Calculate head loss and pressure drop in pipes using Darcy-Weisbach or Hazen-Williams equations. Free online fluid mechanics calculator for pipe sizing and pump selection.
Calculate head loss and pressure drop in pipes using Darcy-Weisbach or Hazen-Williams equations
Formula:
h_f = f × (L/D) × (v²/(2g))
Where: h_f = Head loss, f = Friction factor, L = Length, D = Diameter, v = Velocity, g = Gravity
Leave empty to auto-calculate based on Reynolds number and pipe roughness
Used for pressure loss calculation. Water at 20°C: 1000 kg/m³
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Friction loss, also known as head loss or pressure drop, is the energy lost due to friction as fluid flows through pipes, fittings, and valves. Understanding friction loss is critical for designing efficient piping systems, selecting appropriate pumps, and ensuring adequate flow rates. Our Friction Loss Calculator makes it easy to determine head loss and pressure drop using the Darcy-Weisbach or Hazen-Williams equations.
Whether you're an engineer designing water distribution systems, a plumber sizing pipes, or a technician troubleshooting flow problems, this calculator simplifies friction loss calculations with support for multiple units and both major calculation methods.
Our Friction Loss Calculator supports two calculation methods. Follow these steps:
h_f = f × (L/D) × (v²/(2g))
Where: h_f = Head loss, f = Friction factor, L = Pipe length, D = Pipe diameter, v = Velocity, g = Gravitational acceleration
The Darcy-Weisbach equation is the most accurate method for calculating friction loss. It applies to all flow regimes (laminar and turbulent) and all pipe types. The friction factor (f) depends on the Reynolds number and pipe roughness.
h_f = 10.67 × L × (Q^1.852) / (C^1.852 × D^4.8704)
Where: h_f = Head loss, L = Pipe length, Q = Flow rate, C = Hazen-Williams coefficient, D = Pipe diameter
The Hazen-Williams equation is simpler and widely used for water distribution systems. It's most accurate for turbulent flow in pipes with diameters between 50 mm and 3,600 mm and velocities between 0.3 m/s and 3 m/s.
Head loss can be converted to pressure loss using:
ΔP = ρ × g × h_f
Where: ΔP = Pressure loss, ρ = Fluid density, g = Gravitational acceleration, h_f = Head loss
Friction loss calculations are essential in numerous engineering applications:
The friction factor depends on flow regime and pipe characteristics:
The C coefficient represents pipe smoothness and condition:
A 200 m long, 150 mm diameter PVC pipe carries 50 L/s of water. C = 140. What is the head loss?
h_f = 10.67 × L × (Q^1.852) / (C^1.852 × D^4.8704)
h_f = 10.67 × 200 × (0.05^1.852) / (140^1.852 × 0.15^4.8704)
h_f = 10.67 × 200 × 0.00347 / (12,340 × 0.00000123) = 4.67 m
A 100 m long, 200 mm diameter steel pipe carries water at 2 m/s. Friction factor f = 0.025. What is the head loss?
h_f = f × (L/D) × (v²/(2g))
h_f = 0.025 × (100 / 0.2) × (2² / (2 × 9.80665))
h_f = 0.025 × 500 × 0.204 = 2.55 m
If head loss is 5 m and water density is 1000 kg/m³, what is the pressure loss?
ΔP = ρ × g × h_f = 1000 kg/m³ × 9.80665 m/s² × 5 m = 49,033 Pa = 49.0 kPa
A system requires 30 L/s flow through 500 m of 100 mm diameter pipe (C = 120). What pump head is needed?
h_f = 10.67 × 500 × (0.03^1.852) / (120^1.852 × 0.1^4.8704)
h_f = 10.67 × 500 × 0.00124 / (8,640 × 0.0000001) = 76.5 m
Pump must provide at least 76.5 m of head to overcome friction loss
Several factors influence friction loss in pipes:
Understanding when to use each method:
Recommendation: Use Darcy-Weisbach for precise calculations and non-water fluids. Use Hazen-Williams for quick estimates in water distribution systems.
Friction loss (also called head loss or pressure drop) is the energy lost due to friction as fluid flows through pipes. It's caused by the interaction between the fluid and the pipe walls, resulting in a decrease in pressure and available energy. Friction loss must be overcome by pumps to maintain flow rates.
Use either the Darcy-Weisbach equation: h_f = f × (L/D) × (v²/(2g)), or the Hazen-Williams equation: h_f = 10.67 × L × (Q^1.852) / (C^1.852 × D^4.8704). The Darcy-Weisbach method is more accurate and works for all fluids, while Hazen-Williams is simpler and commonly used for water distribution systems.
Head loss is the energy loss expressed as an equivalent height of fluid (in meters or feet). Pressure loss is the actual pressure drop (in Pascals or psi). They're related by: ΔP = ρ × g × h_f, where ρ is fluid density and g is gravitational acceleration. Head loss is often preferred because it's independent of fluid density.
For laminar flow (Re < 2300), f = 64/Re. For turbulent flow, use the Moody chart or Swamee-Jain equation, which depends on Reynolds number and relative roughness (roughness/diameter). Our calculator automatically estimates the friction factor if not provided, based on Reynolds number and typical pipe roughness.
C values range from 40 (very rough pipes) to 150 (new smooth pipes). Typical values: 130-150 for new PVC/copper, 100-120 for average condition pipes, 80-100 for older pipes, and 60-80 for poor condition pipes. Higher C values mean less friction loss.
Friction loss decreases significantly with increasing pipe diameter. In the Darcy-Weisbach equation, head loss is inversely proportional to diameter (h_f ∝ 1/D). In Hazen-Williams, it's inversely proportional to D^4.8704, meaning doubling the diameter reduces head loss by approximately 30 times for the same flow rate.
Understanding and calculating friction loss is fundamental to designing efficient piping systems, selecting appropriate pumps, and ensuring adequate flow rates. Our Friction Loss Calculator simplifies these calculations, supporting both the accurate Darcy-Weisbach method and the convenient Hazen-Williams method.
Ready to explore more fluid mechanics concepts? Check out our other calculators like the Reynolds Number Calculator for flow regime determination, or the Force Calculator for mechanics calculations that complement fluid flow analysis.
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