**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

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**(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