FLOW IN PIPES

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KNTU CIVIL ENGINEERIG FACULTY

• FLOW IN PIPES

With special thanks to Mr.VAKILZADE
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Velocity profile
open channel
pipe
Friction force of wall on fluid
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For pipes of constant diameter and incompressible
flow

• Vavg stays the same down the pipe, even if the
  velocity profile changes

Vavg
Vavg
Conservation of Mass
same
same
same
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• For pipes with variable diameter, m is still the
  same (due to conservation of mass),
• but V1 ? V2

D1
D2
m
V1
V2
m
2
1
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Laminar and Turbulent Flows
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Definition of Reynolds number

• Re lt 2300 ? laminar
• 2300 Re 4000 ? transitional
• Re gt 4000 ? turbulent

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• Hydraulic diameter

Dh 4Ac/ P
Ac cross-section area
P wetted perimeter
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• Consider a round pipe of diameter D. The flow
  can be
• laminar or turbulent. In either case, the
  profile develops
• downstream over several diameters called the
  entry
• length Lh. Lh/D is a function of Re.

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• Comparison of
• laminar and turbulent flow

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?w,turb gt ?w,lam
?w shear stress at the wall, acting on the
fluid
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Conservation of Mass
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Conservation of x-momentum
Terms cancel since ?1 ?2 and V1 V2
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or
Energy equation (in head form)
cancel (horizontal pipe)
V1 V2, and ?1 ?2 (shape not changing)
hL irreversible head loss it is felt as a
pressuredrop in the pipe
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?w func(??? V, ?, D, ?)
? average oughness of the inside wall of the
pipe
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But for laminar flow, roughness does not affect
the flow unless it is huge
Laminar flow f 64/Re
Turbulent flow f Moody Chart
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Minor Losses
KL is the loss coefficient.
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Energy Line (EL) and Hydraulic Grade Line (HGL)
(Source Larock, Jeppson and Watters, 2000
Hydraulics of Pipeline Systems)
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Pipe Networks
Pipes in series
Pipes in parallel
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Any question?