# Methods & formulas

Source: https://meptools.com/tools/water-pipe-pressure-drop-pump-head/docs/methods/

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.

## Velocity & flow regime

```
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.

## Friction factor

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.

## Straight-pipe friction loss (Darcy-Weisbach)

```
Friction head       h_f = f (L/D) (v² / 2g)
Pressure drop       Δp  = ρ g h_f
```

## Minor loss from fittings and valves (K method)

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
```

## Total pump head

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.

## Pump power

```
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.

## References

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](/tools/water-pipe-pressure-drop-pump-head/docs/warnings-and-limits) for the
transitional-flow caveat.