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  • Q

    Concerning Q 220860 and anemometers:
    What is the Saint-Venant formula?

  • #2
    What do you mean by "anemometers"? are you referring to the air speed indicator?
    In the EASA learning objectives I can find no reference to "Saint-Venant" so it is probably just something somebody thought up to confuse you.

    What are in the learning objectives are the concepts of "impact pressure" and "compressibility error" so you need to understand the relationship between these but you don't need to know the actual equation used to calibrate the airspeed indicator.

    You will remember that

    Dynamic pressure is defined as 1/2 rho V^2


    Total pressure = Static pressure + Dynamic pressure

    However this equation applies ONLY to incompressible flow.

    At high (but still subsonic) mach numbers the compressibility of the air becomes significant so that:

    Total pressure > Static pressure + Dynamic pressure.

    Therefore, for compressible flow, we define a new term called "impact pressure" such that:

    Impact pressure = Total pressure - Static pressure

    From this definition, you will see that for incompressible flow, impact pressure is the same as dynamic pressure. However for compresssible flow impact pressure is greater than dynamic pressure.

    Now the air speed indicator is designed with a capsule which responds to impact pressure (not dynamic pressure). Therefore the airspeed indicator can only be calibrated to display an "airspeed" which is a function of impact pressure. Ideally we would like it to display equivalent airspeed and at sea level this can be achieved. We calibrate the airspeed indicator to display "calibrated airspeed" as a function of impact pressure such that at sea level CAS = EAS. At sea level the calibration equation correctly accounts for compressibility.

    The problem is that the airspeed indicator does not know its altitude the and the calibration equation correctly accounts for compressibility only at sea level. Therefore at high altitude and high airspeed the compressibility is not correctly accounted for and therefore CAS > EAS. The difference between CAS and EAS is called "compressibility error"
    Last edited by Ortac; 13-01-2018, 11:20.


    • #3
      Thanks a lot for your explanation!
      I understand all that and the concept of CAS, EAS and compressibility is clear to me.
      That's why I was a pit confused when I read the terms 'anemometer' (Wikipedia helped me somewhat...) and the "Saint-Venant formula" (which I still don't know what it is...) in question 220860.
      I have come across several questions in the BGS question bank which are not covered in the BGS course, but they are rare.
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