# Direction of wall shear stress

#### Tunneller

What is the definition of shear stress in a cylindrical tube? It seems like sometimes that is written
$$\tau = \mu \frac {\partial u} {\partial r}$$
but then at some magic moment it gets rewritten as
$$\tau = - \mu \frac {\partial u} {\partial r}$$
so as to arrive at formula like
$$\tau = - \frac{r}{2} \frac{dP}{dx}$$
for a value of positive shear stress in uniform flow.

So I guess this is because the one is shear in the fluid and the other is shear seen by the wall, or the other way around....

The slickest explanation I saw of this was to posit
$$\tau = \mu \frac {\partial u} {\partial y}$$
where y was distance from the wall, so with y in the opposite sign of r that gets you to positive shear stress in the fluid again. But again this seems like semantics. Is there an official nomenclature how to speak of the shear that is measured in the direction of the flow versus the shear that is measured against the direction against the flow?

Thanks

Related Mechanical Engineering News on Phys.org

#### Chestermiller

Mentor
Your suspicions about the two equations are correct. To get a fundamental understanding of how to handle stress in fluid and solid mechanics problems, it is imperative to learn about the Cauchy Stress Relationship. Google this, or find it in a text book and master its use.

"Direction of wall shear stress"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving