enter image description here After reviewing formulations for total pressure at low mach numbers, I concluded for a local reference frame that can rotate and accelerate relative to a fixed frame the total pressure for a fluid particle in the local frame is below. I verified this against the governing equations in the non-inertial frame under simplifying conditions and they match. Does this total pressure definition appear correct?

$^L p_{t} = \rho g ^L h + p + \rho \dfrac{^L \bar V_{p/o^{'}}^2}{2} + \rho ^F \bar a_{o^{'}/o} \bar * r_{p/o^{'}} - \rho\dfrac{{(^F \bar \Omega^L \wedge \bar r_{p/o^{'}})}^2}{2} $

You can see it's comprised of a gravitational energy type term $\rho g ^L h$, a static pressure term, a local kinetic energy type term $\rho \dfrac{^L \bar V_{p/o^{'}}^2}{2}$, an euler energy type term $\rho ^F \bar a_{o^{'}/o} \bar * r_{p/o^{'}} $, and a centrifugal energy type term $\rho \dfrac{{(^F \bar \Omega^L \wedge \bar r_{p/o^{'}})}^2}{2}$.


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