Water Pressure Drop Calculator
Calculate pressure drop in water pipes using the Darcy-Weisbach equation combined with the Colebrook-White friction factor for turbulent flow.
Steel≈0.046, Copper≈0.0015, PVC≈0.0015, Cast Iron≈0.26
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Formulas Used
Darcy-Weisbach Equation:
ΔP = f · (L / D) · (ρ · V² / 2)
- ΔP = pressure drop (Pa)
- f = Darcy friction factor (dimensionless)
- L = pipe length (m), D = inner diameter (m)
- ρ = water density (kg/m³), V = mean flow velocity (m/s)
Flow Velocity: V = Q / A = Q / (π D² / 4)
Reynolds Number: Re = V · D / ν (ν = μ / ρ)
Friction Factor:
- Laminar (Re < 2300): f = 64 / Re (Hagen-Poiseuille)
- Turbulent (Re ≥ 4000): Colebrook-White equation (iterated to convergence):
1/√f = −2 log₁₀( ε/(3.7D) + 2.51/(Re √f) ) - Initial guess via Swamee-Jain approximation
Water Density (empirical, 0–100 °C):
ρ = 999.842 − 0.0622T − 0.003821T² + 4×10⁻⁶T³ (kg/m³)
Dynamic Viscosity (Vogel equation):
μ = 2.414×10⁻⁵ × 10^(247.8 / (T + 133.15)) (Pa·s)
Assumptions & References
- Steady-state, fully developed, incompressible flow in a straight circular pipe.
- Does not include minor losses (fittings, bends, valves) — add a safety factor of 10–20% for real systems.
- Colebrook-White equation: Colebrook, C.F. (1939), J. Inst. Civil Engineers, 11, 133–156.
- Darcy-Weisbach: Moody, L.F. (1944), Trans. ASME, 66(8), 671–684.
- Density fit: CRC Handbook of Chemistry and Physics, 97th Ed.
- Viscosity: Vogel, H. (1921), Physikalische Zeitschrift, 22, 645–646.
- Typical roughness values: ASHRAE Handbook — Fundamentals (2021), Chapter 22.
- Recommended velocity range for water in pipes: 0.3 – 3.0 m/s (CIBSE Guide C).