Read the summary and the most important questions on Aerodynamics

• 1 Aerodynamics

• 1.1 Fundamental Equations

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• By which fundamental quantities can we characterize the flow?

  • Pressure 
  • Velocity
  • Temperature
  • Density

  
  And the derivatives of these quantities (changes in time)

• What are the three fundamental equations?

  1. Continuity equation
     
  2. Euler equation
  3. Bernouli equation

• What is pressure and how can we describe it?

  The pressure is the norme force per unit area on a surface.

• How can a perfect gas be described?

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

• How can the equation of state be approximated for an actual gas?

  By the Berthelot equation.
  

• When does the difference between the Berthelot equation and the equation of state become te smallest?

  The difference with the equation of state for a perfect gas becomes smaller as p decreases or T increases.
  So when the distance between the molecules increases.

• Ex. 1Compute the temperature in a point on a wing of a Boeing 747, where pressure and density are given to be:0.7 x 10^5 N/m2 and 0.91 kg/m3(about 3000m standard atmosphere)

  Perfect gass --> P = ρRT
  P =  0.7 x 10^5 N/m2
  ρ = 0.91 kg/m3
  R = 287.0 J/kg K 
  
  T = P / ( ρR)
  T=  0.7 x 10^5  /  (0.91 * 287) = 268.0 K

• What are the pressure, denisity and temperature at sea level / standard conditions?

  Ps = 1.01325*10^5  N/m2
  ρs = 1.225 kg/m3
  Ts = 288.15 K

• Ex. 2Compute the total mass of air in a room of30 m x 15 m x 5 m under standard atmosphericconditions at sea level.

  
  ρ = m / V
  m = V * ρ
  
  V = 30 x 15 x 5 = 2250 m3
  ρ = 1.225 kg/m3
  
  m = 2756 kg

• Ex. 3Compute the density and specific volume of air in a wind tunnel at P = 1.0 bar, and -100 C.

  Pv = RT because 
  P  = RTρ with ρ = 1 / v
  P = 1*10^5  kg / m2
  T = -100 + 273.15 = 173.15 K
  R = 287.0 J/ kg K
  
  v = RT / P
  v = 287.0 * 173.15 / 101325 = 0.50 m3/kg