# Centripetal Force and Pascal's Principle

I am trying to reconcile what I understand about Pascals Law in Fluid Statics and Centripetal Force in Fluid Dynamics

In fluid statics pressure always acts normal to the wall . The explanation I have seen

Is that while a momentum change with the wall of a container/surface has both a tangential and perpendicular components, as a static fluid has completely random motion over many interactions the tangential components of the forces statistically cancel out leaving only the perpendicular components as a net force

In fluid dynamics under a curved flow the change of the organised momentum/ velocity vector of a fluid results in an inwards force radially towards the centre - Centripetal Force

I could be wrong but to me this appears that this force is again purely perpendicular to the surface but under very different conditions - Under fluid dynamics the tangential components are no longer statistically equal so the net forces do not cancel out but yet we are left with the same perpendicular force situation.

As a further example - if we were to reverse the direction flow (at same velocity/ mass flo rate ) we would still experience the same centripetal force in the same radial direction. It appears the original direction of the momentum is irrelevant to the action of this force.

Could someone please explain how this could be ?

A.T.
Under fluid dynamics the tangential components are no longer statistically equal
If the tangential velocity is constant the tangential components must cancel to zero, just like in the static case. To have a constant flow under resistance you need a pressure gradient along the flow.

If the tangential velocity is constant the tangential components must cancel to zero, just like in the static case. To have a constant flow under resistance you need a pressure gradient along the flow.

Thanks For your reply . Ok I get this must be the case otherwise the fluid would be experiencing an acceleration - the force acting on it must only be perpendicular as that leaves a change in vector not magnitude of the velocity.
However
I am just unsure what is actually causing the tangential components to cancel ? What momentum is 'coming' the other way to cancel the tangents as in the static case.
You mention flow under resistance do you mean viscosity ? could we consider this under ideal conditions

A.T.
You mention flow under resistance do you mean viscosity ?
Or friction with the wall itself.

Or friction with the wall itself.

Thanks AT I think that was a very good clue, I managed to find a few articles that mention that the no slip condition relationship to Momentum balance

The summary of the video is that the fluid molecule 'sticks' to the solid wall long enough to achieve thermal equilibrium . Irrelevant of the momentum it possess when it arrived (which has been absorbed as heat) When it leaves its Momentum is completely 'funded' by the random degrees of freedom nature of heat . As such all tangential components will cancel out

A rather more verbose explanation is below - https://www.researchgate.net/post/Can_someone_explain_what_exactly_no_slip_condition_or_slip_condition_means_in_terms_of_momentum_transfer_of_the_molecules [Broken]

with what I think are a few key phrases highlighted

"On the microscopic level the wall consists of billions of billions of interacting, vibrating atoms; their average speed is counted in hundreds of meters per second, and their vibration is pretty chaotic, though centred about some positions in space: that's why the walls appear to be "solid". Liquids and gases also consist of billions of billions of molecules whose average speed is roughly the same as that of the vibrating wall atoms (hundreds of meters per second), but their average position is free to change. That's why than can "flow".
Thus, if a single fluid molecule hits the wall, it can be "reflected" in essentially any direction. What really matters is the AVERAGE fluid particle velocity near the wall. The collisions are always ellastic in that they conserve the total energy of the colliding molecules; however, this does not preclude energy transfer from one particle to the other. Sometimes the energy comes from the wall molecules, sometimes toward the wall molecules. The same concerns the momentum. The wall molecules can then immediatelly transmit this energy/momentum to other molecules that make up the wall. The point is that the mean position of each wall molecule is fixed in space. Hence, the mean position of the fluid particles near the wall should be also very close to zero

Are these explanations a good summary as to how ordered momentum collision containing an unbalanced tangential component results in a purely perpendicular force with all tangential components cancelled ?

Last edited by a moderator:
Chestermiller
Mentor
I am trying to reconcile what I understand about Pascals Law in Fluid Statics and Centripetal Force in Fluid Dynamics

In fluid statics pressure always acts normal to the wall . The explanation I have seen

Is that while a momentum change with the wall of a container/surface has both a tangential and perpendicular components, as a static fluid has completely random motion over many interactions the tangential components of the forces statistically cancel out leaving only the perpendicular components as a net force
Yes.
In fluid dynamics under a curved flow the change of the organised momentum/ velocity vector of a fluid results in an inwards force radially towards the centre - Centripetal Force

I could be wrong but to me this appears that this force is again purely perpendicular to the surface but under very different conditions - Under fluid dynamics the tangential components are no longer statistically equal so the net forces do not cancel out but yet we are left with the same perpendicular force situation.

As a further example - if we were to reverse the direction flow (at same velocity/ mass flo rate ) we would still experience the same centripetal force in the same radial direction. It appears the original direction of the momentum is irrelevant to the action of this force.

Could someone please explain how this could be ?
Can you give a specific example of the type of situation you are asking about here? That would be very helpful.