Engineering calculators · Hydraulics

Pipe pressure drop and head loss calculator

Work out the friction head loss and pressure drop for water flowing full in a circular pipe. Enter the flow, internal diameter, length and pipe material. The calculator uses the Darcy-Weisbach equation with a Colebrook-White friction factor, corrects the water's density and viscosity for temperature, adds fittings and static lift, and shows Hazen-Williams as a cross-check.

Inputs

Choosing a material fills in its roughness and C value. You can then overwrite either one, for example with a manufacturer's figure. Static lift is the rise in level from the start of the pipe to the end; enter a negative number for a fall.

Results

Velocity1.77 m/sRe 176,229, turbulent

Friction head loss2.57 m2.57 m per 100 m of pipe

Pressure drop, pipe + fittings25.2 kPa0.252 bar

Total head, incl. static lift2.57 m25.2 kPa

Quantity	Value	Notes
Water density	998.2 kg/m³	Interpolated from the table at the water temperature [NIST]
Dynamic viscosity	1.002 mPa·s	Log-interpolated from the table [NIST]
Reynolds number	176,229	ρvD/μ
Relative roughness k/D	0.0000150
Darcy friction factor	0.01615	Colebrook-White, or 64/Re when laminar [dff]
Friction loss, Darcy-Weisbach	2.57 m	f × (L/D) × v²/2g
Fittings loss	0 m	ΣK × v²/2g
Static lift	0 m	As entered
Total head	2.57 m	Friction + fittings + static lift
Cross-check: Hazen-Williams friction loss	3.05 m	10.67 L Q^1.852 / (C^1.852 D^4.8704). Valid for water near room temperature only [hw]

Differences between the two methods are normal. Hazen-Williams ignores temperature and velocity effects, and its C values and the roughness values come from separate tables. If the two disagree by a lot, check that the material values suit your pipe's age and condition.

How the calculation works

Velocity v = Q / A, where A = πD²/4 uses the internal diameter. For plastic pipe this is the outside diameter minus two wall thicknesses, so check the SDR or pressure class.
Water properties. Density and viscosity are interpolated between NIST values for liquid water at atmospheric pressure, from 0 to 100 °C [NIST]. Viscosity is interpolated on a log scale because it falls roughly exponentially with temperature.
Reynolds number Re = ρvD/μ. Below 2,300 the flow is laminar, between 2,300 and 4,000 it is transitional, and above 4,000 it is turbulent [dff].
Friction factor. In laminar flow f = 64/Re. Otherwise the Colebrook-White equation, 1/√f = −2 log₁₀(k/3.7D + 2.51/(Re√f)), is solved by iteration from a Swamee-Jain starting value [dff].
Head loss h_f = f (L/D) v²/2g (Darcy-Weisbach), plus fittings ΣK v²/2g, plus the static lift. Pressure = ρ g h.
Pipe roughness and C values come from published tables: roughness after Moody (1944) [rough], and C factors that already allow for some ageing [hwc]. Where the source gives a range, the calculator uses the rough end (largest roughness, smallest C), so it errs towards more head loss.

Material	k used, mm	C used	Published range
Polyethylene (PE, HDPE)	0.0015	140	k 0.0015 mm (PVC, glass and other drawn tubing; no separate PE value given); C 140
PVC-U	0.0015	150	k 0.0015 mm (PVC, glass, other drawn tubing); C 150
Copper	0.0015	130	k 0.0015 mm (drawn tubing); C 130–140
Steel, commercial or welded	0.045	90	k 0.045 mm; C 90–120
Galvanised iron / steel	0.15	120	k 0.15 mm; C 120
Cast iron	0.26	130	k 0.26 mm; C 130 (new)
Concrete	3	100	k 0.3–3.0 mm; C 100–140

What this cannot tell you. It assumes clean water flowing full in a round pipe at steady flow. It does not cover part-full gravity sewers or open channels, and it does not cover sludge, which is non-Newtonian and can have far higher losses. It does not cover gases, or surge and water hammer. Fitting K values depend on the fitting's size and make, so use the manufacturer's data where you have it. For a design, check the result against your own standard and supplier data.

Sources

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