Share:
How It Works
The Weber number compares the disruptive inertial forces in a flow to the cohesive surface-tension forces that hold a droplet or bubble together. At low We, surface tension wins and droplets remain spherical. At high We, inertial forces dominate and the droplet deforms, oscillates, or shatters into smaller fragments.
This makes We the key parameter for fuel injector design, spray coating, inkjet printing, and any process where controlling droplet size matters. The critical Weber number for droplet breakup is typically around 12 for a free-falling drop in a gas stream.
Example Problem
A 2 mm water droplet (ρ = 998 kg/m³, σ = 0.0728 N/m) travels at 5 m/s through air. What is the Weber number?
- We = ρv²L / σ = 998 × 25 × 0.002 / 0.0728
- We = 49.9 / 0.0728 = 685
We = 685 far exceeds the critical breakup threshold (≈ 12), so the droplet will shatter into a fine spray almost immediately.
Frequently Asked Questions
What Weber number causes droplet breakup?
For a liquid drop in a gas stream, the critical Weber number is about 12. Above this value the drop deforms and fragments. The exact threshold depends on the Ohnesorge number (viscosity effects) and the type of breakup (bag, shear-stripping, or catastrophic).
How is the Weber number used in fuel injector design?
Fuel injectors must atomize liquid fuel into fine droplets for efficient combustion. Engineers design nozzle geometry and injection pressure to produce a Weber number well above 12, ensuring rapid breakup. A typical diesel injector produces We on the order of 10,000 to 100,000 at the nozzle exit.
What is the difference between the Weber number and the Bond number?
The Weber number compares inertial forces to surface tension, while the Bond number (or Eotvos number) compares gravitational forces to surface tension. Use We when the flow velocity is the driving mechanism and Bo when gravity (buoyancy) drives the motion, as in rising bubbles in a stagnant liquid.
Does surface tension depend on temperature?
Yes. Surface tension generally decreases with increasing temperature. Water drops from 0.0756 N/m at 0 °C to 0.0589 N/m at 100 °C. This means the Weber number for the same flow conditions increases at higher temperatures, making atomization easier.
Related Calculators
- Cauchy Number Calculator — inertial vs. compressional forces in a fluid.
- Euler Number Calculator — pressure drop relative to dynamic pressure.
- Cavitation Number Calculator — pressure margin above vapor formation in a flow.
- Reynolds Number Calculator — characterize the flow regime alongside surface tension effects.
- Density Converter — convert fluid density units used in Weber number calculations.