A force balance on a fully developed pipe segment relates wall shear to the frictional pressure gradient.
Difficulty
Intermediate
Read time
4 min
Prerequisites
Consistent SI units, algebra, and the physical assumptions listed below
Source
Teng-Jui Lin — Equation SheetsAdapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Changed radius to diameter and made the friction-only pressure drop explicit.
A force balance on a fully developed pipe segment relates wall shear to the frictional pressure gradient. The result holds in either laminar or turbulent fully developed flow when the pressure loss is the friction contribution.
| Symbol | Meaning | Units |
|---|---|---|
| Wall shear-stress magnitude | ||
| Frictional pressure drop | ||
| Internal pipe diameter | ||
| Pipe segment length |
Relate pressure measurements to pipe-wall stress.
Check a wall-friction estimate using a pressure gradient.
A horizontal pipe loses 8000 Pa over 10 m and has diameter 0.04 m. Find the wall shear-stress magnitude.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Changed radius to diameter and made the friction-only pressure drop explicit.
Assumptions
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