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In a pitot-static tube, we have two different pressure, the static pressure $p_s$ and the total pressure $p_0 = p_s + \frac{1}{2}\rho v^2$, which comes from the Beroulli equation for incompressible flows.

Now, lets say we are given an inflow of air from the freestream (assume STP conditions) with a speed of $v_{\infty} = 100$ ft/s. The total pressure would just be $p_0 = p_{\infty} + \frac{1}{2} \rho v_{\infty}^2$, but what I fail to understand is how we would get the static pressure. Would it just be the freestream pressure? Or something else...

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The pitot tube is pointed into the airstream and measures the total pressure. Static pressure must be measured, not calculated. It is done so at a separate location, using a static port.

http://www.b737.org.uk/probes.htm

Both pitot tubes and static ports are needed in order to derive air speed, as this incident sadly illustrates.

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  • $\begingroup$ Some pitots also have a static probe, they are known as pitot-static probes. Examples. $\endgroup$
    – mins
    Oct 25, 2017 at 22:43
  • $\begingroup$ So there is no mathematic expression for it? $\endgroup$
    – Josh Pilipovsky
    Oct 25, 2017 at 23:24
  • $\begingroup$ No not really, pressure is just the average impact energy of the Brownian motion of air molecules, a statistical entity rather than a mathematical expression. It needs to be measured, not derived. $\endgroup$
    – Koyovis
    Oct 25, 2017 at 23:31
  • $\begingroup$ @mins Yes static pressure can be measured at the pitot tube as well, as long as a location is chosen that is relatively insensitive to air stream velocity. $\endgroup$
    – Koyovis
    Oct 26, 2017 at 0:17
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    $\begingroup$ @Trevor Both the static ports and the pitot tube are not insensitive to how the airflow shapes over the aircraft, no matter where they are located. During certification of the aircraft, a separate pitot tube with wings is dragged behind and below the aircraft, in order to take measurements out of the flow field of the aircraft. Data from the drone tube are then compared with the pitot/static ports installed on the aircraft, and used to calibrate the installed instruments. As to sideslip, there are static tubes on both sides of the cockpit - average indication is calibrated as well. $\endgroup$
    – Koyovis
    Oct 26, 2017 at 13:38

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