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