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Instantaneous Waterhammer Equation- Joukowsky Equation

When a transient event is introduced into a hydraulic system, there is a pressure and flow response to the event. If severe enough, the fluctuating pressures can cause damage to the pipeline and other system components. Because of the potential for harm to the system, engineers frequently call upon mathematical models to attempt to predict what the pressure and flow response of a transient phenomenon in the hydraulic system will be. The Joukowsky Equation—also sometimes referred to as the instantaneous waterhammer equation—is used to predict the surge pressure, ΔP, that will result if the transient event happens instantaneously. This pressure is added to the existing static pressure at that location to determine the maximum theoretical pressure in the pipe. The Joukowsky Equation can be seen in Figure 1.

∆P = -ρa∆V

Figure 1: Joukowsky Equation

Where ΔP = pressure surge

ρ = fluid density

a = wave speed

ΔV = change in velocity

Note that exceptions to the maximum pressure predicted by the Joukowsky Equation exist. Some situations in which the maximum pressure could be higher than that predicted by the Joukowsky Equation include: cavitation, pipe size changes, multiple pressure surge sources that can interact, and line packing due to friction. AFT Impulse considers these phenomena and can model the complex interaction of fluid flow through multiple pipes in the pipe network.


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