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Friction for Laminar and Turbulent Flow Through Pipes and Fittings
D. J. Courtemanche, PhD
04/04/2017
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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
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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
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Mechanical Energy Balance
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Laminar versus Turbulent Flow
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Viscosity
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Viscosity
For a Newtonian fluid the viscosity, m, is independent of the shear rate
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Reynolds Number Dimensionless number comparing inertial to viscous forces
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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)
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Shell Momentum Balance Inside a Pipe
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Shell Momentum Balance Inside a Pipe
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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
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Calculating Frictional Pressure Loss in Pipe Fanning Friction Factor
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Fanning Friction Factor
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Calculating Frictional Loss in Fittings
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Example
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Frictional Loss
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Mechanical Energy Balance
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Units??
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Pumping Power Requirement