Flow of Fluid in Pipes: The nature of the flow in a pipe depends upon the value of the Reynolds number. If Re is less than 2100, then flow is laminar, otherwise flow is turbulent if Re is greater than 4000. The skin frictional loss for flowing fluids is given by

where f is a Fanning friction factor that depends upon the Reynolds number and relative roughness of the pipe. Reynolds number (Re) is given as

Friction factor relationship has been plotted in the graphical form in Figure 4.3 (McCabe and Smith, Figure 5-10). It is helpful to merge roughness, ε, and diameter, d, into one parameter, relative roughness RR that is defined as

It should be noted that Moody's friction factor (4 times Fanning friction factor) is also in use in other fields of engineering.

Example 4.7: What is the skin frictional loss when water is flowing at 5 ft/s through a horizontal 100 ft long pipe having inside diameter of 2.067 in and roughness 0.00015 ft. Use the following data:

Density of water = 62.30 lb/ft³, viscosity of water = 6.583 ´ 10^-4 lb/(ft·s)

Roughness of the pipe = 0.00015 ft

Assume that inlet and exit points are at the same elevation and entrance and exit losses are negligible.

Solution:

C Diameter of the pipe, d = 0.17225 ft

C Reynolds number, Re (Equation 4.12):

C Relative roughness, RR (Equation 4.13):

C Fanning friction factor, f (Figure 4.3) = 0.0056

C Frictional losses, h_f (Equation 4.11):