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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 ...
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 ...
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.
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach.
A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
The equation is named after Lord Rayleigh, who introduced it in 1880. [2] The Orr–Sommerfeld equation – introduced later, for the study of stability of parallel viscous flow – reduces to Rayleigh's equation when the viscosity is zero. [3] Rayleigh's equation, together with appropriate boundary conditions, most often poses an eigenvalue ...
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In many engineering applications the local flow velocity vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity ¯ (with the usual dimension of length per time), defined as the quotient between the volume flow rate ˙ (with dimension of cubed length per time) and the cross sectional area (with dimension of square length):