Ohnesorge Number formula |
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\( Oh \;=\; \dfrac{ \mu }{ \sqrt{ \rho \cdot \sigma \cdot l_c } }\) (Ohnesorge Number) \( \mu \;=\; Oh \cdot \sqrt{ \rho \cdot \sigma \cdot l_c } \) \( \rho \;=\; \dfrac{ \mu^2 }{ Oh^2 \cdot \sigma \cdot l_c }\) \( \sigma \;=\; \dfrac{ \mu^2 }{ Oh^2 \cdot \rho \cdot l_c }\) \( l_c \;=\; \dfrac{ \mu^2 }{ Oh^2 \cdot \rho \cdot \sigma }\) |
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| Symbol | English | Metric |
| \( Oh \) = Ohnesorge Number | \( dimensionless \) | \( dimensionless \) |
| \( \mu \) (Greek symbol mu) = Fluid Viscosity | \(lbf - sec \;/\; ft^2\) | \( Pa - s \) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
| \( \sigma \) (Greek symbol sigma) = Fluid Surface Tension | \(lbf \;/\; ft\) | \(N \;/\; m\) |
| \( l_c \) = Flow Characteristic Length | \( ft \) | \( m \) |
Ohnesorge number, abbreviated as Oh, a dimensionless number, that is used in fluid mechanics to describe the balance between viscous forces and surface tension forces in a fluid flow. It is defined as the ratio of the viscous forces to the surface tension forces.
The Ohnesorge number is used to characterize fluid flows in which surface tension effects are significant, such as the breakup of droplets, the formation of liquid jets, and the spreading of thin films. For small numbers, surface tension dominates and the fluid behaves more like a solid, while for large numbers, viscous forces dominate and the fluid behaves more like a liquid. The value of the Ohnesorge number depends on the properties of the fluid and the size of the flow structure, and it is an important parameter in many applications in engineering, physics, and materials science.
Ohnesorge Number Interpretation
- Low Ohnesorge Number (Oh << 1) - Inertia and surface tension. Viscosity is relatively weak, so the liquid tends to break up into droplets more easily. Think of water sprayed from a nozzleit, it forms distinct droplets quickly because surface tension pulls it into spheres, and inertia drives the motion. Droplet formation is clean and predictable, often seen in inkjet printing with thin fluids.
- High Ohnesorge Number (Oh >> 1) - The dominating force is viscosity. The liquid resists breakup because viscous forces dampen the effects of inertia and surface tension. Instead of forming droplets, it might stretch into long threads or remain as a continuous jet. Imagine honey dripping slowly, it doesn’t break into drops as readily. Breakup is suppressed, which might be desirable in applications needing a steady stream, but it can complicate atomization.
Ohnesorge Number formula |
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\( Oh \;=\; \dfrac{ \sqrt{ We } }{ Re }\) (Ohnesorge Number) \( We \;=\; Oh^2 \cdot Re^2 \) \( Re \;=\; \dfrac{ \sqrt{ We } }{ Oh }\) |
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| Symbol | English | Metric |
| \( Oh \) = Ohnesorge Number | \( dimensionless \) | \( dimensionless \) |
| \( We \) = Weber Number | \( dimensionless \) | \( dimensionless \) |
| \( Re \) = Reynolds Number | \( dimensionless \) | \( dimensionless \) |
- Intermediate Ohnesorge Number (Oh ≈ 1) - All three forces (viscosity, inertia, surface tension) are comparable. The liquid’s behavior is transitional, neither fully dominated by viscosity nor entirely by surface tension/inertia. Droplet formation might be irregular or require specific conditions to occur.
