Pipe Pressure Drop Calculation: Darcy-Weisbach Formula Explained
Pressure drop in pipes directly determines your pump size and energy cost. This guide explains the Darcy-Weisbach pressure drop formula, how to find the friction factor, and how to account for fittings and valves in your pipe system design.
Pressure drop in a pipe is the loss of pressure as fluid flows from one point to another due to friction between the fluid and the pipe wall. Every metre of pipe, every elbow, every valve takes energy from the fluid — and that energy must be supplied by the pump.
Calculating pressure drop accurately is essential for pump selection, pipe sizing, and energy cost estimation. Under-estimate it and your pump is too small. Over-estimate it and you waste capital on an oversized pump that operates inefficiently.
The Darcy-Weisbach Equation
The Darcy-Weisbach equation is the standard method for calculating pipe pressure drop:
**ΔP = f × (L/D) × (ρv²/2)**
Or in head loss form: **h_f = f × (L/D) × (v²/2g)**
Where: - ΔP = pressure drop (Pa) - h_f = head loss (metres of fluid) - f = Darcy friction factor (dimensionless) - L = pipe length (m) - D = internal pipe diameter (m) - ρ = fluid density (kg/m³) - v = mean flow velocity (m/s) - g = 9.81 m/s²
Convert: 1 bar = 100,000 Pa = 10.2 m of water head
Finding the Friction Factor (f)
The friction factor depends on the flow regime (Reynolds number) and pipe roughness.
**Reynolds Number: Re = ρvD/μ**
Where μ = dynamic viscosity (Pa·s). For water at 20°C: μ = 0.001002 Pa·s.
- Re < 2,300: Laminar flow → f = 64/Re - Re > 4,000: Turbulent flow → use Moody chart or Colebrook equation - Re 2,300–4,000: Transitional — avoid in design
**Colebrook Equation (turbulent flow):** 1/√f = -2 log(ε/(3.7D) + 2.51/(Re√f))
Where ε = pipe roughness (m). For practical use, the **Swamee-Jain approximation** is accurate to 3%: f = 0.25 / [log(ε/(3.7D) + 5.74/Re⁰·⁹)]²
| Pipe Material | Absolute Roughness ε (mm) | Typical Use |
|---|---|---|
| Drawn copper / brass | 0.0015 | HVAC, instrumentation |
| Commercial steel (new) | 0.046 | Water, oil, gas lines |
| Galvanised steel | 0.15 | General industrial |
| Cast iron (new) | 0.26 | Water mains |
| Concrete | 0.3–3.0 | Sewers, stormwater |
| PVC / HDPE (smooth) | 0.0015–0.007 | Chemical, water supply |
Worked Example: Water Supply Pipe
Calculate the pressure drop in a 100 mm nominal bore commercial steel pipe carrying water at 30 m³/h over a 200 m run.
**Step 1 — Velocity:** Internal diameter (100 mm NB schedule 40) = 102.3 mm = 0.1023 m Flow area A = π/4 × 0.1023² = 0.00822 m² Q = 30/3600 = 0.00833 m³/s v = Q/A = 0.00833/0.00822 = **1.01 m/s** ✓ (target 1.0–2.5 m/s)
**Step 2 — Reynolds Number:** Re = 1,000 × 1.01 × 0.1023 / 0.001002 = **103,200** (turbulent)
**Step 3 — Friction Factor (Swamee-Jain):** ε = 0.046 mm, D = 102.3 mm → ε/D = 0.00045 f = 0.25 / [log(0.00045/3.7 + 5.74/103200⁰·⁹)]² = **0.0198**
**Step 4 — Head Loss:** h_f = 0.0198 × (200/0.1023) × (1.01²/19.62) = **19.9 m**
**Step 5 — Pressure Drop:** ΔP = 1,000 × 9.81 × 19.9 = **195,000 Pa = 1.95 bar**
Add fittings and valves (see below) — typically 20–40% of straight pipe loss.
Accounting for Fittings and Valves
Fittings add pressure drop through the equivalent length method or K-factor method.
**Equivalent Length Method:** Add the equivalent pipe length for each fitting to L in the Darcy-Weisbach equation.
| Fitting / Valve | Equivalent Length (pipe diameters) | Example for 100 mm pipe |
|---|---|---|
| Gate valve (fully open) | 7 D | 0.7 m |
| Globe valve (fully open) | 350 D | 35 m |
| Ball valve (fully open) | 3 D | 0.3 m |
| Check valve (swing) | 100 D | 10 m |
| 90° elbow (standard) | 30 D | 3.0 m |
| 90° elbow (long radius) | 16 D | 1.6 m |
| 45° elbow | 16 D | 1.6 m |
| Tee (straight through) | 20 D | 2.0 m |
| Tee (branch flow) | 60 D | 6.0 m |
Recommended Pipe Velocities
Selecting the right pipe velocity balances pressure drop against pipe size (capital cost). These are industry-standard design velocities:
| Service | Recommended Velocity (m/s) | Notes |
|---|---|---|
| Water supply (suction) | 0.5–1.2 | Low velocity to limit NPSH loss |
| Water supply (discharge) | 1.0–2.5 | Standard design range |
| Cooling water | 1.0–3.0 | Higher velocity improves heat transfer |
| Steam condensate | 0.5–1.5 | Keep low to avoid water hammer |
| Compressed air | 5–15 | Higher due to low density |
| Natural gas (low pressure) | 5–15 | Avoid noise and erosion above 20 |
| Fuel oil | 0.5–2.0 | Limited by viscosity and pump head |
Use the Free Pressure Drop Calculator
Our free Pressure Drop Calculator implements the Darcy-Weisbach equation with automatic friction factor calculation (Swamee-Jain approximation). Enter pipe diameter, length, flow rate, fluid properties, and pipe material roughness — it returns pressure drop in Pa, bar, and metres of head, plus the flow velocity and Reynolds number.
Use it alongside the Pump Power Calculator to complete your pump sizing: calculate total head (static + friction losses), then calculate the pump power required for that head and flow rate.