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In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of friction losses in pipe flow as well as open-channel flow.
The proportionality coefficient is the dimensionless "Darcy friction factor" or "flow coefficient". This dimensionless coefficient will be a combination of geometric factors such as π, the Reynolds number and (outside the laminar regime) the relative roughness of the pipe (the ratio of the roughness height to the hydraulic diameter).
The friction coefficient is an empirical (experimentally measured) structural property that depends only on various aspects of the contacting materials, such as surface roughness. The coefficient of friction is not a function of mass or volume. For instance, a large aluminum block has the same coefficient of friction as a small aluminum block.
Jean Le Rond d'Alembert, Nouvelles expériences sur la résistance des fluides, 1777. In fluid dynamics, friction loss (or frictional loss) is the head loss that occurs in a containment such as a pipe or duct due to the effect of the fluid's viscosity near the surface of the containment.
In engineering, the Moody chart or Moody diagram (also Stanton diagram) is a graph in non-dimensional form that relates the Darcy–Weisbach friction factor f D, Reynolds number Re, and surface roughness for fully developed flow in a circular pipe.
The Hazen–Williams equation has the advantage that the coefficient C is not a function of the Reynolds number, but it has the disadvantage that it is only valid for water. Also, it does not account for the temperature or viscosity of the water, [3] and therefore is only valid at room temperature and conventional velocities. [4]
In general, there are two approaches for the calculation of Stribeck curve in all lubrication regimes. [11] In the first approach, the governing flow and surface deformation equations (the system of the Elastohydrodynamic Lubrication equations [12]) are solved numerically. Although the numerical solutions can be relatively accurate, this ...
The frictional coefficient is related to the diffusion constant D by the Einstein relation D = k B T f t o t {\displaystyle D={\frac {k_{B}T}{f_{tot}}}} Hence, f t o t {\displaystyle f_{tot}} can be measured directly using analytical ultracentrifugation , or indirectly using various methods to determine the diffusion constant (e.g., NMR and ...