turbulent flow through pipes
TRANSCRIPT
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Turbulent Flow Through Pipes
Prof. Rohit Goyal
Professor, Department of Civil Engineering
Malaviya National Institute of Technology Jaipur
E-Mail: [email protected]
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Topics Covered
Pipe Roughness Hydraulically Smooth Pipes
Hydraulically Rough Pipes
Velocity Distribution in Pipes
Equations for Average Velocities
Darcy-Weisbach Equation
Friction Factor Nikuradses Diagram
Moodys Diagram
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Turbulent Flow Through Pipes
Laminar flow analysis through pipes orother types of channels may be complexbut is possible due to application of well
established law such as Newton's law ofviscosity.
However in nature, flow is normallyturbulent, which even for simple cases
may need 3-dimensional considerations. Usually the objective is to compute
frictional resistance to flow.
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Hydraulically Smooth/Rough Pipe
It has been observed that for turbulent flows, wall
roughness plays a crucial role, however even the
finest polished surface have roughness at
microscopic levels which may initiate eddies anddisturbances in turbulent flow which are further
escalated due to turbulence.
It has been observed that pipes of different Degree
of Smoothness behaves likely and so based onroughness of pipe material, pipes are classified as
hydraulically smooth orhydraulically rough.
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Criteria for Smoothness
It has been experimentally observed that thickness
of laminar sub-layer could be calculated by.
When the roughness projections are less than
thickness of laminar sub-layer then pipe is classified
as hydraulically smooth.
This is because roughness projections are now
completely submerged in laminar sub-layer and so
does not matter.
velcoityshearuviscositykinematicwhereu **
&
5
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Hydraulically Rough
When the roughness projections are more than
thickness of laminar sub-layer then pipe is classified
as hydraulically rough.
Now beyond every projection which is more than
laminar sub-layer, a turbulent wake is formed and
so resistance to flow is increased.
Since the classification depends upon thickness of
laminar sub-layer, which depends upon flowconditions, so same pipe may be hydraulically
smooth orhydraulically rough.
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Velocity Distribution (HS Pipes)
It has been observed that the equation derived for
turbulent flow near walls is also valid for
hydraulically smooth circular pipe with the value
of constant B = 5.5 (experimentally observed). andso
5.5log75.5
5.5ln5.2
*
*
*
*
yu
u
u
or
yu
u
u
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Velocity Distribution (HR Pipes)
Forhydraulically rough circular pipe however the
velocity distribution would also depend upon
average value of roughness projections (say k).
It has been experimentally observed that forHR
Pipes
5.8log75.5
5.8ln5.2
*
*
k
y
u
u
or
k
y
u
u
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Average Surface Roughness (k)
Value of k (in cm) for typical surfaces
are as follows
Concrete 0.03 to 0.3
Caste Iron 0.025
Galvanized Iron 0.015
Riveted Steel 0.09 to 0.9 Timber 0.03 to 0.09
Commercial Steel 0.005
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Average Velocity (V)
If we integrate velocity profile for circular pipe(taking y=R-r), where R is radius of pipe andthen compute average velocity (V) then
ForHydraulically Smooth Pipes
ForHydraulically Rough Pipes
These could also be written in log terms.
10
75.1ln5.2 *
*
Ru
u
V
75.4ln5.2*
k
R
u
V
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Darcys Weisbach Equation
Darcy and Weisbach almost simultaneouslyderived the equation for head loss throughcircular pipe as
Where hL is head loss between two sections ldistance apart, V is average velocity and d isdiameter of pipe.
f is known as friction factor. This equation isderived from continuity, momentum equation andis valid for both laminar and turbulent flows.
gdflVh
L2
2
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Friction Factor
Since , so it can be proved that
By combining equations, we can than obtain
Hydraulically Smooth Pipe
Hydraulically Rough Pipe
0
*u
8
* f
V
u
74.1log2
1
8.0log21
k
R
f
fRf
N
pipeofRadiusRandVd
RHereN
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Friction Factor f
Friction factor f has been studied in great
details by various scientists.
Nikuradse, a student of Prandtl, conductednumerous experiments for pipes with varying
surface roughness and derived graph between
Reynolds Number (RN) and friction factor (f) as
shown in next slide Relative Roughness is defined as (k/D), where
D is diameter of the Pipe.
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Nikuradses Diagram
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Observations
In the laminar flow region (RN
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Moodys Diagram
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Observations
In the highly turbulent flow region it can be observed thatf varies only with relative roughness and is independentof RN.
For Turbulent flow through smooth pipes, Blasius also
fitted a equation, which is simple to use and f is only onleft side
Balsius equation holds good till RN < 105.
Friction factor is found to change with age of pipes.Roughness is gradually increased due to rusting. Asimple equation is used to calculate k with time t
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25.0
316.0
NR
f
pipenewofroughnessiskwheretkk00