Engineering
Froude Number (Fr = V / SQRT(gD)) & Weber Number (We = rho*V^2*d / sigma)
Calculate an open-channel Froude number and a separately specified Weber number with explicit length, velocity and density conventions.
Gravity waves vs surface tension: two dimensionless ratios every fluid engineer needs!
For the simplified open-channel model, Fr=V/sqrt(gD) uses mean speed and hydraulic depth D=flow area/top width. It compares flow with shallow gravity-wave propagation. Fr below or above one classifies that model; supercritical flow alone does not prove a hydraulic jump occurs.
Other Froude applications use other length scales. A ship length-based Froude number cannot use the open-channel Fr=1 regime classification without a different physical analysis.
We=rho*U²*d/sigma compares inertial and surface-tension scales. Its density and velocity must match the phenomenon: aerodynamic drop breakup uses surrounding gas density and relative gas/drop speed, whereas a liquid-based jet Weber number uses liquid density. The 1000 kg/m³ example is explicitly liquid-based, not an air-driven drop-breakup calculation.
There is no universal breakup threshold encoded here. Viscosity, density ratio, forcing and geometry matter. Surface-tension stress sigma/d is a scale, not the exact spherical Laplace pressure (4*sigma/d).
| Dimensionless Group | Formula | Inputs (V = 3 m/s, D = 1.5 m) | Calculated Value & Regime |
|---|---|---|---|
| Froude Number (Fr) | B2 / SQRT(B3 * B4) | 3 / SQRT(9.81 * 1.5) | 0.7821 (< 1 Subcritical) |
| Open-Channel Regime | IF(Fr < 1, "Subcritical", ...) | Tranquil river / canal flow | "Subcritical" |
| Flood Spillway (V = 6 m/s) | B2 set to 6 m/s | 6 / SQRT(14.715) = 1.5641 | "Supercritical" (> 1!) |
| Weber Number (2 mm drop) | (B5 * B8^2 * B6) / B7 | (1000 * 9 * 0.002) / 0.072 | 250.00 (liquid-based definition) |
Open-channel Froude number
Use nonnegative mean speed B2, positive g B3 and positive hydraulic depth B4, in consistent SI units.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<0,B3<=0,B4<=0),"Invalid inputs",ROUND(B2 / SQRT(B3 * B4), 4)))Weber number for the specified density and speed convention
B8 supplies the characteristic or relative speed for this Weber calculation independently of the channel speed B2. B5 is the density appropriate to that definition.
=IF(COUNT(B5:B8)<>4,"Invalid inputs",IF(OR(B5<=0,B6<=0,B7<=0,B8<0),"Invalid inputs",ROUND((B5 * (B8 ^ 2) * B6) / B7, 2)))Classify the unrounded channel ratio
Near critical means within a numerical tolerance of 1e-8 of one. It is a calculation policy, not a measurement-uncertainty interval.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<0,B3<=0,B4<=0),"Invalid inputs",LET(flowRatio,B2/SQRT(B3*B4),IF(ABS(flowRatio-1)<=1E-8,"Near critical",IF(flowRatio<1,"Subcritical","Supercritical")))))Try the example
Use the original values or change them to test your understanding.