The term friction loss (or frictional loss) has a number of different meanings, depending on its context.

Jean Le Rond d'Alembert, Nouvelles expériences sur la résistance des fluides, 1777


Friction loss is a significant engineering concern wherever fluids are made to flow, whether entirely enclosed in a pipe or duct, or with a surface open to the air.

Calculating volumetric flow

In the following discussion, we define volumetric flow rate V̇ (i.e. volume of fluid flowing per time) as


r = radius of the pipe (for a pipe of circular section, the internal radius of the pipe).
v = mean velocity of fluid flowing through the pipe.
A = cross sectional area of the pipe.

In long pipes, the loss in pressure (assuming the pipe is level) is proportional to the length of pipe involved. Friction loss is then the change in pressure Δp per unit length of pipe L

When the pressure is expressed in terms of the equivalent height of a column of that fluid, as is common with water, the friction loss is expressed as S, the "head loss" per length of pipe, a dimensionless quantity also known as the hydraulic slope.


ρ = density of the fluid, (SI kg / m3)
g = the local acceleration due to gravity;

Characterizing friction loss

Friction loss, which is due to the shear stress between the pipe surface and the fluid flowing within, depends on the conditions of flow and the physical properties of the system. These conditions can be encapsulated into a dimensionless number Re, known as the Reynolds number

where V is the mean fluid velocity and D the diameter of the (cylindrical) pipe. In this expression, the properties of the fluid itself are reduced to the kinematic viscosity ν


μ = viscosity of the fluid (SI kg / m • s)

Friction loss in straight pipe

The friction loss in uniform, straight sections of pipe, known as "major loss", is caused by the effects of viscosity, the movement of fluid molecules against each other or against the (possibly rough) wall of the pipe. Here, it is greatly affected by whether the flow is laminar (Re < 2000) or turbulent (Re > 4000):[1]

Form friction

Factors other than straight pipe flow induce friction loss; these are known as "minor loss":

For the purposes of calculating the total friction loss of a system, the sources of form friction are sometimes reduced to an equivalent length of pipe.

Surface roughness

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:[3][4][5]

Surface Roughness ε (for water pipes)
Material mm in
Corrugated plastic pipes (apparent roughness) 3.5 0.14[6]
Mature foul sewers 3.0 0.12[6]
Steel water mains with general tuberculations 1.2 0.047[6]
Riveted Steel 0.9–9.0 0.035–0.35
Concrete (heavy brush asphalts or eroded by sharp material),
0.5 0.02[6][7]
Concrete 0.3–3.0 0.012–0.12
Wood Stave 0.2–0.9 5–23
Galvanized metals (normal finish),
Cast iron (coated and uncoated)
0.15–0.26 0.006–0.010[6]
Asphalted Cast Iron 0.12 0.0048
Concrete (new, or fairly new, smooth) 0.1 0.004[6]
Steel Pipes, Galvanized metals (smooth finish),
Concrete (new, unusually smooth, with smooth joints),
Asbestos cement,
Flexible straight rubber pipe (with smooth bore)
0.025–0.045 0.001–0.0018[6]
Commercial or Welded Steel, Wrought Iron 0.045 0.0018
PVC, Brass, Copper, Glass, other drawn tubing 0.0015–0.0025 0.00006–0.0001[6][7]

Values used in calculating friction loss in ducts (for, e.g., air) are:[8]

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


Laminar flow is encountered in practice with very viscous fluids, such as motor oil, flowing through small-diameter tubes, at low velocity. Friction loss under conditions of laminar flow follow the Hagen–Poiseuille equation, which is an exact solution to the Navier-Stokes equations. For a circular pipe with a fluid of density ρ and viscosity μ, the hydraulic slope S can be expressed

In laminar flow (that is, with Re < ~2000), the hydraulic slope is proportional to the flow velocity.


In many practical engineering applications, the fluid flow is more rapid, therefore turbulent rather than laminar. Under turbulent flow, the friction loss is found to be roughly proportional to the square of the flow velocity and inversely proportional to the pipe diameter, that is, the friction loss follows the phenomenological Darcy–Weisbach equation in which the hydraulic slope S can be expressed[9]

where we have introduced the Darcy friction factor fD (but see Confusion with the Fanning friction factor);

fD = Darcy friction factor

Note that the value of this dimensionless factor depends on the pipe diameter D and the roughness of the pipe surface ε. Furthermore, it varies as well with the flow velocity V and on the physical properties of the fluid (usually cast together into the Reynolds number Re). Thus, the friction loss is not precisely proportional to the flow velocity squared, nor to the inverse of the pipe diameter: the friction factor takes account of the remaining dependency on these parameters.

From experimental measurements, the general features of the variation of fD are, for fixed relative roughness ε / D and for Reynolds number Re = V D / ν > ~2000,[a]

The experimentally measured values of fD are fit to reasonable accuracy by the (recursive) Colebrook–White equation,[12] depicted graphically in the Moody chart which plots friction factor fD versus Reynolds number Re for selected values of relative roughness ε / D.

Calculating friction loss for water in a pipe

Water friction loss ("hydraulic slope") S versus flow Q for given ANSI Sch. 40 NPT PVC pipe, roughness height ε = 1.5 μm

In a design problem, one may select pipe for a particular hydraulic slope S based on the candidate pipe's diameter D and its roughness ε. With these quantities as inputs, the friction factor fD can be expressed in closed form in the Colebrook–White equation or other fitting function, and the flow volume Q and flow velocity V can be calculated therefrom.

In the case of water (ρ = 1 g/cc, μ = 1 g/m/s[13]) 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[14][15]
in mm in[16] gpm lps ft/s m/s
1/2 15 0.622 0.01 4467 5.08 0.9 0.055 0.928 0.283
3/4 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
1+1/2 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).

Also note that the given fD in this table is actually a quantity adopted by the NFPA and the industry, known as C, which has the imperial units psi/(100 gpm2ft) and can be calculated using the following relation:

where is the pressure in psi, is the flow in 100gpm and is the length of the pipe in 100ft

Calculating friction loss for air in a duct

A graphical depiction of the relationship between Δp / L, the pressure loss per unit length of pipe, versus flow volume Q, for a range of choices for pipe diameter D, for air at standard temperature and pressure. Units are SI. Lines of constant RefD are also shown.[17]

Friction loss takes place as a gas, say air, flows through duct work.[17] 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.

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.

For specific choices of duct material, and assuming air at standard temperature and pressure (STP), standard charts can be used to calculate the expected friction loss.[8][18] The chart exhibited in this section can be used to graphically determine the required diameter of duct to be installed in an application where the volume of flow is determined and where the goal is to keep the pressure loss per unit length of duct S below some target value in all portions of the system under study. First, select the desired pressure loss Δp / L, say 1 kg / m2 / s2 (0.12 in H2O per 100 ft) on the vertical axis (ordinate). Next scan horizontally to the needed flow volume Q, say 1 m3 / s (2000 cfm): the choice of duct with diameter D = 0.5 m (20 in.) will result in a pressure loss rate Δp / L less than the target value. Note in passing that selecting a duct with diameter D = 0.6 m (24 in.) will result in a loss Δp / L of 0.02 kg / m2 / s2 (0.02 in H2O per 100 ft), illustrating the great gains in blower efficiency to be achieved by using modestly larger ducts.

The following table gives flow rate Q such that friction loss per unit length Δp / L (SI kg / m2 / s2) is 0.082, 0.245, and 0.816, respectively, for a variety of nominal duct sizes. The three values chosen for friction loss correspond to, in US units inch water column per 100 feet, 0.01, .03, and 0.1. Note that, in approximation, for a given value of flow volume, a step up in duct size (say from 100mm to 120mm) will reduce the friction loss by a factor of 3.

Volumetric Flow Q of air at STP where friction loss per unit length Δp / L (SI kg / m2 / s2) is, resp., 0.082, 0.245, and 0.816., for selected Nominal Duct Sizes[19] in smooth duct (ε = 50μm.)
Δp / L 0.082 0.245 0.816
kg / m2 / s2
Duct size Q Q Q
in mm cfm m3/s cfm m3/s cfm m3/s
2+1/2 63 3 0.0012 5 0.0024 10 0.0048
3+1/4 80 5 0.0024 10 0.0046 20 0.0093
4 100 10 0.0045 18 0.0085 36 0.0171
5 125 18 0.0083 33 0.0157 66 0.0313
6 160 35 0.0163 65 0.0308 129 0.0611
8 200 64 0.0301 119 0.0563 236 0.1114
10 250 117 0.0551 218 0.1030 430 0.2030
12 315 218 0.1031 407 0.1919 799 0.3771
16 400 416 0.1965 772 0.3646 1513 0.7141
20 500 759 0.3582 1404 0.6627 2743 1.2945
24 630 1411 0.6657 2603 1.2285 5072 2.3939
32 800 2673 1.2613 4919 2.3217 9563 4.5131
40 1000 4847 2.2877 8903 4.2018 17270 8.1504
48 1200 7876 3.7172 14442 6.8161 27969 13.2000

Note that, for the chart and table presented here, flow is in the turbulent, smooth pipe domain, with R* < 5 in all cases.


Further reading


  1. ^ a b Munson, B.R. (2006). Fundamentals of Fluid Mechanics (5 ed.). Hoboken, NJ: Wiley & Sons.
  2. ^ Allen, J.J.; Shockling, M.; Kunkel, G.; Smits, A.J. (2007). "Turbulent flow in smooth and rough pipes". Phil. Trans. R. Soc. A. 365 (1852): 699–714. Bibcode:2007RSPTA.365..699A. doi:10.1098/rsta.2006.1939. PMID 17244585. S2CID 2636599. Per EuRoPol GAZ website.
  3. ^ "Pipe Roughness". Pipe Flow Software. Retrieved 5 October 2015.
  4. ^ "Pipe Roughness Data". Retrieved 5 October 2015.
  5. ^ "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.
  6. ^ a b c d e f g h Chung, Yongmann. "ES2A7 laboratory Exercises" (PDF). University of Warwick, School of Engineering. Retrieved 20 October 2015.
  7. ^ a b Sentürk, Ali. "Pipe Flow" (PDF). T.C. İSTANBUL KÜLTÜR UNIVERSITY. Retrieved 20 October 2015.
  8. ^ a b "On-Line Duct Friction Loss". Retrieved 8 October 2015.
  9. ^ 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.
  10. ^ Nikuradse, J. (1933). "Strömungsgesetze in Rauen Rohren". V. D. I. Forschungsheft. 361: 1–22.
  11. ^ Moody, L. F. (1944), "Friction factors for pipe flow", Transactions of the ASME, 66 (8): 671–684
  12. ^ Rao, A.; Kumar, B. "Friction Factor for Turbulent Pipe Flow" (PDF). Retrieved 20 October 2015.
  13. ^ "Water - Dynamic and Kinetic Viscosity". Engineering Toolbox. Retrieved 5 October 2015.
  14. ^ "Technical Design Data" (PDF). Orion Fittings. Retrieved 29 September 2015.
  15. ^ "Tech Friction Loss Charts" (PDF). Hunter Industries. Retrieved 5 October 2015.
  16. ^ "Pipe Dimensions" (PDF). Spirax Sarco Inc. Retrieved 29 September 2015.
  17. ^ a b Elder, Keith E. "Duct Design" (PDF). Retrieved 8 October 2015.
  18. ^ Beckfeld, Gary D. (2012). "HVAC Calculations and Duct Sizing" (PDF). PDH Online, 5272 Meadow Estates Drive Fairfax, VA 22030. Retrieved 8 October 2015.
  19. ^ a b "Circular Duct Sizes". The Engineering Toolbox. Retrieved 25 November 2015.