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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 against Reynolds number Re for a variety of relative roughnesses, the ratio of the mean height of roughness of the pipe to the ...
The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...
When the pipes have certain roughness <, this factor must be taken in account when the Fanning friction factor is calculated. The relationship between pipe roughness and Fanning friction factor was developed by Haaland (1983) under flow conditions of 4 ⋅ 10 4 < R e < 10 7 {\displaystyle 4\centerdot 10^{4}<Re<10^{7}}
The proportionality coefficient is the dimensionless "Darcy friction factor" or "flow coefficient". This dimensionless coefficient will be a combination of geometric factors such as π, the Reynolds number and (outside the laminar regime) the relative roughness of the pipe (the ratio of the roughness height to the hydraulic diameter).
Note that the value of this dimensionless factor depends on the pipe diameter D and the roughness of the pipe surface ε. Furthermore, it varies as well with the flow velocity V and on the physical properties of the fluid (usually cast together into the Reynolds number Re). Thus, the friction loss is not precisely proportional to the flow ...
Once the friction factors of the pipes are obtained (or calculated from pipe friction laws such as the Darcy-Weisbach equation), we can consider how to calculate the flow rates and head losses on the network. Generally the head losses (potential differences) at each node are neglected, and a solution is sought for the steady-state flows on the ...
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.
For circular pipes of different surface roughness, at a Reynolds number below the critical value of approximately 2000 [2] pipe flow will ultimately be laminar, whereas above the critical value turbulent flow can persist, as shown in Moody chart. For non-circular pipes, such as rectangular ducts, the critical Reynolds number is shifted, but ...