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

 

[Chestermiller]

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 textbook and master its use.