km
g = gravitational constant, (9,81 m/s2, 32.2 ft/s2)
R = gas constant, for air
(287.08 J/kg.K, 53.342 ft.lbf/lbm.R)
T = constant temperature at stratosphere
216.5 K, 390.15 R
h = the given altitude above 11,000 m
h1 = 11,000 m

Density Variation with Altitude (Stratosphere, 11-25 km)

  g 
  RT  ( h  h )
Where:
e   ρ = density at any altitude above 11 km
1




1 ρ1 = density at 11 km
g = gravitational constant, (9.81 m/s2, 32.2 ft/s2)
R = gas constant, for air
(287.08 J/kg.K, 53.342 ft.lbf/lbm.R)
T = constant temperature at stratosphere
216.5 K, 390.15 R
h = the given altitude above 11,000 m
h1 = 11,000 m

Temperature at Stratosphere (11-25 km) has no variation, constant at...

T  390.15 R
T  216.5 K
Problems:
1. Determine the temperature at the following altitudes:
a.) 2,000 ft - Answer: 447.58 R
b.) 3,500 m - Answer: 265.45 K

2. Determine the pressure at 15,000 ft altitude – Answer: P = 1194.555 psf
3. Determine the pressure at 4500 m altitude – Answer: P = 57, 656.065 Pa
4. Determine the density at 15,000 ft altitude – Answer: ρ = 1.496 x10-3 slugs/ft3
5. Determine the density at 4500 m altitude – Answer: ρ = 0.776 kg/m3
6. Find the Pressure and Density at 14 km height – Answer: P = 1.41 x 104 Pa ρ = 0.226 kg/m3

Altimeter - a pressure gauge which indicates an altitude in the standard atmosphere corresponding to the measured
pressure. A pressure gauge which translates the measured pressure into an altitude reading which corresponds to that
predicted by the standard atmosphere.