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KNTU CIVIL ENGINEERIG
FACULTY
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FLOW IN PIPES
With special thanks to Mr.VAKILZADE
Velocity profile:
Friction force of wall on fluid
open channel
pipe
For pipes of constant diameter and incompressible flow
Vavg stays the same down the pipe, even if the velocity profile changes
same
Vavg Vavg
samesame
Conservation of Mass
For pipes with variable diameter, m is still the same (due to conservation of mass),
but V1 ≠ V2
D2
V2
2
1
V1
D1
m m
Laminar and Turbulent Flows
Re < 2300 laminar
2300 ≤ Re ≤ 4000 transitional
Re > 4000 turbulent
Definition of Reynolds number:
Hydraulic diameter:
Ac = cross-section area
P = wetted perimeter
Dh = 4Ac/ P
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.
Comparison of:
laminar and turbulent flow
Instantaneousprofiles
slope
slope
Laminar Turbulent
ww
w,turb > w,lam w = shear stress at the wall, acting on the fluid
1 2L
w
P1 P2VTake CV inside the pipe wall
Conservation of Mass
Terms cancel since 1 = 2 and V1 = V2
Conservation of x-momentum
or
cancel (horizontal pipe)
V1 = V2, and 1 = 2 (shape not changing)
hL = irreversible head loss & it is felt as a pressuredrop in the pipe
Energy equation (in head form):
w = func( V, , D, )
= average oughness of the inside wall of the pipe
But for laminar flow, roughness does not affect the flow unless it is huge
Laminar flow: f = 64/Re
Turbulent flow: f = Moody Chart
Minor Losses:KL is the loss coefficient.
i pipe sections j components
Energy Line (EL) and Hydraulic Grade Line (HGL)
(Source: Larock, Jeppson and Watters, 2000: Hydraulics of Pipeline Systems)
Pipe Networks :
Pipes in series
Pipes in parallel
1
2
3
A B
1 2 3
1 2 3
f f f ABh h h h
Q Q Q Q
Any question?