Laplace number, abbreviated as La, a dimensionless numbers, is used in fluid dynamics to describe the relative importance of surface tension forces to viscous forces in a fluid flow. The Laplace number is used to determine whether surface tension effects are significant in a particular fluid flow situation. The value of the Laplace number can provide insights into the shape and behavior of liquid drops, bubbles, or menisci (curved liquid surfaces) in various systems.
Laplace Number Interpretation
- High Laplace Number (La ≫ 1) - Indicates that surface tension dominates over viscosity. This happens in systems where the fluid resists deformation due to strong cohesive forces at its surface, like small water droplets or capillary flows in narrow tubes. The fluid behaves more like it’s controlled by its "skin" than its internal friction.
- Low Laplace Number (La ≪ 1) - Suggests that viscous forces overpower surface tension. You’d see this in thicker, stickier fluids (high viscosity) or larger systems where surface effects become less significant, like honey spreading slowly on a surface.
The Laplace number is particularly important in understanding phenomena involving capillary action, droplet formation, and bubble dynamics. It helps engineers and scientists predict how surface tension influences the behavior of fluids in different contexts and can guide the design and analysis of systems where surface tension effects are significant.
Laplace Number Formula |
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\( La \;=\; \dfrac{ \sigma \cdot \rho \cdot l }{ \eta^2 } \) (Laplace Number) \( \sigma \;=\; \dfrac{ La \cdot \eta^2 }{ \rho \cdot l }\) \( \rho \;=\; \dfrac{ La \cdot \eta^2 }{ \sigma \cdot l }\) \( l \;=\; \dfrac{ La \cdot \eta^2 }{ \sigma \cdot \rho }\) \( \eta \;=\; \sqrt{ \dfrac{ \sigma \cdot \rho \cdot l }{ La } } \) |
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| Symbol | English | Metric |
| \( La \) = Laplace number | \(dimensionless\) | \(dimensionless\) |
| \( \sigma \) (Greek symbol sigma) = surface tension | \(lbf\;/\;ft\) | \(N\;/\;m\) |
| \( \rho \) (Greek symbol rho) = density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( l \) = length | \(ft\) | \(m\) |
| \( \eta \) (Greek symbol eta) = viscosity of liquid | \(lbf-sec\;/\;ft^2\) | \(Pa-s\) |
