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The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe (inside) diameter. f stands for the Darcy friction factor. Its value depends on the flow's Reynolds number Re and on the pipe's relative roughness ε / D.
In laminar flow, friction loss arises from the transfer of momentum from the fluid in the center of the flow to the pipe wall via the viscosity of the fluid; no vortices are present in the flow. Note that the friction loss is insensitive to the pipe roughness height ε: the flow velocity in the neighborhood of the pipe wall is zero.
where is the density of the fluid, is the average velocity in the pipe, is the friction factor from the Moody chart, is the length of the pipe and is the pipe diameter. The chart plots Darcy–Weisbach friction factor f D {\displaystyle f_{D}} against Reynolds number Re for a variety of relative roughnesses, the ratio of the mean height of ...
The following table gives Reynolds number Re, Darcy friction factor f D, flow rate Q, and velocity V such that hydraulic slope S = h f / 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 ]
This theory is exact for the situation of an infinite friction coefficient in which case the slip area vanishes, and is approximative for non-vanishing creepages. It does assume Coulomb's friction law, which more or less requires (scrupulously) clean surfaces. This theory is for massive bodies such as the railway wheel-rail contact.
Drag coefficients in fluids with Reynolds number approximately 10 4 [1] [2] Shapes are depicted with the same projected frontal area. In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
When the pipes have certain roughness <, this factor must be taken in account when the Fanning friction factor is calculated. The relationship between pipe roughness and Fanning friction factor was developed by Haaland (1983) under flow conditions of 4 ⋅ 10 4 < R e < 10 7 {\displaystyle 4\centerdot 10^{4}<Re<10^{7}}
Just as certain aspects of the system can increase the fluids energy, there are components of the system that act against the fluid and reduce its energy, velocity, or momentum. Friction and minor losses in pipes are major contributing factors. [1] [2] [3] [4]
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