Friction Factor for Slow Flows

consider the flow of an incompressible fluid in a straight pipe. The pressure drop is a function of the density and viscosity of the fluid, the average velocity of the fluid, and the diameter and length of the pipe. The relationship is usually expressed by means of a friction factor defined as in Eq. (1)  

The usual curve of friction factor is given in Fig. 8.1(a) in a log-log plot. 

For any given Reynolds number, one can read the value of friction factor, and then use Eq. (1) to determine the pressure drop. In the turbulent region, for Re 2200, one correlation is the Blasius formula [Eq. (3)]  

When the definitions are inserted into Eq. (4) for laminar flow, one obtains for the pressure drop  

in laminar flow in a straight channel, the density of the fluid does not affect the pressure drop. To use the correlation for friction factor, or Fig. 8.1(a), one must know the density. This problem is avoided if one plots the product of friction factor and Reynolds number versus Reynolds number, since from their definition  

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