FMM Unit-2

1. UNIT II - FLOW THROUGH CIRCULAR
CONDUITS
• Hydraulic and energy gradient
• Laminar flow through circular conduits
• Circular annuli Boundary Layer concepts
• Types of boundary layer thickness
• Darcy Weisbach equation
• Friction factor
• Moody diagram
• Commercial pipes
• Minor losses
• Flow through pipes in series and parallel.
Dr V.KANDAVEL Asp/Mech. SSMIET, DGL-2 1

2. Overview of Unit-II
CONDUITS means a channel for conveying water or other fluid

3. This unit II has an in dealing of laminar flow through pipes,
boundary layer concept, hydraulic and energy gradient, friction
factor, minor losses, and flow through pipes in series and
parallel.
Boundary layer is the region near a solid where the fluid
motion is affected by the solid boundary. In the bulk of the fluid
the flow is usually governed by the theory of ideal fluids. By
contrast, viscosity is important in the boundary layer.
The division of the problem of flow past an solid object into
these two parts, as suggested by Prandtl in 1904 has proved
to be of fundamental importance in fluid mechanics.
This concept of hydraulic gradient line and total energy line is
very useful in the study of flow This concept of hydraulic
gradient line and total energy line is very useful in the study of
flow of fluids through pipes.

4. Hydraulic and energy gradient
Hydraulic gradient line is basically defined as the line which will give the sum of pressure
head and datum head or potential head of a fluid flowing through a pipe with respect to
some reference line.
Hydraulic gradient line = Pressure head + Potential head or datum head
H.G.L = P/ρg + Z
Where,
H.G.L = Hydraulic gradient line
P/ρg = Pressure head
Z = Potential head or datum head

5. Total energy line:
is basically defined as the line which will give the sum of pressure head,
potential head and kinetic head of a fluid flowing through a pipe with respect to
some reference line.
Total energy line = Pressure head + Potential head + Kinetic head
T.E.L = P/ρg + Z + V2/2g
Where,
T.E.L = Total energy line
P/ρg = Pressure head
Z = Potential head or datum head
V2/2g = Kinetic head or velocity head

6. Relation between hydraulic gradient line and total energy line
H.G.L = E.G.L - V2/2g
Let us see the following figure, there is
one reservoir filled with water and also
connected with one pipe of uniform
cross-sectional diameter.
Hydraulic gradient and energy lines are
displayed in figure.
At Velocity V = 0, Kinetic head will be zero and
therefore hydraulic gradient line and energy
gradient line will be same.
At Velocity V = 0, EGL = HGL

7. Laminar flow through circular conduits
The variation of velocity takes place in a narrow region in the vicinity of solid
boundary. The fluid layer in the vicinity of the solid boundary where the effects of fluid
friction i.e., variation of velocity are predominant is known as the boundary layer.
FLOW OF VISCOUS FLUID THROUGH CIRCULAR PIPE
For the flow of viscous fluid through circular pipe, the velocity distribution across
a section, the ratio of maximum velocity to average velocity, the shear stress distribution
and drop of pressure fora given length is to be determined. The flow through circular pipe
will be viscous or laminar, if the Reynold’s number is less than 2000.
DEVELOPMENT OF LAMINAR AND TURBULENT FLOWS IN CIRCULAR PIPES
1.Laminar Boundary Layer
At the initial stage i.e, near the surface of the leading edge of the plate, the thickness of
boundary layer is the small and the flow in the boundary layer is laminar though the
main
stream flows turbulent. So, the layer of the fluid is said to be laminar boundary layer.
2.Turbulent Boundary Layer
The thickness boundary layer increases with distance from the leading edge in the
down-stream direction. Due to increases in thickness of boundary layer, the laminar
boundary layer becomes unstable and the motion of the fluid is disturbed. It leads to a
transition from laminar to turbulent boundary layer.

8. Actually both would happen - but for different flow rates. The top occurs when the
fluid is flowing fast and the lower when it is flowing slowly. The top situation is known
as turbulent flow and the lower as laminar flow. In laminar flow the motion of the
particles of fluid is very orderly with all particles moving in straight lines parallel to
the pipe walls.

12. Circular annuli Boundary Layer concepts

13. Actually both would happen - but for different flow rates. The top occurs when the
fluid is flowing fast and the lower when it is flowing slowly. The top situation is known
as turbulent flow and the lower as laminar flow. In laminar flow the motion of the
particles of fluid is very orderly with all particles moving in straight lines parallel to
the pipe walls.

19. Types of boundary layer thickness
Boundary layer thickness ‘δ’ is the distance normal
to the wall to a point where the flow velocity has essentially
reached the velocity ‘u”.

20. Contd.,
• Laminar boundary layer flow
– The laminar boundary is a very smooth flow, while the
turbulent boundary layer contains swirls or "eddies." The
laminar flow creates less skin friction drag than the turbulent
flow, but is less stable. Boundary layer flow over a wing
surface begins as a smooth laminar flow. As the flow continues
back from the leading edge, the laminar boundary layer
increases in thickness.
• Turbulent boundary layer flow
– At some distance back from the leading edge, the smooth
laminar flow breaks down and transitions to a turbulent flow.
From a drag standpoint, it is advisable to have the transition
from laminar to turbulent flow as far aft on the wing as
possible, or have a large amount of the wing surface within
the laminar portion of the boundary layer. The low energy
laminar flow, however, tends to break down more suddenly
than the turbulent layer.

26. Darcy Weisbach equation
• The Darcy-Weisbach equation is used for
calculating head loss in a straight pipe. This
equation is one of the most useful equations in
fluid mechanics

27. Derivation of Darcy Weisbach Equation
Step 1: Terms and Assumptions
Consider a uniform horizontal pipe with fixed
diameter d and area A, which allow a steady
flow of incompressible fluid.
For simplicity consider two sections;
S1 and S2 of the pipe separated by the distance L.
At all the point of S1, The pressure is P1, velocity is V1.
At all the point of S2, the pressure is P2 and velocity is V2.
Consider the fluid flow as shown in the figure(1) Thus, the pressure at
S1is greater than the pressure at S2 i.e.,(P1>P2) This pressure difference makes
the fluid flow along the pipe.
When fluid flows there will be the loss of energy due to friction. Thus
we can apply Bernoulli’s principle.
Bernoulli’s principle states that a decrease in the pressure or potential
energy of the fluid increases the velocity/speed of the fluid flow or in other
words, “For incompressible fluid, the sum of its potential energy, pressure, and
velocity remains constant.”

28. Step 2: Applying Bernoulli’s principle

29. here, the direction of the force due to pressure as -ve.

31. This text uses only the Darcy-Weisbach friction factor.
Combining the previous equations, gives the Darcy-Weisbach equation:

32. To use the Darcy-Weisbach equation, the flow should be fully developed
and steady. The Darcy-Weisbach equation is used for either laminar
flow or turbulent flow and for either round pipes or nonround
conduits such as a rectangular duct.
The Darcy-Weisbach equation shows that head loss depends on the
friction factor, the pipe-length-to-diameter ratio, and the mean
velocity squared.
The key to using the Darcy-Weisbach equation is calculating a value of
the friction factor f.
Application of Darcy Weisbach Equation
Is used to calculate the loss of head due to friction
in the pipe.

33. Friction factor
Friction factor may refer to:
Atkinson friction factor, a measure of the resistance to airflow
of a duct
Darcy friction factor, in fluid dynamics
Fanning friction factor, a dimensionless number used as a local
parameter in continuum mechanics
•In fluid dynamics, the Darcy friction factor formulae are
equations that allow the calculation of the Darcy friction factor,
a dimensionless quantity used in the Darcy–Weisbach
equation, for the description of friction losses in pipe flow as
well as open-channel flow.

34. The Fanning friction factor, named after John Thomas Fanning, is
a dimensionless number used as a local parameter in continuum
mechanics calculations. It is defined as the ratio between the local shear
stress and the local flow kinetic energy density:

38. The basic chart plotted against Darcy-Weisbach friction factor against
Reynold’s Number (Re)
for the variety of relative roughness and flow regimes. The relative roughness
is the ratio of the mean
height of roughness of the pipe and its diameter (ε/D).
Moody’s diagram is accurate to about 15% for design calculations and used
for a large number of
applications. It can be used for non-circular conduits and also for open
channels.

42. Commercial pipes
A piping system is a set of pipes, normally closed pipes,
joined together by fittings for transporting fluids. The vast majority
of pipes act as pressure containers, in other words, the fluid wets
the entire cross-sectional area, except for sewage drains or canals
where the fluid can flow in an open surface

43. • The need for using pipes arises from the fact that the point of
storage or flow stream is generally distant from the place where it is
required.
• Piping systems are used to transport all known pourable liquid or
gaseous fluids, for pasty materials or pulp and for fluids in
suspension, covering the whole range of pressure and temperature
used in industrial applications.
• A fluid flowing through a pipe will always carry an amount of energy
loss, which is spent on overcoming resistance opposing the flow
• Flow of fluids in pipes is always accompanied by friction, produced
between the particles themselves and between the fluid and the
pipe wall, in other words, energy loss.
• The energy used to overcome these resistances is called "head loss"
or “pressure loss”, results in a gradual decrease in the pressure of
the fluid, falling from one point to another in the direction of the
flow of the fluid.

54. 0.06
47.74
0.45 M

61. Unit-II Formulae

65. : 01

66. = (1200 x 3.28 x 1.1 ) / 0.8
Re = 5412, FLOW IS TURBULANT

67. : 02

69. : 03
: 04

70. = 560x103 W
: 05

71. : 06 : 07

72. : 08 : 09

76. : 10

77. : 11

81. : 12

84. :13

85. : 14 : 15

86. : 16 : 17

87. Thank you