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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.
The Reynolds number and power number fall from the above analysis if , n, and D are chosen to be the basis variables. If, instead, μ {\textstyle \mu } , n , and D are selected, the Reynolds number is recovered while the second dimensionless quantity becomes N R e p = P μ D 3 n 2 {\textstyle N_{\mathrm {Rep} }={\frac {P}{\mu D^{3}n^{2}}}} .
where is a function of the advance coefficient, is a function of the Reynolds' number, and is a function of the Froude number. Both f 2 {\displaystyle f_{2}} and f 3 {\displaystyle f_{3}} are likely to be small in comparison to f 1 {\displaystyle f_{1}} under normal operating conditions, so the expression can be reduced to:
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.
Roughness function B vs. friction Reynolds number R ∗. The data fall on a single trajectory when plotted in this way. The data fall on a single trajectory when plotted in this way. The regime R ∗ < 1 is effectively that of smooth pipe flow.
A key tool used to determine the stability of a flow is the Reynolds number (Re), first put forward by George Gabriel Stokes at the start of the 1850s. Associated with Osborne Reynolds who further developed the idea in the early 1880s, this dimensionless number gives the ratio of inertial terms and viscous terms. [4]
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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.