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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 flow rate can be converted to a mean flow velocity V by dividing by the wetted area of the flow (which equals the cross-sectional area of the pipe if the pipe is full of fluid). Pressure has dimensions of energy per unit volume, therefore the pressure drop between two points must be proportional to the dynamic pressure q.
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.
For example, halving a pipe's diameter would increase the pressure drop by a factor of = (e.g. from 2 psi to 64 psi), assuming no change in flow. Pressure drop in piping is directly proportional to the length of the piping—for example, a pipe with twice the length will have twice the pressure drop, given the same flow rate. [8]
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 ...
u is the bulk flow velocity (m/s or ft/s) In particular the shear stress at the wall can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area ( 2 π R L {\displaystyle 2\pi RL} for a pipe with circular cross section) and dividing by the cross-sectional flow area ( π R 2 {\displaystyle \pi R^{2}} for a ...
Pipe flow does not have a free surface which is found in open-channel flow. Pipe flow, being confined within closed conduit, does not exert direct atmospheric pressure, but does exert hydraulic pressure on the conduit. Not all flow within a closed conduit is considered pipe flow. Storm sewers are closed conduits but usually maintain a free ...
At cross section 1, the mean flow velocity is equal to v 1, the pressure is p 1 and the cross-sectional area is A 1. The corresponding flow quantities at cross section 2 – well behind the expansion (and regions of separated flow) – are v 2, p 2 and A 2, respectively.