Pipe pressure drop.
Friction pressure loss for a fluid flowing through a pipe. Uses the Darcy-Weisbach equation with the Swamee-Jain explicit friction factor — accurate for turbulent flow in a wide range of pipes.
How this works
The friction pressure drop is calculated by the Darcy-Weisbach equation:
Δp = f × (L/D) × (ρ × v²) / 2
where Δp is pressure drop (Pa), f is the Darcy friction factor (dimensionless), L is pipe length, D is inside diameter, ρ is fluid density, and v is mean velocity.
The friction factor problem
The Darcy friction factor depends on the Reynolds number (Re = ρvD/μ) and the relative pipe roughness (ε/D). For laminar flow (Re < 2300), it's simply f = 64/Re. For turbulent flow, the canonical equation is Colebrook-White, which is implicit and must be solved iteratively. This calculator uses the Swamee-Jain explicit approximation, which is accurate to within 1% of Colebrook-White across the practical range and runs in one step:
f = 0.25 / [log₁₀((ε/3.7D) + (5.74/Re^0.9))]²
Why this matters
Pipe pressure drop scales with the square of velocity. Doubling the flow rate quadruples the pressure drop. Halving the pipe diameter at constant flow rate multiplies pressure drop by about 32× (D drops by 2, velocity quadruples, f doesn't change much). Pipe sizing is dominated by this.
Typical applications
| Application | Acceptable pressure drop | Why |
|---|---|---|
| Residential water supply | 0.5–3 psi over the run | Above this, fixtures lose pressure at peak demand. |
| Hydronic heating loop | 4–10 ft of head | Sets the circulator pump sizing. |
| Compressed air shop main | < 10% of supply pressure | Pressure drop wastes compressor energy. |
| Natural gas appliance line | 0.3" w.c. (water column) | NFPA 54 limit for residential lines. |
| Industrial process water | 10–50 psi per 100 ft | Depends on pump capacity and process need. |
| Long water transmission | 0.5–5 psi per 1000 ft | Energy cost dominates; size up. |
When this calculator is wrong
- Laminar flow at very low velocities. If Re < 2300, the Swamee-Jain isn't strictly correct (it's a turbulent approximation). The calculator automatically switches to f = 64/Re in this case.
- Two-phase flow. Steam, boiling water, slurries, and air-entrained water all have different friction behavior. Single-phase calculation will under-predict.
- Fittings, valves, and bends. This calculator handles straight pipe only. Elbows, tees, valves, and fittings add "equivalent length" — typically 10–50 pipe diameters for a 90° elbow, 30–60 for a globe valve. For a fitting-heavy system, the equivalent length can exceed the actual pipe length.
- Non-Newtonian fluids. Mud, paint, drilling fluids, and slurries don't follow Darcy-Weisbach. They need rheology-specific equations.
- Compressible flow. For gas at high velocity (Mach > 0.3) or large pressure drops (Δp/p > 10%), the incompressible Darcy-Weisbach over-predicts. Use isothermal or adiabatic compressible-flow equations instead.
Sources
- Darcy-Weisbach equation: Henry Darcy & Julius Weisbach, mid-19th century. The modern form appears in any fluid mechanics textbook (e.g., White, Fluid Mechanics).
- Swamee-Jain friction factor: P. K. Swamee and A. K. Jain, "Explicit equations for pipe-flow problems," Journal of the Hydraulics Division, ASCE, 1976. Accuracy claim: within 1% of Colebrook-White for 5×10³ < Re < 10⁸ and 10⁻⁶ < ε/D < 10⁻².
- Pipe roughness values: Crane Technical Paper No. 410 — Flow of Fluids Through Valves, Fittings, and Pipe. Industry standard reference.
- Fluid properties: Density and viscosity at standard conditions from CRC Handbook of Chemistry and Physics.
Disclaimer. This calculator is for educational and rough-sizing use. For pressure-rated systems, regulated installations (gas, fire sprinkler, pressure vessel), or commercial design, use ANSI/ASME-compliant calculations and verify with a licensed engineer.