We were discussing the concept of laminar
and turbulent flow, Reynolds
experiment, frictional
loss in pipes, derivation of expression
for loss of head due to friction in pipes, co-efficient
of friction in terms of shear stress and also the
basics of shear stress in turbulent flow, in the subject of fluid mechanics, in
our recent posts.

If we want to evaluate the loss of head in long pipe, above losses will be small as compared with major loss of head i.e. loss of head due to friction. That’s why above losses are considered as minor losses and we can also neglect such losses for long pipe.

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Now we will go ahead to see minor head losses in
pipe flow, in the subject of fluid mechanics, with the help of this post.

Even we have already seen earlier one post based on
major and minor losses in pipes earlier. Today, we will be interested to secure
the detailed information about the minor head losses in pipe flow only.

**Minor head losses in pipe flow**

Head loss in pipe flow system due to
viscous effect i.e. due to friction will be termed as major head loss and will
be indicated by h

_{L-Major}.
Head loss in pipe flow system due to
various piping components such as valves, fittings, elbows, contractions,
enlargement, tees, bends and exits will be termed as minor head loss and will
be indicated by h

_{L-Minor}.
We will see here the following cases of
minor head losses in pipe flow.

- Loss of head due to sudden enlargement
- Loss of head due to sudden contraction
- Loss of head at the entrance of a pipe
- Loss of head at the exit of a pipe
- Loss of head due to an obstruction in a pipe
- Loss of head due to bend in the pipe
- Loss of head in various pipe fitting

If we want to evaluate the loss of head in long pipe, above losses will be small as compared with major loss of head i.e. loss of head due to friction. That’s why above losses are considered as minor losses and we can also neglect such losses for long pipe.

But if we want to evaluate the loss of
head in small pipe, above losses must be considered as such losses will be
comparable with the loss of head due to friction.

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**Loss of head due to sudden enlargement **

Let us assume that a liquid is flowing
through a pipe which has a sudden enlargement as displayed here in following
figure.

Loss of head due to sudden enlargement
will be given by following equation.

Where,

V

_{1 }= Velocity of fluid flow at section 1-1
V

_{2}= Velocity of fluid flow at section 2-2
h

_{e}= Loss of head due to sudden enlargement
g = Acceleration due to gravity

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**Loss of head due to sudden contraction **

Let us assume that a liquid is flowing
through a pipe which has a sudden contraction as displayed here in following
figure.

Loss of head due to sudden contraction
will be given by following equation.

Where,

V

_{2}= Velocity of fluid flow at section 2-2
h

_{C}= Loss of head due to sudden contraction
k = Minor loss co-efficient

Value of k, for different fittings or
pipe components, might be secured from the post “major and minor
losses in pipes”.

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**Loss of head at the entrance of a pipe **

Loss of head at the entrance of a pipe
is the loss of head when a liquid enters a pipe which is connected with a large
tank or reservoir.

Loss of head at the entrance of a pipe
will be given by the following equation as mentioned here.

Where,

V = Velocity of fluid flow in the pipe

h

_{i}= Loss of head at the entrance of a pipe###
**Loss of head at the exit of a pipe **

Loss of head at the exit of a pipe will
be given by the following equation as mentioned here.

Where,

V = Velocity of fluid flow at the outlet of pipe

h

_{O}= Loss of head at the exit of a pipe

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**Loss of head due to an obstruction in a pipe **

Whenever there will be an obstruction in
a pipe, loss of head will take place due to the reduction of area of the
cross-section of the pipe at the location where obstruction is located. There
will be sudden enlargement of the flow area beyond the obstruction and due to
this reason there will be loss of head.

Let us consider a pipe of
cross-sectional area A with an obstruction as displayed here in following
figure.

Loss of head due to an obstruction in a
pipe

**will be given by the following equation as mentioned here.**
Where,

V = Velocity of fluid flow in the pipe

A = Area of pipe

a = maximum area of the obstruction

C

_{C}= Co-efficient of contraction

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**Loss of head due to bend in pipe **

Loss of head due to bend in pipe

**will be given by the following equation as mentioned here.**
Where,

V = Velocity of fluid flow

h

_{b}= Loss of head due to bend in pipe
k = Co-efficient of bend

Value of k will be dependent over angle
of bend, radius of curvature of bend and diameter of the pipe.

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**Loss of head in various pipe fitting **

Loss of head in various pipe fitting

**will be given by the following equation as mentioned here.**
Where,

V = Velocity of fluid flow

h

_{b}= Loss of head due to bend in pipe
k = Co-efficient of bend

Further we will go ahead to see the basics of
hydraulic gradient and total energy line, in the subject of fluid mechanics,
with the help of our next post.

Do you have any suggestions? Please write in comment
box.

### Reference:

Fluid mechanics, By R. K. Bansal

Image courtesy: Google

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