Weber number, abbreviated as We, a dimensionless number, is used in fluid mechanics, often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is a measure of the relative importance of the fluid's inertia compared the its surrface tension. The reason this number is important is it can be used to help analyze thin film flows and how droplets and bubbles are formed. The Weber number indicates how likely a fluid flow is to overcome surface tension forces. The magnitude of the Weber number provides insights into the behavior of the fluid in various situations.
The Weber number is essential in various fields, including fluid dynamics, engineering, and materials science, where understanding the interaction between fluid flow and surface tension is crucial. It helps predict and explain phenomena such as droplet formation in inkjet printing, spray painting, and the behavior of liquid fuel sprays in combustion processes.
Weber Number Interpretation
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Low Weber Number (We << 1) - Surface tension dominates over inertial forces. The fluid tends to hold its shape, droplets stay spherical, jets remain intact, and interfaces resist breaking apart. This happens with slow flows, small scales, or high surface tension (tiny water droplets in air).
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High Weber Number (We >> 1) - Inertial forces dominate over surface tension. The fluid’s momentum overcomes surface tension, leading to deformation, breakup, or atomization. Droplets flatten or shatter, jets disintegrate into sprays, and interfaces become unstable. This occurs with fast flows, large scales, or low surface tension (a high-speed water jet hitting a surface).
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Transitional Weber Number (We ≈ 1) - This is the crossover regime where inertial and surface tension forces are comparable. Behavior depends on the specific system, droplets might start to deform but not fully break, or jets might wobble before splitting. Critical values for breakup or instability (We ≈ 10–20 for droplet shattering) vary by context.
Weber number formula |
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\( We \;=\; \dfrac{ \rho \cdot v^2 \cdot l_c }{ \sigma }\) (Weber Number) \( \rho \;=\; \dfrac{ We \cdot \sigma }{ v^2 \cdot l_c }\) \( v \;=\; \sqrt{ \dfrac{ We \cdot \sigma }{ \rho \cdot l_c } } \) \( l_c \;=\; \dfrac{ We \cdot \sigma }{ \rho \cdot v^2 }\) \( \sigma \;=\; \dfrac{ \rho \cdot v^2 \cdot l_c }{ We }\) |
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| Symbol | English | Metric |
| \( We \) = Weber Number | \( dimensionless \) | \(dimensionless\) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( v \) = Fluid Velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( l_c \) = Characteristic Length | \( ft \) | \( m \) |
| \( \sigma \) (Greek symbol sigma) = Surface Tension | \(lbf\;/\;ft\) | \(N\;/\;m\) |
