How this instrument works
Head loss to friction is the energy a flowing fluid surrenders to the pipe wall, expressed as an equivalent height of the fluid column: metres of water a pump must lift just to keep the flow moving through a straight run. The Darcy-Weisbach equation, h_f = f·(L⁄D)·(v²⁄2g), builds that height from four ingredients. Length over diameter (L⁄D) counts how many pipe-diameters of travel the fluid endures — its geometric exposure to the wall. Velocity squared over twice gravity (v²⁄2g) is the fluid's kinetic energy per unit weight, the dynamic pressure that friction is stealing from. The friction factor f scales the whole thing to the pipe's actual roughness and flow regime.
The equation carries two names because two engineers reached it independently in the 1850s. Henry Darcy, testing cast-iron mains for the water supply of Dijon, measured how head loss grew with length and with the square of velocity; Julius Weisbach supplied the dimensionless coefficient that made the relationship general enough for any pipe and fluid. Their friction factor f is four times the Fanning friction factor used in some chemical-engineering texts — pull a value from the wrong chart and the head loss comes out off by exactly that factor.
f is not a fixed property of the pipe. It depends on the Reynolds number, which tracks whether the flow is laminar or turbulent, and on the pipe's relative roughness — wall texture divided by diameter — so engineers read it from a Moody chart or solve the Colebrook-White equation rather than treating it as a constant. The formula also covers only major loss: straight-run skin friction. Bends, valves, and fittings add their own minor losses, tallied separately, before a pump's total dynamic head is complete.
- Enter the Darcy friction factor — read it from a Moody chart or a Colebrook-White solver for your Reynolds number and relative roughness; 0.02 is typical for turbulent flow in an aged steel or plastic main.
- Enter the Pipe length, the straight run you are checking, in metres or feet.
- Enter the Pipe diameter — the internal bore, not the nominal pipe size — in mm, cm, m, or inches.
- Enter the Flow velocity, the mean speed of the fluid in the pipe; divide flow rate by cross-sectional area if you only have a rate.
- Read the Head loss in mm, cm, or m — the friction component you add to elevation change and minor losses for total pump head.
Worked example — 100 m of 100 mm pipe at 2 m/s
Size a 100 m service run of 100 mm bore pipe carrying water at 2 m/s — a common design velocity chosen to limit erosion and noise in mains — with a Darcy friction factor of 0.02, typical for turbulent flow in an aged steel line. The equation gives h_f = 0.02 × (100 ⁄ 0.1) × (2² ⁄ (2 × 9.80665)) = 0.02 × 1000 × 0.203946 = 4.079 m, or 4.078865 m at the sheet's full precision — just over four metres of head the pump has to supply for friction alone, on top of any elevation change.
The same pipe at 4 m/s instead of 2 m/s does not double that figure — it quadruples it, to 16.315 m, because velocity is squared in the formula. That is the practical lesson pump and pipe sizing turns on: raising a pipe's diameter for the same flow rate drops velocity, and with it friction loss, far faster than the extra pipe costs, which is why oversizing a main by one size is so often the cheaper choice over a pump's operating lifetime.
Questions
Why does the friction factor need a chart instead of a fixed number?
Because f is not a material property — it depends on the Reynolds number (laminar versus turbulent flow) and on the pipe's relative roughness (wall texture divided by diameter). Engineers read it off a Moody chart or solve the Colebrook-White equation for the specific velocity and pipe in question; smooth plastic pipe in fast turbulent flow often lands near 0.02, but the same pipe at a trickle can sit an order of magnitude higher in the laminar range.
What is the difference between the Darcy and Fanning friction factor?
A factor of exactly four. The Darcy friction factor used in this equation is four times the Fanning friction factor found in some chemical-engineering references, because Fanning's definition is built around wall shear stress rather than the head-loss form Darcy and Weisbach used. Pulling a Fanning value into this formula without multiplying by four understates the head loss by 75 percent — check which convention your chart or software uses before entering f.
Does this formula include losses from bends, valves, and fittings?
No — it covers only major loss, the straight-run friction against the pipe wall. Fittings, valves, elbows, and entrances add minor losses, usually tallied with a loss coefficient K for each fitting or converted to an equivalent length of straight pipe and added to L. A full pump-sizing calculation adds this instrument's head loss to the minor losses and any static elevation change.
Why does head loss grow with the square of velocity, not velocity itself?
Because friction loss tracks the kinetic energy of the flow, and kinetic energy scales with velocity squared. Halving the flow velocity — by using a larger pipe for the same flow rate — cuts the friction head to a quarter, not a half, which is the main reason engineers oversize mains rather than run them at the smallest diameter that fits the flow.
What friction factor should I use without a Moody chart handy?
For fully turbulent flow in a moderately rough commercial pipe, 0.02 to 0.03 is a common planning estimate, but treat it only as a starting point. For an actual design, calculate the Reynolds number from velocity, diameter, and the fluid's kinematic viscosity, estimate the pipe's relative roughness from its material, and solve the Colebrook-White equation or read the Moody chart directly.
Can I use this equation for fluids other than water?
Yes — the equation itself is fluid-agnostic; the fluid's properties only enter through the friction factor and the Reynolds number used to find it. Oil, air in a duct, or any other Newtonian fluid obeys the same h_f = f·(L⁄D)·(v²⁄2g) relationship, provided the friction factor is calculated for that fluid's viscosity and density at the flow's Reynolds number.