How to Calculate Friction Loss in Pipe: Step-by-Step Guide

Friction loss in a pipe is the pressure drop that occurs as water flows through it, caused by the fluid’s friction against the pipe wall. The Hazen-Williams equation is the standard empirical formula used for water distribution systems in imperial units. It takes flow rate (GPM), internal pipe diameter (inches), and a pipe-material roughness coefficient (C) as inputs and returns head loss in feet of water per 100 feet of pipe. Multiply that rate by the actual pipe length to get total head loss.

How Do You Calculate Pipe Friction Loss Step by Step?

The full calculation runs in four steps: choose the C-coefficient for your pipe material, apply the Hazen-Williams formula to find head loss per 100 feet, scale to the actual pipe length, and compare to the available head in the system.

1. Identify the pipe material and find its Hazen-Williams C-coefficient.
2. Measure or confirm the actual internal pipe diameter from specification sheets.
3. Apply the Hazen-Williams formula to find head loss per 100 feet, then scale by actual pipe length.

Pipe Roughness C-Coefficient Reference

The C-coefficient represents the smoothness of the pipe interior. Higher values mean smoother pipes and lower friction loss.

Pipe Material	Typical C Value
PVC / Plastic	140 to 150
Copper	130 to 140
New Steel	140
Cast Iron (unlined, older)	80 to 100
Ductile Iron (cement-lined)	140

Hazen-Williams Formula

The formula gives head loss per 100 feet of pipe:

h₁₀₀ = 0.2083 × (100 ÷ C)^1.852 × (q^1.852 ÷ d^4.8655)

Where:

• h₁₀₀: head loss in feet of water per 100 feet of pipe
• q: flow rate in gallons per minute (GPM)
• d: actual internal pipe diameter in inches
• C: Hazen-Williams roughness coefficient

Total head loss (ft) = h₁₀₀ × (actual pipe length ÷ 100)

Hazen-Williams Worked Example: Full Calculation

Inputs: 50 GPM through a nominal 2-inch Schedule 40 PVC pipe (actual internal diameter = 2.067 inches, C = 150) over a 200-foot run.

Step 1: Calculate (100 ÷ C)^1.852 100 ÷ 150 = 0.6667 0.6667^1.852 = 0.4719 (rounded to four decimal places)

Step 2: Calculate q^1.852 50^1.852 = 1,401.2 (rounded to one decimal place)

Step 3: Calculate d^4.8655 2.067^4.8655 = 34.22 (rounded to two decimal places)

Step 4: Assemble the formula h₁₀₀ = 0.2083 × 0.4719 × (1,401.2 ÷ 34.22) h₁₀₀ = 0.2083 × 0.4719 × 40.94 h₁₀₀ = 0.2083 × 19.32 h₁₀₀ = 4.03 ft per 100 ft (rounded to two decimal places)

Step 5: Scale to 200 feet Total head loss = 4.03 × (200 ÷ 100) = 4.03 × 2 = 8.05 ft (rounded to two decimal places)

Result: Friction head loss over 200 feet is 8.05 feet of water. A pump supplying this run must have at least 8.05 feet of additional head capacity to maintain the 50 GPM flow rate at the outlet.

Use the friction loss calculator to quickly determine head loss for any pipe size and flow rate.

What Is the Hazen-Williams C-Coefficient?

The C-coefficient is a single-value measure of pipe wall smoothness calibrated through field and laboratory observation of water pipelines. It is specific to water and does not account for fluid viscosity or temperature changes beyond a narrow range. The coefficient decreases as pipe walls become rougher due to corrosion, scaling, or age. A cast iron main that started at C = 130 when new may reach C = 80 to 100 after decades of service. For design calculations, engineers typically use a derated C value to account for future degradation rather than the as-new figure.

The formula is not accurate for fluids other than water, for pipe velocities above 3 m/s (approximately 10 ft/s), or for very small pipe diameters below 50 mm (2 inches). For those situations, the Darcy-Weisbach equation with a friction factor from the Moody chart is the appropriate method because it accounts for fluid viscosity and flow regime (laminar versus turbulent).

What Is the Difference Between Head Loss and Pressure Drop?

Head loss and pressure drop both describe friction resistance in a pipe, but they use different units. Head loss is in feet (or metres) of water column, a unit of energy per unit weight of fluid. Pressure drop is in pounds per square inch (PSI) or pascals. The conversion is: pressure drop (PSI) = head loss (ft) × 0.4335. For the worked example above, 8.05 ft of head loss converts to 8.05 × 0.4335 = 3.49 PSI (rounded to two decimal places). Use head loss when working with pump curves, which are typically plotted in feet of head. Use PSI when reading pressure gauge readings or specifying fittings.

Sources

• Engineering Toolbox: Hazen-Williams Equation, formula coefficients and imperial unit application.
• Pipeflow: Hazen-Williams C-Coefficient Reference Table, material-specific C values and accuracy limits.

Calculate flow rate with the GPM calculator or see all tools in the engineering calculators hub.