Friction for Laminar and Turbulent Flow Through Pipes and Fittings

D. J. Courtemanche, PhD

04/04/2017

References

• Transport Phenomena • Bird, Stewart, and Lightfoot

• Transport Processes and Unit Operations • Christie J. Geankoplis

• Chemical Engineers’ Handbook • R. H. Perry and C. H. Chilton

Frictional Pressure Losses Associated with Flow Through Piping • One of the most common engineering calculations performed by a

chemical engineer

• Used to determine • Pumping requirements

• Required pipe pressure ratings

• Design of pressure relief systems

• Practicality of piping arrangements

Mechanical Energy Balance

Laminar versus Turbulent Flow

Viscosity

Viscosity

For a Newtonian fluid the viscosity, m, is independent of the shear rate

Reynolds Number Dimensionless number comparing inertial to viscous forces

Shell Momentum Balance Inside a Pipe

The sum of the forces on the Control Volume = Flux of Momentum from Control Volume Assumptions • r is constant • m is constant • No time dependence (steady state) • No entrance effects (flow is established)

Shell Momentum Balance Inside a Pipe

Shell Momentum Balance Inside a Pipe

Velocity Profiles

Note that in Mechanical Energy Balance we represent Kinetic Energy using (VAV)2 , where we really need to use (V2)av

For laminar profile (V2)av = ½ (VAV)2 For turbulent profile (V2)av = (VAV)2 approximately

Hence the term a is equal to 2 for laminar flow and equal to 1 for turbulent flow

Calculating Frictional Pressure Loss in Pipe Fanning Friction Factor

Fanning Friction Factor

Calculating Frictional Loss in Fittings

Example

Frictional Loss

Mechanical Energy Balance

Units??

Pumping Power Requirement