k n t u civil engineerig faculty
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`. K N T U CIVIL ENGINEERIG FACULTY. FLOW IN PIPES. With special thanks to Mr.VAKILZADE. Velocity profile:. open channel. pipe. Friction force of wall on fluid. For pipes of constant diameter and incompressible flow. - PowerPoint PPT PresentationTRANSCRIPT
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KNTU CIVIL ENGINEERIG
FACULTY
`
FLOW IN PIPES
With special thanks to Mr.VAKILZADE
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Velocity profile:
Friction force of wall on fluid
open channel
pipe
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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
same
Vavg Vavg
samesame
Conservation of Mass
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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
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Laminar and Turbulent Flows
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Re < 2300 laminar
2300 ≤ Re ≤ 4000 transitional
Re > 4000 turbulent
Definition of Reynolds number:
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Hydraulic diameter:
Ac = cross-section area
P = wetted perimeter
Dh = 4Ac/ P
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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
Instantaneousprofiles
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slope
slope
Laminar Turbulent
ww
w,turb > w,lam w = shear stress at the wall, acting on the fluid
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1 2L
w
P1 P2VTake CV inside the pipe wall
Conservation of Mass
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Terms cancel since 1 = 2 and V1 = V2
Conservation of x-momentum
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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):
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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.
i pipe sections j components
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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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1
2
3
A B
1 2 3
1 2 3
f f f ABh h h h
Q Q Q Q
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Any question?