**
Theory
**

When a fluid is flowing through a pipe, the fluid experiences some resistance due to which some of the energy of the fluid is lost. This loss of energy is classified as:

**
1)
Major energy losses:
**
The viscosity causes loss of energy in the flows, which is known as frictional loss or major energy loss and it is calculated by the following formula;

(a)Darcy-weisbach formula

The loss of head can be measured by the following equations

h
_{
f
}
=4f L V
^{
2
}
/ (2gD)

Where hf
_{
}
= Loss of head due to friction

f = Co-efficient of friction which is a function of Reynolds number

f = 64/R
_{
e
}
(for Re <2000) (laminar flow)

L = Length of pipe

V = mean velocity of flow

D = Diameter of pipe

**
2)
Minor energy losses:
**
The loss of energy due to change of velocity of the flowing fluid in magnitude or direction is called minor loss of energy

**.**The minor loss of energy includes the following cases

**
(a)
Sudden expansion of pipe:
**

The head loss due to sudden expansion equation is he = (V
_{
1
}
-V
_{
2
}
)
^{
2
}
/2g

Where V
_{
1
}
is the velocity at section 1

V
_{
2
}
is the velocity at section 2

**
(b)
Sudden contraction of pipe
**

The head loss due to sudden contraction equation is hc =k (V
_{
2
}
^{
2
}
/2g)

Where k = ((1/C
_{
c
}
)-1)
^{
2
}

V
_{
2
}
is the velocity at section 2

**
(c)
Bending in pipe:
**

The head loss due to bending equation is h
_{
b
}
=k (V
^{
2
}
/2g)

Where V is the velocity of the flow.

k is the co-efficient of the bend ,which depends on the angle of the bend, radius of curvature of bend and diameter of the pipe