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Who discovered fluid viscosity and what is the history behind the concept of fluid viscosity? Further, who first defined or parametrized viscosity as shown in Equation 1.1-2 below?

Equation 1.1-2 (below) of the textbook Transport Phenomena by Bird, Stewart, and Lightfoot is given with the following footnote:

$$\tag{1.1-2} \tau_{yx}=-\mu \frac{dv_x}{dy}$$

Actually Eq. 1.1-2 does not appear in Sir Isaac Newton's Philosophiae Naturalis Principia Mathematica, but the germ of the idea is there. For illuminating comments, see D.J. Acheson, Elementary Fluid Dynamics, Oxford University Press, 1990., Sec. 6.1

I do not have Acheson's book.

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  • $\begingroup$ I'd probably say who "defined, or parametrized" viscosity. People knew a zillion [arbitrary time unit] ago that tree sap flowed slower than water. :-) $\endgroup$ – Carl Witthoft Jan 28 at 13:33
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The following insight appears in the text you referenced (Acheson, Elementary Fluid Dynamics, OUP, 1990). It is basically a quote from Principa.

"In Book II of the Principia (1687) Newton writes: SECTION IX The circular motion of fluids HYPOTHESIS The resistance arising from the want of lubricity in the parts of a fluid is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another. PROPOSITION LI. THEOREM XXXIX If a solid cylinder infinitely long, in an uniform and infinite fluid, revolves with an uniform motion about an axis given in position, and the fluid be forced round by only this impulse of the cylinder, and every part of the fluid continues uniformly in its motion: I say, that the periodic times of the parts of the fluid are as their distances from the axis of the cylinder. This is the essence of what Newton has to say about viscous flow. The hypothesis, of course, gets the subject off to a good start, but it is contained and applied wholly within a section on the circular motion of fluids, and it is immediately followed by a proposition which is false"

The unabridged version of Oxford English Dictionary also quotes Robert Boyle from 1669: R. Boyle Contin. New Exper. Physico-mech. (1682) ii. 140 That liquor is very thin, and hath no viscosity to resist the pervading body.

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  • $\begingroup$ How about the ancient (I suspect) "blood is thicker than water" :-) from the Thirteenth Century. $\endgroup$ – Carl Witthoft Jan 28 at 13:35

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