Pipe Friction Loss Calculations

pipe friction loss through shear stress and turbulence Flow of fluid through a pipe is resisted by viscous shear stresses within the fluid and the turbulence that occurs along the internal pipe wall, which is dependent on the roughness of the pipe material.

This resistance is termed pipe friction and is usually measured in feet or metres head of the fluid, which is why it is also refered to as the head loss due to pipe friction.

Head Loss in a Pipe

A large amount of research has been carried out over many years to establish various formulae that can calculate head loss in a pipe. Most of this work has been developed based on experimental data.

Overall head loss in a pipe is affected by a number of factors which include the viscosity of the fluid, the size of the internal pipe diameter, the internal roughness of the inner surface of the pipe, the change in elevation between the ends of the pipe and the length of the pipe along which the fluid travels.

Valves and fittings on a pipe also contribute to the overall head loss that occurs, however these must be calculated separately to the pipe wall friction loss, using a method of modeling pipe fitting losses with k factors.

Darcy Weisbach Formula

The Darcy formula or the Darcy-Weisbach equation as it tends to be referred to, is now accepted as the most accurate pipe friction loss formula, and although more difficult to calculate and use than other friction loss formula, with the introduction of computers, it has now become the standard equation for hydraulic engineers.

Weisbach first proposed the relationship that we now know as the Darcy-Weisbach equation or the Darcy-Weisbach formula, for calculating friction loss in a pipe.

Darcy-Weisbach equation:

hf = f (L/D) x (v^2/2g)

where:
hf = head loss (m)
f = friction factor
L = length of pipe work (m)
d = inner diameter of pipe work (m)
v = velocity of fluid (m/s)
g = acceleration due to gravity (m/s²)

or:

hf = head loss (ft)
f = friction factor
L = length of pipe work (ft)
d = inner diameter of pipe work (ft)
v = velocity of fluid (ft/s)
g = acceleration due to gravity (ft/s²)

The establishment of the friction factors was however still unresolved, and indeed was an issue that needed further work to develop a solution such as that produced by the Colebrook-White formula and the data presented in the Moody chart.

The Moody Chart

The Moody Chart finally provided a method of finding an accurate friction factor and this encouraged use of the Darcy-Weisbach equation, which quickly became the method of choice for hydraulic engineers.

The introduction of the personnel computer from the 1980's onwards reduced the time required to calculate the friction factor and pipe head loss. This itself has widened the use of the Darcy-Weisbach formula to the point that most other equations are no longer used.

Hazen-Williams Formula

Before the advent of personal computers the Hazen-Williams formula was extremely popular with piping engineers because of its relatively simple calculation properties.

However the Hazen-Williams results rely upon the value of the friction factor, C hw, which is used in the formula, and the C value can vary significantly, from around 80 up to 130 and higher, depending on the pipe material, pipe size and the fluid velocity.

Also the Hazen-Williams equation only really gives good results when the fluid is Water and can produce large inaccuracies when this is not the case.

The imperial form of the Hazen-Williams formula is:

hf = 0.002083 x L x (100/C)^1.85 x (gpm^1.85 / d^4.8655)

where:
hf = head loss in feet of water
L = length of pipe in feet
C = friction coefficient
gpm = gallons per minute (USA gallons not imperial gallons)
d = inside diameter of the pipe in inches

The empirical nature of the friction factor C hw means that the Hazen-Williams formula is not suitable for accurate prediction of head loss. The friction loss results are only valid for fluids with a kinematic viscosity of 1.13 centistokes, where the velocity of flow is less than 10 feet per sec, and where the pipe diameter has a size greater than 2 inches.

Notes: Water at 60° F (15.5° C) has a kinematic viscosity of 1.13 centistokes.

Common Friction Factor Values of C hw used for design purposes are:

Asbestos Cement 140
Brass tube 130
Cast-Iron tube 100
Concrete tube 110
Copper tube 130
Corrugated steel tube 60
Galvanized tubing 120
Glass tube 130
Lead piping 130
Plastic pipe 140
PVC pipe 150
General smooth pipes 140
Steel pipe 120
Steel riveted pipes 100
Tar coated cast iron tube 100
Tin tubing130
Wood Stave 110

These C hw values provide some allowance for changes to the roughness of internal pipe surface, due to pitting of the pipe wall during long periods of use and the build up of other deposits.

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