Turbulent flow rough pipe, relationship

In laminar flow/ = 16/Re, whereas in turbulent flow the dependence of/ on Re is a function of the specific rheological behavior of the fluid and roughness of the walls of the inside of the drill pipe (91). A number of functional relationships between / and Re have been proposed for turbulent flow. Ignoring the effects of the roughness of the surface of the drill pipe, / can be approximately related to Re by a generalized form of the well-known Blasius equation for Newtonian fluids (90, 95)... 

There are a number of correlations for pipe friction factors [14]. Here we only use the relationship by Moody, which applies to turbulent flow in hydraulically rough pipes. It is... 

A correct value of friction factor is required for the estimation of pressure drop. The value of the friction factor depends upon the flow characteristics. For laminar flow less than 2100), the friction factor varies inversely with the Re5molds number, whereas for turbulent flow, the friction factor has a complex relationship with the pipe diameter, roughness of the pipe, and the Reynolds number. 

There is turbulence, if Re > 2,300 and hydraulic roughness, if Re > 1,300. Below an example for the stationary discharge from a pipe leak is given. Non-stationary problems in which the internal pressure pi decreases because of loss of fluid can be treated in analogy to the flow diagram of Fig. 10.9. Then the relationships for gas used there have to be replaced by those for liquids from Example 10.3. 

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