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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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The flow in closed conduit ( flow in pipe ) is differ from this occur in open channel
where the flow in pipe is at a pressure ( does not have a free surface ) .
The flow in pipe can be demonstrated such as :- Laminar flow ,
- Transitional flow ,
- Turbulent flow .
To distinction between the above features , the well known “ Reynold, s Number”
can be used , according to experiments that given by “ Osborn Reynold in 19th
century “ .
1-Reynold’s Experiment
In 1883, Osborne Reynolds demonstrated that there are two distinctly different
types of flow by injecting a very thin stream of colored fluid having the same
density of water into a large transparent tube through which water is flowing. And
from the feature of streaming this dye fluid , Reynold give a number can be
considered as a boundary between flow faces , this number is a function of , flow
velocity , fluid density , pipe diameter , and fluid viscosity , where ;
R= f (V , ρ , υ (or μ ) , D ) …………………….. (1)
and then , R= VDρ/μ or R = VD/υ ;
R= Reynolds No.,
μ = dynamic viscosity ,
υ = kinematic viscosity .
See Figure(1) , below for Reynold”s experiments ;
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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Fig.(1) : Experiments shows the flow state as demonstrated by Reynolds
Observations (dye)
Reynolds
Number, Re
Flow
Classification
<2000
Laminar Flow
2000 - 4000
Transitional
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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Transitional/
Turbulent
> 4000
Turbulent
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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2-Viscous (Real) Flow in Conduits ,Head Loss in Pipes from Friction
( Major Losses)
The head loss between two points in a circular pipe carrying a fluid under pressure
can be found by ; hf=
ΔP
γ
Where: ∆p = p1 − p2 , and can be measured by using piezometer tubes.
The velocity of the flow can be found by using a Pitot tube. The reading of the
Pitot tube is the total head = pressure head + velocity head
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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The total “ friction head loss “ (hL) , can be calculated using “ Darcy Equation” by
well estimating of “ friction factor , f “ ; where :-
Also the “ friction head loss“ (hL) , can be calculated by using Hazen William
Equation , where ;
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
3-Head Loss versus Discharge
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Lect.No.8
Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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The friction factor of “Darcy Equation” can be estimated , using “ Moody Diagram”
as shown in Fig.(2) , below ;
Fig.(2): Friction Factor estimation as presented by Moody
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Flow Dynamics in Closed Conduit (Pipe Flow)
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4-Method to Determine Darcy-Weisbach friction factor ( f )
PIPE FLOWS
Laminar (R < 2,000)
Turbulent (R > 4,000)
f = 64/R
Smooth
(δv > e)
Transitional
Wholly Rough
(0.071e ≤ δv ≤ e) (δv < 0.071e)
Turbulent (Smooth):
Prandtle ………..
1
√f
Blasisus ……….. f =
= 2 log (
0.316
R0.25
R√f
2.51
for R > 4000
)
for 3000 < R < 100000
Turbulent ( Transitional) :
Colebrook ……..
1
√f
= -2 log [
e
D
3.7
+
Turbulent ( Wholly Rough ):
Von- Karamen …
1
√f
= 2 log (
3.7
e
D
)
2.51
R√f
]
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Asst.Prof.Dr. Jaafar S. Maatooq
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Flow Dynamics in Closed Conduit (Pipe Flow)
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5-Minor Losses in Pipe
Losses caused by fittings, bends, valves, enlargement , contraction .
Losses are proportional to – velocity of flow, geometry of device , where;
hL= K (V2/2g)
The value of K is typically provided for various devices , where , K is a loss
factor - has no units (dimensionless) .
The following variation in design and installation devices in pipe systems which
cause “ minor losses “ :-
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Flow Dynamics in Closed Conduit (Pipe Flow)
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• Sudden enlargement :
Energy lost is because of turbulence. Amount of turbulence depends on the
differences in pipe diameters . The values of K have been experimentally
determined and provided in Fig.(3) , below .
Fig.(3): Loss Factor for Sudden Enlargement
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Asst.Prof.Dr. Jaafar S. Maatooq
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Flow Dynamics in Closed Conduit (Pipe Flow)
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• Gradual Enlargement :
If the enlargement is gradual , the energy losses are less. The loss again depends on
the ratio of the pipe diameters and the angle of enlargement.
hL= K (V12/2g)
K can be determined from Fig.(4) , Below ;
Fig.(4): Loss Factor for Gradual Enlargement
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Flow Dynamics in Closed Conduit (Pipe Flow)
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Notes ;
• If angle increases (in pipe enlargement) – minor losses increase
• If angle decreases – minor losses decrease, but you also need a longer pipe to
make the transition – that means more FRICTION losses - therefore there is a
tradeoff and minimum loss including minor and friction losses occur for angle of 7
degrees .
• Exit Loss :
• Case of where pipe enters a tank – a very large enlargement ,
• The tank water is assumed to be stationery, that is, the velocity is zero.
• Therefore all kinetic energy in pipe is dissipated .
hL= 1.0 (V12/2g)
where K=1 for this case of exit .
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Asst.Prof.Dr. Jaafar S. Maatooq
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Flow Dynamics in Closed Conduit (Pipe Flow)
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• Sudden Contraction :
Decrease in pipe diameter ;
Loss is given by :hL= K (V22/2g)
Note that the loss is related to the velocity in the second (smaller) pipe . The loss is
associated with the contraction of flow and turbulence at the change of diameter
and vena contracta ,which is formed at the beginning of the smaller diameter . See
fig.(10.8) , below .
The section at which the flow is the narrowest is called Vena Contracta , at vena
contracta, the velocity is maximum .
K can be computed based on diameter ratio and velocity of flow using Fig.(5)
below. Note that the energy losses for sudden contraction are less than those for
sudden enlargement .
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Asst.Prof.Dr. Jaafar S. Maatooq
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Flow Dynamics in Closed Conduit (Pipe Flow)
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Fig.(5): Loss Factor for Sudden Contraction
• Gradual Contraction:
Again a gradual contraction will lower the energy loss (as opposed to sudden
contraction). θ is called the cone angle.
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Asst.Prof.Dr. Jaafar S. Maatooq
2nd Semester
Flow Dynamics in Closed Conduit (Pipe Flow)
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hL= K (V22/2g)
K is given by Fig.(6) , below , Note that K values increase for very small angles
(less than 15 degrees) .
Fig.(6): Loss Factor for Gradual Contraction
Lect.No.8
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Flow Dynamics in Closed Conduit (Pipe Flow)
• Entrance Losses :
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Lect.No.8
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Flow Dynamics in Closed Conduit (Pipe Flow)
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• Resistance Coefficient for Valves and Fittings :
The minor losses resulting when using any fittings (such as valve , elbow , bend ,
etc. ) can be computed by :hL= K (V 2/2g)
Where “ K “ is computed by using a so called “ Equivalent Length “ as :K=
Le
D
fT
Le = equivalent length (length of pipe with same resistance as the fitting/valve) ,
fT = friction factor .
The equivalent ratio (Le/D) for various valves/fittings , and “fT” for new steel
pipe can be computed using Tables below ;
For OLD pipes however, fT cannot be computed by this table. You have to use the
procedure we used for Moody’s diagram :• Get “ε” for the pipe type from Table(3.8) ,
• Determine “D/ ε” for the pipe ,
• Then use the Moody diagram to determine the value of “fT” , for the zone of
complete turbulence .
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Flow Dynamics in Closed Conduit (Pipe Flow)
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Lect.No.8
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Flow Dynamics in Closed Conduit (Pipe Flow)
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