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Flow Through Pipe:  the analysis of fluid flow within pipes
Dr. Indrajeet Sahu Fluid Mechanics VCE 2
Dr. Indrajeet Sahu Fluid Mechanics VCE 3
Dr. Indrajeet Sahu Fluid Mechanics VCE 4
5
Dr. Indrajeet Sahu Fluid Mechanics VCE
6
Characterization of flow based on Reynolds number
Osborne Reynolds (a British engineer) conducted a flow experiment, i.e. by
injecting dye into pipe flow to classify the types of flow.
Turbulent
Near laminar
Dr. Indrajeet Sahu Fluid Mechanics VCE
7
Three types of flow:
Laminar flow
Transitional flow
Reynolds number Re is the ratio of the inertia force on an element of fluid to
the viscous force.

VD

Re

VD

Re < 2300
Re > 4000
2300 < Re < 4000
where V = average velocity, D = diameter of pipe,  = fluid density,  =
dynamic viscosity, and  = kinematic viscosity
Re is dimensionless.
Turbulent flow
Reynolds number is one of the important dimensionless number used in the
dimensional analysis in fluid mechanics and hydraulics.
Dr. Indrajeet Sahu Fluid Mechanics VCE
8
The transition from laminar to turbulent flow depends on the geometry,
surface roughness, flow velocity, surface temperature, and type of fluid.
The flow regime depends mainly on the ratio of inertial forces to viscous
forces (Reynolds number).
Dr. Indrajeet Sahu Fluid Mechanics VCE
9
Dr. Indrajeet Sahu Fluid Mechanics VCE
10
Example 4.1
Determine the range of average velocity of flow for which the flow
would be in the transitional region if an oil of S.G. = 0.89 and
dynamic viscosity = 0.1 Ns/m2 is flowing in a 2-in pipe.
Solution:
For transitional flow,
When Re = 2000,
When Re = 4000,
4000
Re
2000 


VD

Re
D
V


Re

 
0254
0
2
890
1
0
000
2
.
.
V




m/s
424
4.
V 
 
0254
0
2
890
1
0
000
4
.
.
V




m/s
847
8.
V 
Therefore, for the flow to be in transitional state, the average velocity V should
be between 4.424 m/s and 8.847 m/s.
Dr. Indrajeet Sahu Fluid Mechanics VCE
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Dr. Indrajeet Sahu Fluid Mechanics VCE
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Dr. Indrajeet Sahu Fluid Mechanics VCE
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Hydrodynamic entrance region: The region from the pipe inlet to the point at
which the boundary layer merges at the centerline.
Hydrodynamic entry length Lh: The length of this region.
Hydrodynamically developing flow: Flow in the entrance region. This is the
region where the velocity profile develops.
Hydrodynamically fully developed region: The region beyond the entrance
region in which the velocity profile is fully developed and remains unchanged.
Fully developed: When both the velocity profile and the normalized
temperature profile remain unchanged.
Hydrodynamically fully developed
In the fully developed flow region of a
pipe, the velocity profile does not
change downstream, and thus the wall
shear stress remains constant as well.
Dr. Indrajeet Sahu Fluid Mechanics VCE
14
The variation of wall shear stress
in the flow direction for flow in a
pipe from the entrance region into
the fully developed region.
The pressure drop is higher in the entrance regions of a pipe, and the
effect of the entrance region is always to increase the average friction
factor for the entire pipe.
Dr. Indrajeet Sahu Fluid Mechanics VCE
15
Entry Lengths
The hydrodynamic entry length is usually taken to be the distance from the pipe entrance to
where the wall shear stress (and thus the friction factor) reaches within about 2 percent of the
fully developed value.
hydrodynamic entry length for
laminar flow
hydrodynamic entry length for
turbulent flow
hydrodynamic entry length for
turbulent flow, an approximation
Dr. Indrajeet Sahu Fluid Mechanics VCE
16
LAMINAR FLOW IN PIPES
 We consider steady, laminar, incompressible flow of a fluid with constant properties in the fully
developed region of a straight circular pipe.
 In fully developed laminar flow, each fluid particle moves at a constant axial velocity along a streamline
and the velocity profile u(r) remains unchanged in the flow direction.
Free-body diagram of a ring-shaped differential fluid
element of radius r, thickness dr, and length dx
oriented coaxially with a horizontal pipe in fully
developed laminar flow.
 There is no motion in the radial direction, and thus the
velocity component in the direction normal to the pipe
axis is everywhere zero. There is no acceleration since
the flow is steady and fully developed.
Dr. Indrajeet Sahu Fluid Mechanics VCE
17
Boundary
conditions
Maximum velocity at
centerline
Velocity
profile
Dr. Indrajeet Sahu Fluid Mechanics VCE
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 .
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Dracy-Weisbach
Equation
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 .
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 .
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 .
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36
 .
 .
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 .
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 .
 .
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 .
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Dr. Indrajeet Sahu Fluid Mechanics VCE
V 2
Take Velocity and
50
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 .
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 .
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 .
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 .
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 .
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 .
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 .
 .
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 .
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 .
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 .
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Dr. Indrajeet Sahu Fluid Mechanics 90

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Flow Through Pipe: the analysis of fluid flow within pipes