Formula & Engineering Reference
| Symbol | Variable | Unit (SI) |
|---|---|---|
| ΔP | Pressure drop due to friction | Pa |
| f | Darcy-Weisbach friction factor | dimensionless |
| L | Pipe length | m |
| Di | Internal diameter | m |
| ρ | Fluid density | kg/m³ |
| v | Average flow velocity | m/s |
| hL | Head loss | m fluid |
| g | Gravitational acceleration | 9.80665 m/s² |
Reynolds Number:
| Re Range | Flow Regime | Friction Factor |
|---|---|---|
| < 2300 | Laminar | f = 64 / Re |
| 2300 – 4000 | Transition | Uncertain; use laminar conservatively |
| > 4000 | Turbulent | Swamee-Jain (below) |
Swamee-Jain Explicit Approximation (turbulent):
Where ε is absolute roughness (m) and D is internal diameter (m). This explicit form has <3% error versus the Colebrook-White equation for Re: 10&sup4; to 10&sup8;.
- Straight pipe friction loss only. Fittings, valves, and bends are not included
- Single-phase, fully developed, steady-state, incompressible flow assumed
- For compressible gas flow at high Mach number (>0.3), use dedicated compressible flow equations
- Two-phase flow (liquid + gas) requires specialized correlations not covered here
- Pipe roughness values are estimates; actual values depend on pipe age, fluid, and corrosion
- Fluid properties (density, viscosity) must be at the actual operating temperature and pressure
- For pump system design, add static head and fitting losses to this straight-pipe result
- This tool is for preliminary engineering estimates only. Verify all critical designs with detailed analysis
ΔP = f × (L/D) × (ρv²/2). The friction factor f accounts for pipe roughness and flow regime. The term (L/D) is the pipe length-to-diameter ratio, a pure geometric scaling factor. The term ρv²/2 is the dynamic pressure (kinetic energy per unit volume). Together they give pressure drop in Pascal.
Laminar (Re < 2300): f = 64/Re. Turbulent (Re > 4000): Swamee-Jain explicit approximation f = 0.25 / [log(ε/(3.7D) + 5.74/Re0.9)]², which has <3% error vs Colebrook-White. Transition zone (2300–4000): flow regime is unstable; results should be treated as approximate.
Re = ρvD/μ, the ratio of inertial to viscous forces. Below 2300: laminar (smooth, layered). Above 4000: turbulent (chaotic mixing). Between 2300–4000: transition, unpredictable. High Reynolds numbers occur in large-diameter, high-velocity, low-viscosity flows.
New carbon steel pipe: ε = 0.046 mm (default). Galvanized steel: 0.15 mm. Concrete: 0.3–3 mm. Drawn tubing / stainless: 0.015 mm. Aged/corroded carbon steel: 0.1–0.5 mm depending on service years and fluid corrosivity. The relative roughness ε/D decreases with larger pipe diameter, so large-bore pipes have lower friction factors at the same Reynolds number.
Head loss hL = ΔP / (ρg) is pressure drop expressed as an equivalent height of fluid column. For water: 1 m head = 9810 Pa = 0.0981 bar. Head loss is used in pump system design because pump specifications (and pump curves) are in meters of head. Pump head required = static head + friction head loss.
No, straight pipe friction only. Fitting losses (elbows, tees, valves) can be estimated by the equivalent length method: convert each fitting to its equivalent pipe length (K/f for each fitting type), add to the straight pipe length, then recalculate. For rough estimates, add 20–50% to the straight pipe pressure drop for typical process piping.
Water dynamic viscosity: 1.002 mPa·s at 20°C, 0.655 mPa·s at 40°C, 0.282 mPa·s at 80°C. Viscosity decreases significantly with temperature, so always use the value at the operating temperature. For steam, use steam viscosity from steam tables (typically 0.01–0.02 mPa·s). For gas, use the gas viscosity at operating pressure and temperature.
In turbulent flow, where most engineering flows operate, the friction factor f is nearly constant (depends weakly on Re in the rough turbulent regime). Since ΔP = f(L/D)(ρv²/2) and f is approximately constant, ΔP ∝ v². Doubling velocity quadruples pressure drop. This v² dependence is why large pumps are needed for high-velocity systems.
Swamee-Jain has <3% maximum error vs the implicit Colebrook-White equation for Re between 10⁴ and 10⁸ and ε/D between 10⁻⁶ and 10⁻². This accuracy is sufficient for all practical engineering purposes. The uncertainty in pipe roughness alone is typically ±50% for aged pipe, far exceeding the 3% formula error.
In the transition zone, flow alternates between laminar and turbulent unpredictably. The friction factor cannot be reliably predicted. This calculator uses the laminar formula (f = 64/Re) as a conservative estimate and displays a warning. In practice, most engineering flows are either well into the turbulent regime (Re > 10,000) or fully laminar. The transition zone is rarely encountered in steady-state process piping.
Pressure Drop Engineering Guide
5 topics • Darcy-Weisbach & Moody referencePressure drop calculation is at the heart of pipe sizing and pump selection. Every fluid system with a pump, compressor, or pressure source has a maximum available driving pressure, the difference between the source pressure and the minimum required pressure at the delivery point. The sum of all friction losses in the piping system must not exceed this available pressure if flow is to be maintained at design rate.
The Darcy-Weisbach equation is the fundamental tool for this calculation. Unlike empirical formulas such as the Hazen-Williams equation (water only), Darcy-Weisbach applies to any fluid (liquid, gas, or steam) at any flow rate, in any pipe size, and in any flow regime. Its inputs are the fluid density, viscosity, flow velocity, pipe geometry, and pipe roughness. The friction factor that connects these inputs is described by the Moody diagram or the Colebrook-White equation.