Joukowsky Equation Formula |
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\( \Delta p \;=\; \rho \cdot a \cdot \Delta v \) (Joukowsky Equation) \( \rho \;=\; \dfrac{ \Delta p }{ a \cdot \Delta v }\) \( a \;=\; \dfrac{ \Delta p }{ \rho \cdot \Delta v }\) \( \Delta v \;=\; \dfrac{ \Delta p }{ \rho \cdot a }\) |
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| Symbol | English | Metric |
| \( \Delta p \) = Pressure Surge | \(lbf \;/\; ft^2\) | \(Pa\) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
| \( a \) = Wave Speed | \(ft \;/\; sec\) | \(m \;/\; s\) |
| \( \Delta v \) = Change in Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
Joukowsky Equation, abbreviated as \( \Delta p \), also called Joukowsky shock, describes the pressure change caused by a sudden change in the velocity of a fluid, especially during a watter hammer event in pipelines. When a flowing fluid is abruptly stopped or its velocity changes quickly, such as when a valve closes, the fluid’s momentum creates a pressure wave that travels through the pipe. The Joukowsky equation expresses this pressure rise as being directly proportional to the fluid’s density, the speed at which the pressure wave travels through the pipe, and the magnitude of the velocity change. This equation is widely used in hydraulic engineering to predict and prevent damaging pressure surges in water distribution systems, oil pipelines, and other pressurized fluid networks.
