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So I'm having trouble understanding velocity gradients conceptually, I have little physics training passed physics 101 (I'm a biologist), but I'm currently working in an endothelium research lab with a lot of fluid physics. I came up with an example in my kitchen and I tried to work it out based on youtube videos of fluid mechanics I was watching.

If you have a tall glass and you fill it with water, then spin it around it's long axis (so the bottom doesn't move but it spins like a disc) it seems like the water inside doesn't move as quickly as you spin the glass. I'm guessing based on "no-slip" the water touching the glass is moving at the speed of the glass it touches... the water in the center of the column probably moves the least. If you stop spinning the glass the water continues to move (inertia) but it slowly stops (not sure why)...

So my question is this: where is the water moving in fastest in that moment you stop spinning the cup/column... originally the velocity in the center was the lowest and the velocity on the glass was highest, but then wouldn't the glass be the source of friction and stop it? so is the velocity initially fasted on the periphery but then the layer with the fastest velocity moves away toward the center of the cup/column?

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Just to add my hypothesis:

"So my question is this: where is the water moving in fastest in that moment you stop spinning the cup/column... originally the velocity in the center was the lowest and the velocity on the glass was highest, but then wouldn't the glass be the source of friction and stop it?"

"However if you where able to stop the cup instantly, theoretically the highest velocity will be located infinitesimally close to the wall."

The only thing not explained is that the total net force acting on the 'spinning' water is not only the action/reaction of water with the glass (kinematical friction) but also the action of spinning water (with a relatively lower angular velocity) with the spinning cross-sectional segment of the water with the highest velocity et cetera -- which is actually a natural unit called as velocity gradient. However, even though velocity gradient may be challenging to measure, recalling molecular interactions within a Newtonian fluid may give an excellent visual when discussing fluid viscosity.

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  • $\begingroup$ I am sorry I am very remedial in physics, I am happy to hear this is that velocity gradient I am reading so much about. Thanks! $\endgroup$
    – Jasand Pruski
    Commented Jun 6, 2017 at 13:32
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Water is a viscous fluid. Its viscosity is much lower than that of familiar fluids like honey, but water has some as well. Water will behave as a Newtonian fluid, which means that there will be a linear relation between the shearing stresses (internal forces acting on the water) and the rate of shearing strain (velocity gradient). The curve representing this relation also contains the origin.

This indeed means that there will be no slip with the surface of the cup, but due to the inertia of the water it will take some time before the rest of the water will change its velocity as well. However in the real world you can not stop the cup instantly, so some of the water, closest to the glass wall, will have slowed down when it has come to a stop. So, the highest velocity of the water will be located somewhere between the wall and the center, depending on the time scale at which the cup comes to a stop. However if you where able to stop the cup instantly, theoretically the highest velocity will be located infinitesimally close to the wall.

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  • $\begingroup$ "a linear relation between the shearing stresses (internal forces acting on the water) and the rate of shearing strain (velocity gradient)." interesting, this wasn't covered in the videos I watched... i'll have to look more into this... "The curve representing this relation also contains the origin." i'm not sure I understand the significance of this statement... " theoretically the highest velocity will be located infinitesimally close to the wall." and then it moves toward the center but never to the very center? $\endgroup$
    – Jasand Pruski
    Commented Jul 15, 2014 at 11:33
  • $\begingroup$ The velocity at the center is zero, because it rotates around it, so only if everything is at rest than you could say that the center has the highest velocity, but so does the rest of the water. And with: "The curve representing this relation also contains the origin." I mean that if the shearing strain is zero the shearing stress is zero as well, because there are also non-Newtonian fluids which do not behave like this. $\endgroup$
    – fibonatic
    Commented Jul 15, 2014 at 11:42

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