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The roughness of the pipe surface influences neither the fluid flow nor the friction loss. In turbulent flow, losses are proportional to the square of the fluid velocity, V 2; here, a layer of chaotic eddies and vortices near the pipe surface, called the viscous sub-layer, forms the transition to the bulk flow. In this domain, the effects of ...
In laminar flow, friction loss arises from the transfer of momentum from the fluid in the center of the flow to the pipe wall via the viscosity of the fluid; no vortices are present in the flow. Note that the friction loss is insensitive to the pipe roughness height ε: the flow velocity in the neighborhood of the pipe wall is zero.
Before choosing a formula it is worth knowing that in the paper on the Moody chart, Moody stated the accuracy is about ±5% for smooth pipes and ±10% for rough pipes. If more than one formula is applicable in the flow regime under consideration, the choice of formula may be influenced by one or more of the following: Required accuracy
The Darcy Weisbach Formula , also called Moody friction factor, is 4 times the Fanning friction factor and so a factor of has been applied to produce the formula given below. Re, Reynolds number ; ε, roughness of the inner surface of the pipe (dimension of length);
The Darcy-Weisbach equation was difficult to use because the friction factor was difficult to estimate. [7] In 1906, Hazen and Williams provided an empirical formula that was easy to use. The general form of the equation relates the mean velocity of water in a pipe with the geometric properties of the pipe and the slope of the energy line.
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.
Friction loss (or head loss) represents energy lost to friction as fluid flows through the pipe. This equation can be derived from Bernoulli's Equation. For incompressible liquids such as water, Static lift + Pressure head together equal the difference in fluid surface elevation between the suction basin and the discharge basin.
Right: The reduction in flux passing through a surface can be visualized by reduction in F or dS equivalently (resolved into components, θ is angle to normal n). F•dS is the component of flux passing through the surface, multiplied by the area of the surface (see dot product). For this reason flux represents physically a flow per unit area.