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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 quantifies the impact of surface irregularities and obstructions on the flow of water. One roughness coefficient is Manning's n-value. [2] Manning's n is used extensively around the world to predict the degree of roughness in channels. The coefficient is critical in hydraulic engineering, floodplain management, and sediment transport studies.
The Hazen–Williams equation is an empirical relationship that relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe systems [ 1 ] such as fire sprinkler systems , [ 2 ] water supply networks , and irrigation systems.
Note: the Strickler coefficient is the reciprocal of Manning coefficient: Ks =1/ n, having dimension of L 1/3 /T and units of m 1/3 /s; it varies from 20 m 1/3 /s (rough stone and rough surface) to 80 m 1/3 /s (smooth concrete and cast iron). The discharge formula, Q = A V, can be used to rewrite Gauckler–Manning's equation by substitution for V.
The Morison equation contains two empirical hydrodynamic coefficients—an inertia coefficient and a drag coefficient—which are determined from experimental data. As shown by dimensional analysis and in experiments by Sarpkaya, these coefficients depend in general on the Keulegan–Carpenter number, Reynolds number and surface roughness. [4] [5]
Surface roughness has a strong effect on the contact angle and wettability of a surface. The effect of roughness depends on if the droplet will wet the surface grooves or if air pockets will be left between the droplet and the surface. [10] If the surface is wetted homogeneously, the droplet is in Wenzel state. [11]
Churchill equation [24] (1977) is the only equation that can be evaluated for very slow flow (Reynolds number < 1), but the Cheng (2008), [25] and Bellos et al. (2018) [8] equations also return an approximately correct value for friction factor in the laminar flow region (Reynolds number < 2300). All of the others are for transitional and ...
Surface roughness, often shortened to roughness, is a component of surface finish (surface texture). It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, the surface is rough; if they are small, the surface is smooth.