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In fluid flow, friction loss (or skin friction) is the loss of pressure or “head” that occurs in pipe or duct flow due to the effect of the fluid's viscosity near the surface of the pipe or duct.[1] In mechanical systems such as internal combustion engines, the term refers to the power lost in overcoming the friction between two moving surfaces, a different phenomenon.

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

## Economics

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

• Historically, it is a concern in aqueducts of all kinds, throughout human history. It is also relevant to sewer lines. Systematic study traces back to Henry Darcy, an aqueduct engineer.
• Natural flows in river beds are important to human activity; friction loss in a stream bed has an effect on the height of the flow, particularly significant during flooding.
• The economies of pipelines for petrochemical delivery are highly affected by friction loss. The Yamal–Europe pipeline carries methane at a volume flow rate of 32.3 × 109 m3 of gas per year, at Reynolds numbers greater than 50 × 106.[2]
• In hydropower applications, the energy lost to skin friction in flume and penstock is not available for useful work, say generating electricity.
• Friction loss is a significant economic concern wherever fluids are made to flow, whether entirely enclosed in a pipe or duct, or with a surface open to the air.

• Historically, it is a concern in aqueducts of all kinds, throughout human history. It is also relevant to sewer lines. Systematic study traces back to Henry Darcy, an aqueduct engineer.
• Natural flows in river beds are important to human activity; friction loss in a stream bed has an effect on the height of the flow, particularly significant during flooding.
• The economies of pipelines for petrochemical delivery are highly affected by friction loss. The Yamal–Europe pipeline carries methane at a volume flow rate of 32.3 × 109 m3 of gas per year, at Reynolds numbers greater than 50 × 106.[2]
• In hydropower applications, the energy lost to skin friction in flume and penstock is not available for useful work, say generating electricity.
• Irrigation water is pumped at large yearly volumes of flow, entailing significant expense.
• HVAC systems pump conditioning air on a widespread basis.
• In refrigeration applications, energy is expended pumping the coolant fluid through pipes or through the condenser. In split systems, the pipes carrying the coolant take the place of the air ducts in HVAC systems.
• Wells and domestic water systems must be engineered for effective and economical operation.

## Definition

In the following discussion, we define volumetric flow rate V̇ (i.e. volume of fluid flowing) V̇ = πr2v

where

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

${\displaystyle {\frac {\Delta p}{L}}.}$

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.

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.