ENERGY LOSS IN PIPES, Darcy- weicbach formula, Chezy's formula, minor losses in pipe



When ever there is flow of fluid in pipes there will be resistance which add to energy loss. For our study, we have classified the losses in two section, these are
  • Major losses in pipe
  • Minor losses in pipe
Major losses are mostly due to friction which is basically experienced by 
  • Surface of pipe and layer of fluid flowing over it.
  • Subsequent layer of fluids creating resistance to neighboring layer.
It can be calculated by Darcy - weisbach formula and Chezy's formula.

Darcy - weisbach formulaDarcy - weisbach formula
hf = head loss
L = length of pipe
d = diameter of pipe
f = coefficient of friction
V = mean velocity of flow

Chezy's formula.Chezy's formula
hf = loss of head due to friction
P = perimeter of pipe
A = area of cross section of pipe
L = length of pipe
V = mean velocity of flow

Minor losses in energy can arise from several factors. Some of them are as under.

  • Any obstruction in pipe
  • Bending in pipe
  • Unanticipated contraction
  • Unexpected expansion
  • Fittings etc in pipe
Also losses occurs at entrance and exit of pipes which are unavoidable. All such losses accounts for loss of head of fluid in pipe. These are minor losses as compared to frictional loss which can be neglected for long pipes but are taken into account when we deal with short pipes.

Loss of head due to sudden enlargement and contraction

Consider a pipe of diameter D1 (smaller) with sudden enlargement having diameter D2 (larger). The liquid moving from smaller to larger diameter pipe experiences sudden change in boundry an is not able to follow the abrupt change in boundary resulting into formation of turbulence or eddies. This adds to the loss of head in the pipe.

When fluid is flowing in larger diameter pipe and suddenly experiences change in diameter (reduced diameter of flow), the flow goes on decreasing upto section C - C and then suddenly increases causing loss of head. Then section C - C is also known as vena-contracta.

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