Pipe Head Loss⚠ unverified
Physics / Fluids · Compute the Darcy-Weisbach head loss in a pipe
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| friction_factor | frictionfactor | — | 1.0 | Darcy friction factor, dimensionless |
| length | length | m | 1.0 | Pipe length |
| diameter | diameter | m | 1.0 | Pipe internal diameter |
| velocity | velocity | m/s | 1.0 | Mean flow velocity |
| gravity | gravity | m/s**2 | 1.0 | Gravitational acceleration |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | hf | m | Head loss, in metres (m) |
The science & history
Understanding the Parameters
-
$f$ — from Moody chart / Colebrook as a function of Reynolds Number and relative roughness. The calculator treats $f$ as a given input (does not compute Colebrook).
-
$L/D$ — longer or narrower pipes lose more head.
- $v^{2}/(2g)$ — velocity head; loss scales as $v^{2}$.
- $g$ — set ≈ 9.81 m/s²; default may be placeholder
1.0in registry. - $h_f$ — multiply by $\rho g$ for pressure drop $\Delta p = \rho g h_f$.
Derivation (Approaching a Proof)
Dimensional wall shear and momentum balance in a straight duct lead to $\Delta p = f (L/D) (\rho v^{2}/2)$. Dividing by $\rho g$ converts pressure drop to head:
$$h_f = \frac{\Delta p}{\rho g} = f\frac{L}{D}\frac{v^{2}}{2g}.$$
This is empirical in $f$, exact as a definition once $f$ is defined that way.
History
Darcy, Weisbach, and later Moody standardised pipe friction calculations still used in civil and mechanical piping design.
Related Concepts: Reynolds Number, Bernoulli Total Pressure, Mass Flow Rate, Dynamic Pressure
Notes: Registry calculator pipe-head-loss (unverified). Darcy $f$, not Fanning. Fully developed
straight-pipe friction only (no fittings).