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Minor losses in pipe flow

## Summary

Minor losses in pipe flow are a major part in calculating the flow, pressure, or energy reduction in piping systems. Liquid moving through pipes carries momentum and energy due to the forces acting upon it such as pressure and gravity. Just as certain aspects of the system can increase the fluids energy, there are components of the system that act against the fluid and reduce its energy, velocity, or momentum. Friction and minor losses in pipes are major contributing factors.[1][2][3][4]

## Friction Losses

Before being able to use the minor head losses in an equation, the losses in the system due to friction must also be calculated.

Equation for friction losses:

${\displaystyle H_{Lf}={v^{2} \over gR_{h}}(\sum _{i}L_{i})f}$ [5][3][1]

${\displaystyle H_{Lf}}$ = Frictional head loss

${\displaystyle v}$ = Downstream velocity

${\displaystyle g}$  = Gravity of Earth

${\displaystyle R_{h}}$  = Hydraulic radius

${\displaystyle \sum _{i}L_{i}}$  =Total length of piping

${\displaystyle f}$  = Fanning friction factor

After both minor losses and friction losses have been calculated, these values can be summed to find the total head loss.

Equation for total head loss, ${\displaystyle H_{L}}$ , can be simplified and rewritten as:

${\displaystyle H_{L}={v^{2} \over 2gR_{h}}[(2\sum _{i}L_{i})f+R_{h}(\sum _{i}e_{v,i})]}$ [5]

${\displaystyle H_{L}}$ = Frictional head loss

${\displaystyle v}$ = Downstream velocity

${\displaystyle g}$  = Gravity of Earth

${\displaystyle R_{h}}$  = Hydraulic radius

${\displaystyle \sum _{i}L_{i}}$  =Total length of piping

${\displaystyle f}$  = Fanning friction factor

${\displaystyle \sum _{i}e_{v,i}}$ = Sum of all kinetic energy factors in system

Once calculated, the total head loss can be used to solve the Bernoulli Equation and find unknown values of the system.[1][5]