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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.
In fluid dynamics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. [2] At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent.
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]
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.
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.
Reynolds’ 1883 experiment on fluid dynamics in pipes Reynolds’ 1883 observations of the nature of the flow in his experiments. In 1883 Osborne Reynolds demonstrated the transition to turbulent flow in a classic experiment in which he examined the behaviour of water flow under different flow rates using a small jet of dyed water introduced into the centre of flow in a larger pipe.
The Churchill–Bernstein equation is valid for a wide range of Reynolds numbers and Prandtl numbers, as long as the product of the two is greater than or equal to 0.2, as defined above. The Churchill–Bernstein equation can be used for any object of cylindrical geometry in which boundary layers develop freely, without constraints imposed by ...
= / is the Reynolds number. This turbulent boundary layer thickness formula assumes 1) the flow is turbulent right from the start of the boundary layer and 2) the turbulent boundary layer behaves in a geometrically similar manner (i.e. the velocity profiles are geometrically similar along the flow in the x-direction, differing only by ...