Where ∆P is the magnitude of the pressure surge caused by the velocity change and is what we are trying to calculate: ΔV is the velocity change causing the surge: p is the density of the fluid and c is the wave speed. Still, it follows from Newton's Second Law, force = mass times acceleration, combined with the physical fact that no disturbance can travel through a fluid any faster than the wave speed (the wave speed being roughly 300 m/s in gas pipelines and around 1-1.5 km/s in liquid pipelines). I won't try to derive the Joukowksy equation here. In addition to coming up with this equation, Zhukovsky was the first person to physically explain the lift on an airplane wing and produced many other important results in engineering and mathematics.
(In this blog entry, I will stick with the more common spelling of the equation, "Joukowsky"). It is named after Nikolay Zhukovsky, a founding father of aerodynamics and also hydrodynamics. The Joukowsky Equation lets us perform surge calculations by hand. It's always good to have a pencil-and-paper calculation to fall back on as a sanity check on a complex piece of software, even if it's Atmos SIM. There is actually an easy way to do that sort of transient analysis by hand, which works for both gas and liquid pipelines and which is quite accurate in many situations.
#Gas dynamics calculator simulator#
Still, if they want to look at anything transient - for example, the pressure surge from closing a valve suddenly or from a rupture – a simulator is a must. Many engineers feel like they can do steady-state analysis in a spreadsheet.
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