The exact equations used — area, velocity, Reynolds number, friction factor, Darcy-Weisbach, minor loss, pump head, and power.
The calculation is fully transparent: every number in the result panel comes from one of the equations below, and the same list appears in the report's Formulas & references card. Standard gravity is g = 9.80665 m/s² throughout.
Pipe area A = π D² / 4
Mean velocity v = Q / A
Reynolds number Re = ρ v D / μ
Flow regime is classified from Re:
| Regime | Condition |
|---|---|
| Zero flow | Re ≤ 0 (zero or no flow) |
| Laminar | Re < 2300 |
| Transitional | 2300 ≤ Re ≤ 4000 |
| Turbulent | Re > 4000 |
The regime thresholds follow common engineering convention; the transition band in particular depends on real-world disturbances, so treat transitional results as approximate.
The Darcy friction factor f is chosen by Reynolds number:
Laminar (Re < 2300) f = 64 / Re
Otherwise (Re ≥ 2300) f = 0.25 / [ log10( ε/(3.7 D) + 5.74 / Re^0.9 ) ]² (Swamee-Jain)
The Swamee-Jain equation is an explicit approximation to Colebrook-White. Note the boundary:
the laminar 64/Re relation is used only below Re 2300, so transitional flow (2300–4000) uses the
Swamee-Jain expression, even though it is labelled "Transitional" in the regime readout — the
Swamee-Jain approximation is least reliable in this range.
Friction head h_f = f (L/D) (v² / 2g)
Pressure drop Δp = ρ g h_f
Each fitting's loss uses the velocity head; the total uses the summed coefficient ΣK:
Per fitting h_i = K_i (v² / 2g)
Total h_minor = ΣK (v² / 2g)
Pressure drop = ρ g h_minor
The pump head is a simple energy balance of the four components on the path:
H = h_f + h_minor + h_static + h_residual
where h_residual = P_residual / (ρ g)
h_static is the entered static/elevation head (positive lift, negative gravity assist).h_residual converts the required outlet pressure to an equivalent head.Hydraulic power P_hyd = ρ g Q H
Shaft power P_shaft = P_hyd / η
Shaft power is only reported when a pump efficiency η is entered; otherwise the panel shows hydraulic power only.
The report's Formulas and references card lists every equation above with a short reference note, and links out for Reynolds number, the Swamee-Jain / Darcy friction factor, and the Darcy-Weisbach equation. The regime thresholds and the Swamee-Jain approximation are the two items where engineering judgement matters most — see Warnings & limits for the transitional-flow caveat.