# Energy Losses in Pipe Flow

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