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Summary Aerodynamics

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A snapshot of the summary - Aerodynamics

  • 1 Aerodynamics

  • 1.1 Fundamental Equations

  • 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. 1
    Compute 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. 2
    Compute the total mass of air in a room of
    30 m x 15 m x 5 m under standard atmospheric
    conditions 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. 3

    Compute 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
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