# Newton's Laws of fluid motion

Can someone explain the similarity between friction and viscous force?

This is what I have understood:

Friction and viscous force come into play in presence of relative motion. They are dissipative and both are dependent on a constant ,unique for a medium.

1. The very famous saying "A body is accelerated if there is an external force acting on it". Is it violated for liquids ? Every layer is acted upon by an external force (viscous friction) but the acceleration of a particular layer is nil.

2. Now why does friction brings a body to rest but viscous drag doesn't stop a liquid completely ?

3. Friction doesn't maintain the velocity of a body but viscous force does not change the velocity of a particular layer.

4. Why does viscous force depend on area and velocity but friction is independent of it?

Assistance using simple terms will be appreciated.

• Is there a way to consolidate all of these questions into one big overarching question, or should this be multiple separate questions? Mar 16 '21 at 8:00
• By friction you mean friction between solid surfaces, right? Mar 16 '21 at 8:12
• Moreover, your point 3 is wrong: it is not true that viscosity mantains the velocity of a layer (steer the fluid in a cup, after a while it stops). Similarly, in astrophysics, differentially rotating bodies (i.e. fluid bodies having non-uniform rotation), after a while start rotating uniformly because of viscosity: the velocity of layers changes in the process. Mar 16 '21 at 8:18
• Also point 2 is wrong, and it depends on the context. If the fluid is isolated, then the total momentum is conserved (this is it does not stop, but maybe reaches a configuration witha certain angular momentum or linear momentum). Also in the case of friction the same conservation is valid, but you have to consider the total system (both surfaces). If one surface it the planet and the other is something sliding, then the analysis performed on the partial (small) system hides the conservation of momentum. Mar 16 '21 at 8:23
• @Quillo...point 3.. but wont the rotating bodies stop rotating because of viscosity ? or does it have some other reasons wayy outta my league ?
– puma
Mar 16 '21 at 9:01

2. Friction (in the naive sense) is a constant force, and hence brings a body to rest with a constant acceleration until the friction breaks down at rest (a half parabola in the $$x(t)$$ diagram). By contrast, viscous forces are not constant but proportional to velocity, so the smaller the velocity has already become, the smaller the "braking" forces get, and so the motion never stops (a decaying exponential in the $$x(t)$$ diagram). Actually both, friction and viscosity (applied to macroscopic bodies instead of fluids) can both be put under the umbrella of nonlinear velocity dependent forces. For viscosity the "nonlinearity" is just "linear". For friction, the dependency is constant up to a small threshold velocity where sliding friction breaks down and (usually higher) sticking friction begins to take over. In the sticking regime, elasticity starts to become more important, so there is a more or less smooth transition in the $$F(v)$$ diagram between stick and slip. This causes challenging stick-slip phenomena (also in the numerical treatment) in technical systems, that cause vibrations (think e.g. of a wine glass, the rim of which you rub with your wet finger, causing a tone). For these more accurate models of friction, see for example this page