Friction Loss Calculator

Background.

Water pushed through a long pipe arrives with less energy than it set out with. The fluid drags against the pipe wall and churns against itself, and that friction turns pressure into a little heat, metre after metre. Engineers express the loss as head: the height of a column of the same fluid whose weight would supply the lost pressure. A head loss of 2 m in a water line means the pump must find an extra 2 m of lift, about 20 kPa, just to overcome the pipe.

The Darcy-Weisbach equation is the standard estimate for a straight run of constant diameter. The loss equals a friction factor times the pipe's length-to-diameter ratio times the velocity head, v²/2g, the height the fluid would rise to if all its kinetic energy were turned into lift. Long pipes lose more, wide pipes less, and fast flow a great deal more, because the velocity is squared.

That squared term combines with diameter in a way that surprises people. For a fixed flow rate the velocity rises with the inverse square of the diameter, so stepping down from a 100 mm to an 80 mm bore roughly triples the friction loss over the same length, if the friction factor stays similar.

The friction factor is the hard part, and here you supply it. It depends on the Reynolds number and on the wall roughness relative to the diameter, and is usually read from a Moody chart or worked out with the Colebrook equation; in laminar flow it is simply 64 divided by the Reynolds number. The result is the straight-pipe, or major, loss only. Bends, valves, entrances and exits add minor losses of their own, and any change in elevation or pump head is a separate term in the energy balance.

What is friction loss calculator?

Friction head loss is the mechanical energy a fluid loses per unit of its weight to wall shear and turbulence as it flows along a pipe, written as an equivalent height of that fluid in metres. Multiplied by the fluid's density and by g it becomes a pressure drop in pascals. The Darcy-Weisbach equation gives it for fully developed flow in a straight pipe of uniform bore, laminar or turbulent, provided the factor used is the Darcy friction factor, which is four times the Fanning factor quoted in some chemical-engineering texts.

How to use this calculator.

1. 01Enter the Darcy friction factor, found from a Moody chart or the Colebrook equation using your Reynolds number and relative roughness, or as 64/Re for laminar flow. If your source gives a Fanning factor, multiply it by four first.
2. 02Enter Pipe length in metres, counting only straight pipe of one diameter. Sections of different diameter need separate runs of the calculation, added together afterwards.
3. 03Enter the actual Inside diameter in metres rather than the nominal size; a nominal 4-inch schedule 40 steel pipe, for instance, has a bore of about 0.1023 m.
4. 04Enter Mean velocity in m/s. If you know the flow rate instead, divide it by the bore area, π × D²/4: 15.7 litres per second in a 0.1 m bore is about 2 m/s.
5. 05Leave Gravitational acceleration at standard gravity, 9.80665 m/s², unless you need a local value, and multiply the head loss by density and g if you want it as a pressure.

The formula.

h_f = f_D × (L/D) × v²/(2g). Here f_D is the dimensionless Darcy friction factor, L the pipe length, D the inside diameter, v the mean velocity (volumetric flow divided by bore area) and g the gravitational acceleration. The term v²/(2g) is the velocity head, the flow's kinetic energy per unit weight expressed as a height. L/D counts how many diameters long the pipe is, and f_D sets how much of a velocity head is lost per diameter of length. Multiplying both sides by ρg gives the pressure form, Δp = f_D (L/D) ρv²/2, in which g cancels, so the gravity input changes only the conversion to head, not the physical pressure drop. Velocity matters most because it is squared, and through velocity so does diameter at a fixed flow. The friction factor is held at whatever you enter, although in reality it drifts with Reynolds number when the velocity changes.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Munson et al., Fundamentals of Fluid Mechanics, 9th ed. (PRINT).
2. [2]Nuclear Regulatory Commission, Thermodynamics, Heat Transfer, and Fluid Flow handbook.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.