Euler number formula |
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\( Eu \;=\; \dfrac{ \Delta p }{ \rho \cdot U^2 }\) (Euler Number) \( \Delta p \;=\; Eu \cdot \rho \cdot U^2 \) \( \rho \;=\; \dfrac{ \Delta p }{ Eu \cdot U^2 }\) \( U \;=\; \sqrt{ \dfrac{ \Delta p }{ Eu \cdot \rho } }\) |
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| Symbol | English | Metric |
| \( Eu \) = Euler Number (See Physics Constant) | \( deminsionless \) | \( deminsionless \) |
| \( \Delta p \) = Pressure Change | \(lbf \;/\; in^2\) | \(Pa\) |
| \( \rho \) (Greek symbol rho) = Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
| \( U \) = Characteristic Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
Euler number, abbreviated as Eu, a dimensionless number, used in fluid dynamics problems. It is different than the constant that carries the same name, the Euler Number. Euler Number is used for analyzing flow where the differential pressure between two points is important. Fundamentally, it is the relationship between local pressure drop caused by a restriction and and the volumetric kinetic energy in the flow stream. The number is a method of characterizing the energy losses in the flow stream. When friction losses equal zero, as in a perfect flowstream, the Euler number is zero.
Euler Number Interpretation
- Low Euler Number (Eu ≪ 1) - Suggests that inertial forces dominate, typical in high-speed flows with small pressure differences, like in aerodynamics or turbulent flows.
- High Euler Number (Eu ≫ 1) - Indicates that pressure forces dominate over inertial forces. This might occur in flows with large pressure drops or low velocities, such as in highly viscous or slow-moving fluids.
