A Newtonian fluid's shear-stress magnitude is proportional to its velocity 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. Used stress magnitudes to avoid mixing traction and momentum-flux sign conventions.
A Newtonian fluid's shear-stress magnitude is proportional to its velocity gradient. The proportionality is dynamic viscosity; a faster change in velocity across a narrow gap produces a larger shear stress.
| Symbol | Meaning | Units |
|---|---|---|
| Shear-stress magnitude | ||
| Dynamic viscosity | ||
| Velocity gradient normal to the flow |
Relate a measured shear stress to a controlled shear rate.
Estimate shear loading in a locally parallel fluid layer.
A Newtonian oil has viscosity 0.12 Pa·s and a velocity gradient of 250 s⁻¹. Find the 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. Used stress magnitudes to avoid mixing traction and momentum-flux sign conventions.
Assumptions
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