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 | \(lbf\;/\;ft\) | \(N\;/\;m\) |
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 forces dominate over inertial forces. This typically occurs in small-scale systems or slow-moving fluids, where the shape of a liquid interface (droplets or bubbles) is primarily governed by surface tension. For example, small water droplets in air tend to remain spherical due to strong surface tension effects.
- Intermediate Weber Number (We ≈ 1) - This represents a balance between inertial and surface tension forces, often seen in transitional regimes where both effects are significant. This might occur during the formation or deformation of droplets in processes like spray painting or inkjet printing.
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High Weber Number (We >> 1) - Inertial forces dominate over surface tension forces. This is common in high-speed flows or larger systems, where the fluid's momentum overcomes surface tension, leading to phenomena like droplet breakup, splashing, or atomization. For instance, when a fast-moving liquid jet hits a surface, it may disintegrate into smaller droplets.
Weber Number Applications
Capillary Flows - In microfluidics or small-scale systems (ink flow in a pen), a low Weber number suggests that surface tension keeps the fluid cohesive and stable.
Aerodynamics - When analyzing the interaction of air with liquid films (raindrops on an airplane wing), the Weber number helps predict whether the liquid will stay intact or fragment.
