The two kinds of flow has been categorized using the Reynold's number. Those fluid flowing under or equal to 2100 are known to be laminar and those having a greater value are considered turbulent. Using Fanning's equation based on Hagen-Poiseuille law, the friction factor for laminar flow is:
This formula shows that the friction factor is a function of the Reynold's number only. The material roughness is not a factor in determining the value for f.
However, for turbulent flows, the roughness of the material matters. Prandtl and von Karman determined formulas for turbulent flow as follows:
For smooth pipes:
For pipes with fully developed turbulence:
From these empirical formulas, one can conclude:
- For laminar flow, friction factor is dependent on the Reynold's number.
- For hydraulically smooth pipes, friction factor is also just a function of the Reynold's number.
- For pipes where turbuence is fully developed, the friction factor is a function of the relative roughness only.
Recommended K values for common pipe materials are listed below:
| KIND OF PIPE (NEW) | K |
|---|---|
| (IN FEET) | |
| Wrought iron and steel | 0.00015 |
| Asphalted cast iron | 0.0004 |
| Galvanized iron | 0.0005 |
| Cast iron | 0.00085 |
| Wood stave | 0.0006 to 0.0030 |
| Concrete | 0.001 to 0.010 |
| Riveted steel | 0.003 to 0.030 |
Application of the equations above is facilitated by using the Moody Diagram.
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