Darcy-Weisbach Pressure Drop
Pressure drops as fluid flows through pipes due to wall friction (major losses) and fittings (minor losses). Calculating total pressure drop lets you correctly size pumps and compressors.
Major Loss (Friction)
h_f = f × (L/D) × (v²/2g) [in metres head]
ΔP_f = f × (L/D) × (ρv²/2) [in Pascals]
f = Darcy friction factor (from Moody chart)
Laminar (Re<2300): f = 64/Re
Turbulent (smooth): f ≈ 0.316/Re^0.25 (Blasius)Worked Example
50mm steel pipe, 30m long, water at 3 m/s:
Re = 1000×3×0.05/0.001 = 150,000 (turbulent)
f = 0.316/150000^0.25 = 0.0163
ΔP = 0.0163 × (30/0.05) × (1000×9/2) = 44,010 Pa = 0.44 barMinor Losses (Fittings)
ΔP_minor = K × (ρv²/2)
K values:
90° elbow: 0.9 | 45° elbow: 0.4
Globe valve (open): 10 | Gate valve (open): 0.2
Sudden expansion: (1 - A1/A2)²Rule of Thumb
- Allow fittings = 30-50% of straight pipe losses for typical runs
- Water systems: target ΔP < 200 Pa/m for supply lines
- Gas systems: pressure drop < 1 mbar/m for low-pressure distribution
Calculate pressure drop: Free Pressure Drop Calculator
Darcy-Weisbach Equation
ΔP = f × (L/D) × (ρV²/2). ΔP = pressure drop (Pa), f = Darcy friction factor, L = pipe length (m), D = internal diameter (m), ρ = fluid density (kg/m³), V = mean flow velocity (m/s). The friction factor f for turbulent flow is found from the Moody chart or Colebrook-White equation, which depends on Reynolds number and relative roughness (ε/D). Smooth pipes (copper, PVC): ε ≈ 0.0015 mm. Commercial steel: ε ≈ 0.046 mm. Rough cast iron: ε ≈ 0.26 mm.
Approximate Friction Factors
- Laminar flow (Re < 2300): f = 64/Re
- Turbulent, smooth pipe (Re ≈ 10⁵): f ≈ 0.018
- Turbulent, rough pipe (Re > 10⁶, rough): f ≈ 0.02–0.04
- Fully rough (high Re, commercial steel): f ≈ 0.025
Frequently Asked Questions
How does pipe roughness affect pressure drop?
In turbulent flow, rougher pipes have higher friction factors and greater pressure drops. A corroded steel pipe may have effective roughness 10× higher than new steel, increasing friction factor by 20–40% and pressure drop correspondingly. Regular cleaning (pigging, chemical treatment) maintains hydraulic efficiency. Lining old pipes with smooth epoxy or polyethylene can restore flow capacity close to that of new smooth pipe.
What is the difference between pressure drop and head loss?
Head loss (h_L, metres) = ΔP / (ρg). Both express the same energy loss — pressure drop in Pascals is convenient for engineering calculations; head loss in metres is intuitive for pump selection (pump head must exceed system head loss). For water at standard conditions: 1 m head ≈ 9,810 Pa ≈ 0.098 bar.
How do I minimise pressure drop in a system?
Key strategies: increase pipe diameter (ΔP ∝ D⁻⁵ for turbulent flow — doubling D reduces ΔP by a factor of 32); reduce pipe length (direct routes, avoid unnecessary loops); minimise fittings (elbows, valves, tees add local losses); use smoother pipe material; lower flow velocity (ΔP ∝ V²). In HVAC design, limiting index circuit (the flow path with highest resistance) must be sized to keep total pressure drop within fan/pump duty.