Minor losses in pipe flow

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]

• Hydraulic head
• Total dynamic head