That fluid is in laminar flow. But what does it actually mean when it's viscosity is higher than it's inertia?
Viscosity is the resistance of the fluid to flow
Inertia is the state of fluid of doing nothing unless a force is exerted on it.
I am confused by this. I do not know how these two things are linked.
Let a driving force is exerted on such a fluid and then switched off after a while. Now assume the fluid flow is across a pipe but with zero friction between the fluid and pipe's inner walls, even in such zero friction case the flow of the viscous fluid will come to a stop since the viscosity (resisting force) is greater than its inertia.
Compare the scenario with Newton's first law case, where an object keeps on moving on a friction-less surface due to its inertia, if none external force acts on it!
Dear Md Badriadib Aldrin Suhaini,
you may find the Womersly number useful. It describes the relationship between viscous and internal forces in pulsatile pipe flow.
Inertia forces become more prominent, if the fluid is accelerated back and forth as in pulsatile blood flow and further if the accelerated fluid volume (i.e. the mass) is large. Meaning that for small fluid volumes and almost stationary fluid flow the inertial forces can be neglected. The internal forces are often small compared to the viscous forces.
The viscous forces depend on fluid viscosity, fluid velocity and the gradient of fluid velocity within the fluid or from fluid to the boundary. They increase with increasing velocity and its gradient.
The Womersly number tells you, if you can neglect the inertial forces in your computation.
Best wishes,
Stefan
I haven't yet heard a phrase like, "a fluid's viscosity is higher than its inertia". The phrase itself is ambiguous, possibly because the units of these two quantities, viscosity and inertia, are different. Dynamic viscosity is kg/(m.s), kinematic viscosity is m^2/s. The term, inertia, by itself is also somewhat ambiguous but it could be argued to be mass, i.e. kg. So the comparison of the magnitudes of either type of viscosity with inertia makes no sense, and could be different depending on one's choice of units.
Perhaps you are comparing viscous forces to inertial forces, in which case we are probably talking about the magnitude of the Reynolds number.
The example, in an above reply, of flow in a pipe with zero wall friction is incorrect. As the walls offer no resistance to flow, then the mass flux will remain constant, assuming that the pipe is uniform. On the other hand, the shear stress will evolve towards zero everywhere whilst maintaining the mass flux, and the ultimate state is that of a uniform plug flow with a constant velocity profile. This is directly analogous to the evolution in time of an initially parabolic temperature profile in a finite domain with insulating boundaries where the ultimate temperature profile is constant, and at a value which is the mean of the initial profile.
@ Andrew
I did not get your point about the incorrectness of my reply above. Please clarify.
My apologies.
If there is zero friction between the wall and the fluid, then there is no force which will stop the fluid from moving, and therefore it will continue to move.The mass flux will remain conserved.
On the other hand, if there is shear within the fluid, as will happen when the velocity profile varies with distance, then that is internal friction. It is this which will speed up the more slowly moving fluid and slow down the faster moving fluid. The eventual steady-state is a fluid moving with a uniform velocity.
But the primary issue is that you quoted a friction-free wall, and therefore it will offer no resisting force to the fluid. This means that there is no contradiction with Newton's laws. The momentum is conserved.
Thanks for the clarification. I agree with your latest post. Also, my point was that even in the case of zero friction between the wall and the fluid, and if the viscosity of the fluid is of "high enough" then it will stop the fluid flow.
Viscosity takes over the inertia of motion!
Also my whole point was to justify Newton's laws, since first law is applicable when no force acts on the body. In the example I mentioned, even if the driving force and friction are absent, but if the fluid is highly viscous (so resistive forces come into play!) then the motion is stopped! Totally in accordance to Newton's laws!
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