# Is Viscosity = Slope?

studying fluid mechanics, I see that viscosity relates shear stress to shear rate, like a slope. However, on graphs I see that they draw a triangle, and where I would expect to see $$\Delta \tau$$, I see $$\mu_{ap}$$ instead. Why is the slope being "drawn" along the y-axis, and not represented as the usual math slopes I have come across: $$\frac{d\tau} {d \dot{\gamma}}$$.

• Why can’t engineers plot what they want or need instead of following maths? Jan 9 at 19:38
• It is not about cannot, they are also supposed to follow maths, they use math all the time to describe physical systems...jesus. Second, this has more to do with "improper" labeling which may have a reason to be, and I may not know about it; that is why I am asking this question. However, the way is represented on the graph, would imply $\mu = \Delta \tau$ which is incorrect.
– RSM
Jan 9 at 19:51
• I always remember Tor = mu dv/dy when I start playing around with viscosity whether to do with rheopectic or thixotropic or even newtonian. Jan 9 at 19:58
• Yes, that equation shows $\mu$ to be the slope of Shearing stress. Reason why I do not see why show $mu$ as part of the $\tau$ axis in a graph.
– RSM
Jan 9 at 20:02
• I am afraid I don't understand what you are asking. Looking at Wikipedia, I see a triangle that might be what you are asking about in this link but on the next diagram, we a see the shear stress increasing with increased velocity which is what viscosity is. Jan 10 at 0:50