Pipe Friction Factor | Civil Engineering Optional Notes for UPSC PDF Download

The Pipe Friction

Reynolds Number (Re): This dimensionless number characterizes the flow regime in the pipe and is defined as the ratio of inertial forces to viscous forces within the fluid. It is calculated using the formula: 

where 
ρ is the fluid density, 
V is the velocity of the fluid, 
D is the hydraulic diameter of the pipe, and 
μ is the dynamic viscosity of the fluid.

Relative Roughness (ε/D): Relative roughness is a measure of the surface roughness of the pipe relative to its diameter. It is calculated by dividing the absolute roughness (ε) of the pipe by its diameter (D). It influences the friction factor, particularly in turbulent flow regimes.
The friction factor for flow in pipes can vary depending on several factors, including the Reynolds number, relative roughness of the pipe, and the flow regime (whether laminar or turbulent).

Flow Regimes: For laminar flow (Reynolds number < 2000), the friction factor (f) can be calculated using the Hagen-Poiseuille equation, and it's a function of Reynolds number only:

For turbulent flow (Reynolds number>4000  ), the friction factor depends on the pipe roughness relative to its diameter (ε/D) and the Reynolds number. There are several empirical correlations used to determine the friction factor in turbulent flow, with the most common being the Colebrook-White equation:

This equation is implicit, and iterative methods are often used to solve for the friction factor.

Moody Chart: The Moody chart is a graphical representation of the Colebrook-White equation and provides friction factor values as a function of Reynolds number and relative roughness. It is a valuable tool for engineers to quickly determine the friction factor without solving complex equations.