Pump Head Calculator (Total Dynamic Head)

Calculate total dynamic head from static lift plus pipe friction loss using the Hazen-Williams equation, with flow velocity and pressure output.

Inputs

Vertical distance the water is raised, from source surface to discharge.

Developed length of pipe (include an allowance for fittings as equivalent length).

Internal diameter of the pipe in millimetres.

Design flow rate through the pipe.

Hazen-Williams roughness coefficient — higher = smoother pipe.

Result

Total dynamic head
11.04 m
36.2 ft of water
  • Static head (lift)10.00 m
  • Friction head loss1.04 m
  • Flow velocity1.06 m/s
  • Equivalent pressure108.3 kPa · 1.08 bar · 15.7 psi
Note — The Hazen-Williams equation is valid for water near 15 °C in turbulent flow. Add fittings as equivalent pipe length. For non-water fluids or very low temperatures use Darcy-Weisbach instead.

Step-by-step

  1. Convert flow to m³/s: 500 L/min ÷ 60000 = 0.008333 m³/s.
  2. Convert diameter to m: 100 mm = 0.1 m; pipe area = π·(d/2)² = 0.007854 m².
  3. Friction loss (Hazen-Williams) = 10.67 · 100 · 0.008333^1.852 / (150^1.852 · 0.1^4.8704) = 1.04 m.
  4. Total dynamic head = static 10 m + friction 1.04 m = 11.04 m.

How to use this calculator

  • Enter the static head — the vertical rise from the water source surface to the discharge point.
  • Enter the total pipe length; add an equivalent-length allowance for elbows and valves.
  • Enter the pipe inner diameter (mm) and the design flow rate (L/min).
  • Pick the pipe material to set the Hazen-Williams C coefficient, then read total dynamic head and velocity.

About this calculator

Total dynamic head (TDH) is the total resistance a pump must overcome, expressed as an equivalent height of water column. It is the sum of the static head — the vertical distance the water is lifted — and the friction (or dynamic) head, the pressure lost to friction as water moves through pipe and fittings. This calculator computes friction loss with the Hazen-Williams equation, the industry-standard empirical formula for water in pressurised pipes, using a roughness coefficient C that depends on pipe material. It also reports the flow velocity (which should generally stay below ~1.5–2.5 m/s to limit losses and water hammer) and converts the head to pressure in kPa, bar, and psi. Use TDH to select a pump whose head-flow curve meets your duty point.

How it works — the formula

TDH = Static head + Friction head Friction (Hazen-Williams, SI): h_f = 10.67 · L · Q^1.852 / (C^1.852 · d^4.8704) Pressure: ΔP = ρ · g · h (ρ=1000 kg/m³, g=9.80665 m/s²)

Friction loss grows with the 1.852 power of flow and falls steeply with diameter (4.87 power), so modest pipe upsizing sharply cuts losses. Head in metres of water converts to pressure via the hydrostatic relation ΔP = ρgh.

Worked examples

Example 1
100 m of 100 mm PVC (C=150) at 500 L/min, 10 m lift
Inputs:
staticHead=10, length=100, diameter=100, flow=500, cFactor=150
Output:
friction ≈ 1.04 m → TDH ≈ 11.04 m
Example 2
50 m of 50 mm steel (C=120) at 200 L/min, no lift
Inputs:
staticHead=0, length=50, diameter=50, flow=200, cFactor=120
Output:
friction ≈ 4.22 m → TDH ≈ 4.22 m
Example 3
200 m of 150 mm copper (C=130) at 1000 L/min, 20 m lift
Inputs:
staticHead=20, length=200, diameter=150, flow=1000, cFactor=130
Output:
friction ≈ 1.36 m → TDH ≈ 21.36 m

Limitations

  • Valid for water near 15 °C in turbulent flow; not for gases or viscous fluids.
  • Fittings must be added manually as equivalent pipe length.
  • Does not include velocity head or suction-side NPSH considerations.

Engineering estimate. Confirm pump selection against the manufacturer's certified head-flow and NPSH curves.

Frequently asked

Total dynamic head (TDH) is the total equivalent height of water a pump must work against: the static lift plus all friction losses in the pipe and fittings at the design flow rate. Pump curves are published as head versus flow, so TDH is exactly the number you match against the curve to select a pump.

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