Pipe Pressure Drop
Friction head loss and pressure drop along a pipe run.
Equivalent to 1.903 m of head over 50 m of pipe.
Above 4000 the flow is turbulent; f comes from the Swamee-Jain explicit fit to the Colebrook equation, accurate to about 1%.
Velocity × cross-sectional area. That is 56.55 m³/h.
This covers friction along straight pipe only. Bends, valves, and fittings add minor losses that often exceed the straight-run loss in a compact system — they are usually handled as equivalent lengths or K-factors and added on top.
Darcy-Weisbach gives head loss as hf = f(L/D)(v²/2g). Water at 2 m/s through 50 m of 100 mm steel pipe loses about 1.9 m of head, or 18.7 kPa — and the loss scales with the square of velocity.
Velocity is the expensive variable
The single most useful thing in this formula is the v² term. Doubling the flow velocity quadruples the friction loss, which is why pipe sizing is such a consequential decision: dropping one pipe size to save on material can multiply the pumping energy needed for the entire life of the system.
That is also why building services keep water velocity around 1–3 m/s. Below that, pipes get large and expensive; above it, friction losses, pumping cost, and noise all climb steeply.
Two flow regimes, two different rules
The Reynolds number decides which physics applies. Below about 2300 the flow is laminar: fluid moves in orderly layers, the friction factor is exactly 64/Re, and — remarkably — pipe roughness has no effect at all, because the wall is shielded by a stationary boundary layer.
Above about 4000 the flow is turbulent, mixing chaotically, and roughness begins to matter. Between the two lies a transitional band where the flow is unstable and neither correlation is reliable — a genuinely awkward region that good design avoids rather than calculates through.
ν is kinematic viscosity and ε absolute roughness. The turbulent expression is the Swamee-Jain explicit fit to the Colebrook equation, within about 1% over the normal range.
Worked example: 50 m of 100 mm steel pipe at 2 m/s
Establish the regime, then the friction factor, then the loss:
- 1 Compute the Reynolds number. vD/ν = 2 × 0.1 ÷ 1.004e−6 ≈ 1.99 × 10⁵ — comfortably turbulent.
- 2 Take the relative roughness. Commercial steel is ε = 0.045 mm, so ε/D = 0.00045.
- 3 Find the friction factor. Swamee-Jain gives f ≈ 0.0187. Colebrook would need iteration for essentially the same answer.
- 4 Apply Darcy-Weisbach. 0.0187 × (50 ÷ 0.1) × 2² ÷ (2 × 9.81) ≈ 1.90 m of head.
- 5 Convert head to pressure. 1000 kg/m³ × 9.81 × 1.90 ≈ 18.7 kPa.
- 6 Test the velocity sensitivity. At 4 m/s instead of 2, the loss rises to roughly four times this — the v² term dominating.
Absolute roughness of common pipe materials
ε in millimetres. Roughness only affects turbulent flow; in laminar flow it is irrelevant.
| Material | ε (mm) |
|---|---|
| Drawn tubing, PVC, glass | 0.0015 |
| Commercial steel | 0.045 |
| Galvanised iron | 0.15 |
| Cast iron | 0.26 |
| Riveted steel | 1.5 |
| Concrete | 3.0 |
What this leaves out
The biggest omission is minor losses — the pressure dropped across bends, valves, tees, expansions, and entries. The name is misleading: in a compact system with many fittings, these frequently exceed the straight-pipe friction entirely. They are handled either as K-factors applied to the velocity head or as equivalent lengths of straight pipe added to L.
Two other practical points. Roughness values apply to new pipe; scaling, corrosion, and biofilm increase ε substantially over decades, and a system designed with no margin for that will underperform long before it wears out. And viscosity is strongly temperature-dependent — water at 5 °C is roughly 50% more viscous than at 20 °C, which shifts both the Reynolds number and the friction factor enough to matter in heating and chilled-water systems.
Finally, this is friction loss only. A complete calculation also accounts for elevation change and any velocity change between the inlet and outlet, which is what the full Bernoulli energy equation handles.