Darcy Friction Factor (f)
In pipes, fluid loses energy due to the friction. This loss is overcome by loss of pressure. The loss of energy is characterized by the friction factor (f)
f is a dimensionless parameter that describes friction of pipe walls. It can be obtained by dividing Δp by dynamic pressure ½ ρV2. Here we can express the pressure drop in terms of f as shown below.
In Fluid Mechanics I (pipe flow) you had obtained the expression for average velocity as:
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Dividing by dynamic pressure
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f is called the Darcy friction factor. For laminar pipe flows, f is the well-known expression
Alternatively, we can write friction factor in terms of wall shear stress as: [pic]
What is Fanning friction factor and how is it different from Darcy’s friction factor?
Show that Fanning friction factor f ’ is equal to f/4 and for laminar pipe flow, it is 16 / Re
Hint: Equate pressure force to shear force
Concept of Turbulent Flow in Pipes
Experiments reveal that turbulent spots or eddies appear at the near wall region. In laminar flow, the turbulent spots are sheared by the layer of laminar fluid. As Re increases, more and more eddies appear and the layer of laminar fluid at the wall is no more able to shear them.
As a result these eddies escape through the laminar layer near the wall into the rest of the flow region. The turbulent eddies then grow larger, merge and finally fill the entire cross-section of the pipe.
Shear stress in pipe is given as the summation of laminar shear stress and turbulent shear stress i.e.
τ = τlam + τturb
Laminar shear stress is dominant near the pipe wall and the turbulent shear stress dominates the flow at center of pipe.
The equations for shear stress that were obtained for laminar flow in pipes can also be used for turbulent flows in pipes. i.e:
[pic] and [pic]...