Friction Factor in Turbulent Flow through a Rough Pipe

Friction factor is an important parameter to determine the pressure drop in a pipeline. In fully turbulent flow through a rough pipe, the friction factor f is a function of Reynolds number (Re) and relative roughness (S/D).

Reynolds Number

Reynolds number is a dimensionless parameter that determines the nature of the flow. It is defined as the ratio of inertial forces to viscous forces in a fluid. For a turbulent flow, Reynolds number is greater than 4000.

Relative Roughness

Relative roughness is a dimensionless parameter that represents the roughness of the pipe wall with respect to its diameter. It is defined as the ratio of the height of the roughness elements on the pipe wall to the diameter of the pipe. It is denoted by S/D.

Friction Factor

Friction factor is a dimensionless parameter that represents the resistance to flow in a pipe. It is defined as the ratio of shear stress to dynamic pressure in a fluid. The friction factor depends on the nature of the flow, which is determined by Reynolds number and relative roughness.

Function of Reynolds Number and Relative Roughness

In fully turbulent flow through a rough pipe, the friction factor f is a function of Reynolds number and relative roughness. This is because the nature of the flow is determined by these parameters. The roughness of the pipe wall causes turbulence in the flow, which increases the resistance to flow. This resistance is represented by the friction factor. As Reynolds number increases, the flow becomes more turbulent, which increases the resistance. Similarly, as relative roughness increases, the resistance also increases. Therefore, the friction factor is a function of both Reynolds number and relative roughness.

Conclusion

In conclusion, the friction factor in fully turbulent flow through a rough pipe is a function of Reynolds number and relative roughness. This is because the nature of the flow and the resistance to flow are determined by these parameters.