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The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe.
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. It can be used to predict pressure drop or flow rate down such a pipe.
Note that for the case of a circular pipe, D H = 4 π R 2 2 π R = 2 R {\displaystyle D_{\text{H}}={\frac {4\pi R^{2}}{2\pi R}}=2R} The need for the hydraulic diameter arises due to the use of a single dimension in the case of a dimensionless quantity such as the Reynolds number , which prefers a single variable for flow analysis rather than ...
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
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 ]
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
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For example, it is used to calculate flow through circular and non-circular tubes in order to examine flow conditions (i.e., the Reynolds number). In those cases, the characteristic length is the diameter of the pipe or, in case of non-circular tubes, its hydraulic diameter D h {\displaystyle D_{h}} :