Few books get down to fundamentals and these are books that are written by authors that really love understanding those fundamentals. I strongly maintained that FM White was far beyond reckoning in presenting basic fluid mechanics. Till I read Kundu.
And this description of viscosity simply sent me overboard! Kundu takes the flow over a flat plate and discusses the diffusivity theory. Just note how the “equivalent” simply swoops in to present the truest description, thus far, of viscosity! This was precisely why I began discussing viscosity with this article in my FM class last year.
Next, consider the effect of velocity gradient du/dy. It is clear that the macroscopic fluid velocity u will tend to become uniform due to the random motion of the molecules, because of intermolecular collisions and the consequent exchange of molecular momentum. Imagine two railroad trains traveling on parallcl tracks at different speeds, and workers shoveling coal from one train to the other. On the avcrage, the impact of particles of coal going horn the slower to the faster train will tend to slow down the faster trajn, and similarly the coal going from the faster to the slower train will Lend to speed up the latter. The net effect is a tendency to equalize the speeds of the two trains. An analogous process takes place in the fluid flow problem. The velocity distlribution here tends toward the dashed linc (forget the dashed line thingy), which can be dcscribed by saying that the x-momentum (determined by its “concentration” u) is being transferred downward. Such a momentum flux is equivalent to the existence of a shear stress in the fluid, just as the drag cxperienced by the two trains results from the momentum exchangc through the transfer or coal particles. Thc fluid above AB tends to push the fluid underneath forward, whereas the fluid below AB tends to drag the uppcr fluid backward.
Now that’s viscosity for you! Whoa! Bravo, Kundu!
