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I know that depending on the duct circuit (bends, complex geometries...etc), the static pressure will be defined. If we assume air is flowing in the circuit with varying speed and/or varying density. Will the static pressure be always the same, and only the total (static +dynamic) pressure will vary?

In the other words, what is the static pressure sensitive to?

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  • $\begingroup$ By static, do you mean thermal particle pressure? $\endgroup$
    – honeste_vivere
    Commented May 11, 2015 at 12:31
  • $\begingroup$ Please see my edit. The wikipidea defines it as simply pressure to avoid ambiguity $\endgroup$
    – user2536125
    Commented May 11, 2015 at 13:17

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Static pressure in a compressible flow depends on the density but not the speed (not directly). Speed and geometry may affect the density.

For isentropic flow (neglecting gravitational potential):

$$ {p \over \rho^\gamma} = constant, \gamma = {c_p \over c_v} $$

which could be turned into this:

$$ {p \over p_0} = ({1 \over 1+{(\gamma-1) \over 2}Ma^2})^{\gamma \over \gamma-1} $$

There's also a more complicated relation for constant area adiabatic flow with friction (Fanno flow) and constant area non-adiabatic frictionless flow (Rayleigh flow) which you could find in Fundamentals of Fluid Mechanics by Munson.

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  • $\begingroup$ Meaning that, if we assume a non-compressible flow, the static pressure will always be the same, and only the dynamic pressure will vary with varying mass flow? $\endgroup$
    – user2536125
    Commented May 11, 2015 at 13:16
  • $\begingroup$ @user2536125 yes $\endgroup$
    – Azad
    Commented May 11, 2015 at 13:18
  • $\begingroup$ @user2536125 so long as you don't have a significant change of altitude $\endgroup$
    – Azad
    Commented May 11, 2015 at 13:19

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