Minor losses in pipe flow

Introduction

Minor losses 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]

This article will focus on what geometries and components of piping are categorized as minor losses. It will explore to what extent these minor losses effect flow and discuss how to use derived values for these components to solve equations like Bernoulli analyses.

Minor Losses

Below is a list of common piping components and their kinetic energy factor, $e_{v}$ .

Kinetic energy factors for specific components of piping systems. Provided by John Berg, Chemical Engineering, University of Washington.

The kinetic energy factor is used to calculate the configurational head loss, the energy loss to the components of the system. The configurational head loss, $H_{Lc}$ , can be calculated using the following equation.

$H_{Lc}={v^{2} \over 2g}(\sum _{i}e_{v,i})$ ^[5]^[2]^[6]

Where:

$H_{Lc}$ = Configurational head loss

$v$ = Downstream velocity

$g$ = Gravity of Earth

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

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:

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

$H_{Lf}$ = Frictional head loss

$v$ = Downstream velocity

$g$ = Gravity of Earth

$R_{h}$ = Hydraulic radius

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

$f$ = Fanning friction factor

Total Head Loss

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

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

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

$H_{L}$ = Frictional head loss

$v$ = Downstream velocity

$g$ = Gravity of Earth

$R_{h}$ = Hydraulic radius

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

$f$ = Fanning friction factor

$\sum _{i}e_{v,i}$ = 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]

Resources

^[5]^[6]^[1]^[3]^[2]^[4]

Notes

1 2 3 4 "Losses in Pipes". my.me.queensu.ca. Retrieved 23 January 2017.
1 2 3 Anderson, Gunther; Ryan Barr; Risa Benvega. "Minor Losses" (PDF). Retrieved 23 January 2017.
1 2 3 "Head Loss in Piping Systems - TechInfo". www.hydromatic.com. Retrieved 2017-01-22.
1 2 "Objectives_template". nptel.ac.in. Retrieved 23 January 2017.
1 2 3 4 5 Lightfoot, R. Byron Bird; Warren Stewart; Edwin N. (2007). Transport phenomena (Rev. 2. ed.). New York [u.a.]: Wiley. ISBN 978-0-470-11539-8.
1 2 "Minor Loss Calculation for Liquid and Gas Flow". www.lmnoeng.com. Retrieved 2017-01-22.

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