This document discusses boundary layer theory and flow through pipes. It defines boundary layer, boundary layer thickness, and the types of boundary layer thickness. It also discusses major and minor losses that occur in pipes due to friction or changes in flow direction or geometry. Pipes can be connected in series or parallel configurations. Moody's diagram is introduced to determine friction factor from Reynolds number and relative roughness.

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2. Hydraulic and Energy Gradient
• The pipe the total energy is plotted at
different sections to scale and joined by a line called
total energy gradient line (T.E.L).
• Hydraulic gradient is the piezometric head which is
the sum of potential head and datum head.
• Energy gradient is the sum of hydraulic gradient and
kinetic head.
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3. Boundary Layer
When a real fluids past a solid body, the fluid particles
will adhere to the boundary and condition of no slip will
occurs.
• If the boundary is stationary, the velocity of fluid at the
boundary is zero,
• Farther away from the boundary, the velocity will be
higher.
This variation of boundary from zero to free stream
velocity in the direction normal to the boundary takes
place in a narrow region in the vicinity (surrounding or
near by region) of solid boundary.
This narrow region of the fluid is called boundary layer
and the theory dealing with boundary layer flow is known
as boundary layer theory. 3

4. Boundary layer growth over a flat plate
•The boundary layer is called laminar boundary layer if the
Reynolds number of the flow is less than 5 X 10 5.
•If the Reynolds number of the flow is greater than 5 X 10 5,
the boundary layer is called turbulent boundary layer.
•The length of the zone over which the boundary layer flow
changes from laminar to turbulent is called as transition
zone. 4

5. Boundary Layer Thickness
The distance from the surface of the solid body in the
direction perpendicular to flow, where the velocity of
fluid is approximately equal to 0.99 times the free stream
velocity is called boundary layer thickness and it is
denoted by δ.
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6. Boundary Layer Thickness - Types
• Displacement thickness
• Momentum thickness
• Energy thickness
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7. Displacement Thickness
• It is defined as the distance by which the
boundary surface would have to be displaced outside
so that the total actual discharge would be same as
that of an ideal past the displaced boundary.
• It is defined as the distance measured
perpendicular to the boundary by which the
mainstream is displaced to an account of formation of
boundary layer.
Displacement thickness,
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8. Momentum Thickness
• It is defined as the distance measured from the
actual boundary surface such that the momentum flux
corresponding to the main stream velocity V through
this distance θ is equal to the deficiency or loss of
momentum due to the boundary layer formation.
• It is defined as the distance, measured
perpendicular to the boundary, by which the boundary
should be displaced to compensate for the reduction
in momentum of flowing fluid on account of
boundary layer formation.
Momentum thickness,
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9. Energy Thickness
It is defined as the distance measured from the actual
boundary surface such that the energy flux
corresponding to the main stream velocity V through
this distance δE is equal to the deficiency or loss of
energy due to boundary layer formation.
It is defined as the distance measured perpendicular
to the boundary, by which the boundary should be
displaced to compensate for the reduction of kinetic
energy of flowing fluid on account of boundary layer
formation.
Energy thickness,
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10. • Moody’ s Diagram is plotted between various values
of friction factor (f), Reynolds Number (Re) and
Relative Roughness (R/K).
• For any turbulent value problem, the value of friction
factor can be determined from Moody’s diagram.
Moody Diagram
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13. Water at a flows at a rate of 0.05 cm/s in a 20-cm
diameter asphalted cast-iron pipe. What is the head
loss per km of pipe and its Reynolds Number is 3.2 x
105?
– Calculate Velocity (1.59 m/sec)
– Compute ks/D (6E-4)
– Find f using the Moody’s diagram (.019)
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How to read Moody Diagram

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15. Losses in pipes
The loss of energy in pipe mainly classified into two
types
• Major losses
• Minor losses
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16. Major Losses
• The loss of head or energy due to friction in a pipe is
known as major loss.
• Major losses are calculated by using the
(a) Darcy – Weisbach Formula
(b) Chezy’s Formula
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17. Minor Losses
The loss of energy due to change in velocity of the
flowing fluid in magnitude or direction is called
minor loss. This is due to
– Loss of energy due to sudden enlargement.
– Loss of energy due to sudden contraction.
– Loss of energy at the entrance of a pipe.
– Loss of energy at the exit of a pipe.
– Loss of energy due to an obstruction in pipe.
– Loss of energy in bends.
– Loss of energy in various pipe fittings.
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18. 1 2
Loss of energy due to sudden
enlargement
V1=Velocity at section 1-1
V2=Velocity at section 2-2
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19. Loss of energy due to sudden
contraction
1 2
V2=Velocity at section 2-2
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20. Loss of energy at the entrance of the
pipe
V=Velocity of flow at inlet of
pipe
Loss of energy at the exit of the pipe
V=Velocity of flow at outlet of
pipe
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21. Loss of energy due to bend in pipe
k = coefficient of bend
V=Velocity of flow
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22. Loss of energy due to various pipe fittings
k = coefficient of pipe fitting
V=Velocity of flow
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23. Flow through pipes in series & parallel
Pipes in series is defined as the pipes of different
lengths and different diameters connected end to end
to form a pipe line.
When a main pipeline divides into two or more
parallel pipes, which again join together to form a
single pipe and continue as a main line. These pipes
are said to be pipes in parallel.
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