Explain major and minor energy losses in pipe flow

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

• Major energy losses.

• Minor energy losses.

Major energy losses : This is due to friction and it is calculated by the following formulae ;

a. Darcy – Weisbach Formula

hf = ( 4 . f . L . V² ) / d × 2g

where, hf = loss of head due to friction

f = co – efficient of friction which is the function of Reynolds number

L = length of pipe

V = mean velocity of flow

d = Diameter of pipe

b. Chezy’s Formula

hf = ( f’ / rho × g ) × P / A × L × V

now Chezy’s formula ;

V = C × √ mi

where, hf = loss of head due to friction

P = wetted perimeter of pipe

A = area of cross-section of pipe

L = length of pipe

V = mean velocity of flow

C = Chezy’s constant

m = hydraulic mean depth

i = Loss of head per unit length of pipe

Minor energy losses : The loss of head due to change of velocity of the fluid in magnitude or direction is known as minor loss of energy. Minor losses of energy includes the following cases :

a. Loss of head due to sudden enlargement

he = ( V1 – V2 )² / 2g

b. Loss of head due to sudden contraction

hc = V2² / 2g [ ( 1 / Cc ) – 1 ] ²

c. Loss of head at the entrance of the pipe

hi = 0.5 V² / 2g

d. Loss of head at the exit of a pipe

ho = V² / 2g

e. Loss of head due to an obstruction in pipe= ( Vc – V )² / 2g = V² / 2g [ ( A / Cc ( A – a ) ) – 1 ] ²

f. Loss of head due to the bend in a pipe

hb = kV² / 2g

g. Loss of head in various pipe fittings = kV² / 2g