Friction loss

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In fluid flow, friction loss is the loss of pressure or “head” that occurs in pipe or duct flow due to the effect of viscosity near the surface of the pipe or duct.[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 surface and the fluid flowing within, that flow being characterized as 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 surface, where it is zero. In turbulent flow (obtained at higher velocity) a layer of chaotic eddies and vortices near the surface forms the transition to the bulk flow. For turbulent flow, the pressure drop is influenced by the roughness of the 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. Viscosity is the property of a fluid that gives rise to friction.
  • 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 transition, fitting, or control valve—anything that changes the course of motion of the flowing fluid.

Surface Roughness[edit]

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

Surface Roughness ε (for water pipes)
Material mm in
Riveted Steel 0.9–9.0 23–229
Concrete 0.3–3.0 0.012–0.12
Wood Stave 0.2–0.9 5–23
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

Values used in calculating friction loss in ducts (for, e.g., air) are:[5]

Surface Roughness ε (for air ducts)
Material mm in
Flexible Duct (wires exposed) 3.00 0.120
Flexible Duct (wires covered) 0.90 0.036
Galvanized Steel 0.15 0.006
PVC, Stainless Steel, Aluminum, Black Iron 0.05 0.0018

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[6]

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


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;
D = hydraulic diameter of the pipe (for a pipe of circular section, the internal diameter of the pipe).

For a given pipe diameter D, the hydraulic slope S is proportional 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.

The volumetric flow rate Q (in volume per unit time) is related to the flow velocity V and pipe diameter D:

Q = V \left( \frac{\pi}{4} \right) D^2 .

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.

Calculating Friction Loss for Water in a Pipe[edit]

In a design problem, 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–Weisbach equation to eliminate the factor V × √fD in favor of the hydraulic slope S,

 \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)

Thus, for a given pipe diameter D, the Darcy friction factor fD can be expressed in closed form with independent variable hydraulic slope S and (implied) dependent variable flow velocity V.

In the case of water (ρ = 1 g/cc, μ = 1 g/m/s[7]) flowing through a 12-inch (300 mm) Schedule-40 PVC pipe (ε = 0.0015 mm, D = 11.938 in.), a hydraulic slope S = 0.01 (1%) is reached at a flow rate Q = 157 lps (liters per second), or at a velocity V = 2.17 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[8][9]
in mm in[10] gpm lps ft/s m/s
½ 15 0.622 0.01 4467 5.08 0.9 0.055 0.928 0.283
¾ 20 0.824 0.01 7301 5.45 2 0.120 1.144 0.349
1 25 1.049 0.01 11090 5.76 3.8 0.232 1.366 0.416
40 1.610 0.01 23121 6.32 12 0.743 1.855 0.565
2 50 2.067 0.01 35360 6.64 24 1.458 2.210 0.674
3 75 3.068 0.01 68868 7.15 70 4.215 2.899 0.884
4 100 4.026 0.01 108615 7.50 144 8.723 3.485 1.062
6 150 6.065 0.01 215001 8.03 430 26.013 4.579 1.396
8 200 7.981 0.01 338862 8.39 892 53.951 5.484 1.672
10 250 10.020 0.01 493357 8.68 1631 98.617 6.360 1.938
12 300 11.938 0.01 658254 8.90 2592 156.765 7.122 2.171

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

Calculating Friction Loss for Air in a Duct[edit]

Friction loss also takes place as a gas, say air, flows through ductwork. The difference in the character of the flow from the case of water in a pipe stems from the differing Reynolds number Re and the roughness of the duct.

For specific choices of duct material, and assuming air at standard temperature and pressure, standard charts can be used to calculate the friction loss.[11][5]

The friction loss is customarily given as pressure loss for a given duct length, Δp / L, in units of (US) inches of water for 100 feet or (SI) kg / m2 / s2.


  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. ^ "Pipe Friction Loss Calculations". 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 account for surface roughness.
  5. ^ a b "On-Line Duct Friction Loss". Retrieved 8 October 2015. 
  6. ^ 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. 
  7. ^ "Water - Dynamic and Kinetic Viscosity". Engineering Toolbox. Retrieved 5 October 2015. 
  8. ^ "Technical Design Data" (PDF). Orion Fittings. Retrieved 29 September 2015. 
  9. ^ "Tech Friction Loss Charts" (PDF). Hunter Industries. Retrieved 5 October 2015. 
  10. ^ "Pipe Dimensions" (PDF). Spirax Sarco Inc. Retrieved 29 September 2015. 
  11. ^ Beckfeld, Gary D. (2012). "HVAC Calculations and Duct Sizing" (PDF). PDH Online, 5272 Meadow Estates Drive Fairfax, VA 22030. Retrieved 8 October 2015. 

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