π Lesson 4
D3
Weber Number, Ohnesorge Number, and Their Role in Droplet Breakup
The Weber number tells us whether a liquid droplet will stay together or break apart when hit by air or another fluid β like deciding if a water droplet from a sprayer nozzle will splash or fly smoothly.
π― Learning Objectives
- β Calculate Weber and Ohnesorge numbers for given nozzle operating conditions
- β Analyze droplet breakup regimes (bag, shear, catastrophic) using We and Oh maps
- β Explain how nozzle geometry and fluid properties influence spray atomization quality
- β Apply WeβOh correlation charts to select optimal hydraulic pressure and fluid formulation for mining dust suppression nozzles
π Why This Matters
In mining operations, effective dust suppression relies on fine, stable droplets that reach airborne particulates before evaporating. If droplets are too large, they fall short; if too small, they drift or evaporate instantly. Weber and Ohnesorge numbers are the foundational physics tools that predict whether your sprayer nozzle produces the right droplet size distribution β directly impacting regulatory compliance (e.g., MSHA 30 CFR Β§56.12001), water efficiency, and equipment maintenance.
π Core Principles
Droplet breakup is governed by competition among three forces: inertia (driving deformation), surface tension (holding droplet together), and viscosity (resisting internal flow). The Weber number isolates inertia vs. surface tension β high We (>10) favors fragmentation; low We (<1) favors intact droplets. The Ohnesorge number adds viscosity into the balance: Oh < 0.1 indicates low-viscosity fluids (e.g., water-based suppressants) where surface tension dominates at small scales; Oh > 1 implies highly viscous fluids (e.g., polymer-modified slurries) where viscosity suppresses breakup. Together, We and Oh define universal breakup regime maps validated across nozzle types β critical for scaling lab tests to field sprayers handling abrasive mine water with suspended solids.
π Key Calculations
Weber number (We) and Ohnesorge number (Oh) are calculated from measurable fluid and flow parameters. We predicts primary breakup onset; Oh refines prediction for viscous or low-velocity flows. Both are essential for interpreting high-speed imaging data and correlating nozzle K-factor with Sauter Mean Diameter (SMD).
π‘ Worked Example
Problem: A mining dust suppression nozzle operates with water (Ο = 998 kg/mΒ³, Ο = 0.072 N/m, ΞΌ = 8.9 Γ 10β»β΄ PaΒ·s) at exit velocity U = 25 m/s and characteristic droplet diameter D = 200 Β΅m (2 Γ 10β»β΄ m). Calculate We and Oh.
1.
Step 1: Compute We = ΟΒ·UΒ²Β·D / Ο = (998)(25)Β²(2Γ10β»β΄) / 0.072
2.
Step 2: Numerator = 998 Γ 625 Γ 0.0002 = 124.75; We = 124.75 / 0.072 β 1733
3.
Step 3: Compute Oh = ΞΌ / β(ΟΒ·ΟΒ·D) = (8.9Γ10β»β΄) / β(998 Γ 0.072 Γ 2Γ10β»β΄) = 0.00089 / β(0.01437) β 0.00089 / 0.1199 β 0.0074
Answer:
We β 1730 (indicating vigorous bag-and-stamen or shear breakup); Oh β 0.0074 (confirming low-viscosity, surface-tension-dominated regime). This aligns with observed fine mist generation in high-pressure mining fog cannons.
ποΈ Real-World Application
At Newmontβs Boddington Mine (Western Australia), engineers redesigned dust suppression nozzles on haul truck loading points after observing poor capture of PMββ. High-speed imaging revealed oversized droplets (SMD > 350 Β΅m) due to low exit velocity and excessive orifice wear. Using WeβOh analysis, they increased pump pressure from 7 MPa to 12 MPa (raising U by ~1.2Γ), selected tapered-orifice nozzles to reduce Dβ, and reformulated with 0.05% non-ionic surfactant (reducing Ο by ~18%). Result: We increased from 850 to 1620, Oh remained < 0.01, and SMD dropped from 380 Β΅m to 145 Β΅m β achieving 92% PMββ suppression (vs. 63% baseline) per MSHA-compliant validation testing.
π§ Interactive Calculator
π§ Open Sprayer Nozzle Hydraulic Performance Characterization Calculatorπ Case Connection
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