Friction loss

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In fluid flow, friction loss is the loss of pressure or “head” that occurs in pipe flow due to the effect of viscosity near the surface of the pipe.[1] Friction Loss is considered a "major loss", not to be confused with “minor loss”, which includes energy lost due to obstructions. In mechanical systems such as internal combustion engines, the term refers to the power lost overcoming the friction between two moving surfaces, a different phenomenon.

This mode of energy loss is due to the shear stress between the fluid and the pipe surface and is characterized by the flow being either laminar or turbulent. In the case of laminar flow, obtained at low flow velocity, that velocity varies smoothly between the bulk of the fluid and the wall, where it is zero. In turbulent flow (obtained at higher velocity) a layer of chaotic eddies and vortices near the pipe surface forms the transition to the bulk flow. For turbulent flow, the pressure drop is influenced by the roughness of the pipe surface; in the laminar case, such effects are negligible because the velocity near the surface is zero.[1]


Friction loss has several causes, including:

  • Frictional losses depend on the conditions of flow and the physical properties of the system.
  • Movement of fluid molecules against each other, i. e., viscosity.
  • Movement of fluid molecules against the inside surface of a pipe or the like, particularly if the inside surface is rough, textured, or otherwise not smooth.
  • Bends, kinks, and other sharp turns in hose or piping.

In pipe flows, the losses due to friction are of two kinds: skin-friction and form-friction. The former is due to the roughness of the inner part of the pipe where the fluid comes in contact with the pipe material, while the latter is due to obstructions present in the line of flow--perhaps a bend, control valve, or anything that changes the course of motion of the flowing fluid.

Surface Roughness[edit]

The roughness of the surface of the pipe affects the fluid flow in the regime of turbulent flow. Usually denoted by ε, the values for some representative materials are:[2][3][4]

Surface Roughness ε
Material mm in
Riveted Steel 0.9–9.0
Concrete 0.3–3.0 0.012–0.12
Wood Stave 0.2–0.9
Cast Iron 0.26 0.010
Galvanized Iron 0.15 0.006
Asphalted Cast Iron 0.12 0.0048
Commercial or Welded Steel, Wrought Iron 0.045 0.0018
PVC, Brass, Copper, Glass, other drawn tubing 0.0015 0.00006

Calculating friction loss[edit]


One of the accepted methods to calculate friction losses resulting from fluid flow in pipes is the Darcy–Weisbach equation. For a circular pipe with a fluid of given density ρ and viscosity μ, the head loss hf per unit length L of pipe (the hydraulic slope S) can be expressed[5]

S = \frac{h_f }{ L } = \frac{ \Delta p }{ \rho \cdot g \cdot L} =\frac{ f_D }{ 2g } \frac{V^2}{D} = \frac{ 8 f_D }{\pi^2 g } \frac{Q^2}{D^5}


S = the hydraulic slope (dimensionless)
hf = head loss due to friction, given in units of length;
L = Pipe length;
Δp = pressure loss due to friction, given in force per unit area;
ρ = fluid density, given in mass per unit volume;
g = the local acceleration due to gravity;
fD = Darcy friction factor (see Confusion with the Fanning friction factor );
V = average flow velocity, experimentally measured as the volumetric flow rate Q per unit cross-sectional wetted areaD2/4);
D = hydraulic diameter of the pipe (for a pipe of circular section, the internal diameter of the pipe);
Q = volumetric flow rate (in volume per unit time),

For a given pipe diameter D, the hydraulic slope S is proportional to the square of volumetric flow Q or to the square of the fluid velocity V. At a given velocity of fluid flow V, the hydraulic slope S is inversely proportional to the hydraulic diameter of the pipe D, while at a given volume of fluid flow Q, the hydraulic slope S is inversely proportional to the fifth power of D.

The value of fD is given by the (recursive) Colebrook equation:

 \frac{1}{\sqrt{f_D}}= -2 \log_{10} \left( \frac { 1 }{ 3.7 } \frac { \varepsilon } { D} + \frac {2.51} {\mathrm{Re} \sqrt{f_D}} \right)

where ε is the surface roughness and Re is the Reynolds number,

 \mathrm{Re} = \frac{\rho V D }{ \mu }

and μ is the fluid's viscosity.


For a given design flow volume Q, one may select pipe for a particular hydraulic slope S, based on the candidate pipe material's roughness ε and diameter D. Expressing the Colebrook equation in these terms, and using the formula for Re,

 \frac{1}{\sqrt{f_D}} = -2 \log_{10} \left( \frac { 1 }{ 3.7 } \frac { \varepsilon } { D} + \frac {2.51} {\frac{\rho V D }{ \mu } \sqrt{f_D}} \right)

and, using the Darcy–Welsbeck equation to eliminate the factor V × √fD,

 \frac{1}{\sqrt{f_D}} = -2 \log_{10} \left( \frac { 1 }{ 3.7 } \frac { \varepsilon } { D} + \frac {2.51} {\frac{\rho D}{ \mu } \sqrt{2 g D S}} \right)

In the case of water (ρ = 1 g/cc, μ = 1 g/m/s[6]) flowing through a 12-inch (300 mm) Schedule-40 PVC pipe (ε = 0.0015mm, D = 11.938 in.), a hydraulic slope S = 0.01 (1%) is reached at a flow rate Q = 151 lps (liters per second), or at a velocity V = 2.09 m/s (meters per second). The following table gives Reynolds number Re, Darcy friction factor fD, flow rate Q, and velocity V such that hydraulic slope S = hf / L = 0.01, for a variety of nominal pipe (NPS) sizes.

Volumetric Flow Q where Hydraulic Slope S is 0.01, for selected Nominal Pipe Sizes (NPS) in PVC[7][8]
in mm in[9] gpm lps ft/s m/s
½ 15 0.622 0.01 6575 5.08 1.3 0.082 0.862 0.283
¾ 20 0.824 0.01 8711 5.45 2 0.143 1.064 0.349
1 25 1.049 0.01 11090 5.76 4 0.247 1.269 0.416
40 1.610 0.01 23121 6.32 12 0.743 1.724 0.565
2 50 2.067 0.01 35360 6.64 23 1.458 2.054 0.674
3 150 3.068 0.01 68867 7.15 67 4.215 2.695 0.880
4 100 4.026 0.01 108614 7.50 138 8.723 3.240 1.062
6 150 6.065 0.01 215001 8.03 412 26.013 4.257 1.396
8 200 7.981 0.01 338861 8.39 855 53.951 5.098 1.672
10 250 10.020 0.01 493357 8.68 1563 98.617 5.912 1.938
12 300 11.938 0.01 658253 8.90 2485 156.764 6.621 2.170

Note that the cited sources recommend that flow velocity be kept below 5 feet / second (~1.5 m/s).


  1. ^ a b Munson, B.R. (2006). Fundamentals of Fluid Mechanics 5th Edition. Hoboken, NJ: Wiley & Sons. 
  2. ^ "Pipe Roughness". Pipe Flow Software. Retrieved 5 October 2015. 
  3. ^ "Pipe Roughness Data". Retrieved 5 October 2015. 
  4. ^ Formula "Pipe Friction Loss Calculations" Check |url= scheme (help). Pipe Flow Software. Retrieved 5 October 2015.  The friction factor C in the Hazen-Williams formula takes on various values depending on the pipe material in an attempt to accommodate surface roughness.
  5. ^ Brown, G.O. (2003). "The History of the Darcy-Weisbach Equation for Pipe Flow Resistance". Environmental and Water Resources History. American Society of Civil Engineers. pp. 34–43. doi:10.1061/40650(2003)4. 
  6. ^ "Water - Dynamic and Kinetic Viscosity". Engineering Toolbox. Retrieved 5 October 2015. 
  7. ^ "Technical Design Data" (PDF). Orion Fittings. Retrieved 29 September 2015. 
  8. ^ "Tech Friction Loss Charts" (PDF). Hunter Industries. Retrieved 5 October 2015. 
  9. ^ "Pipe Dimensions" (PDF). Spirax Sarco Inc. Retrieved 29 September 2015. 

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