From: tjroberts137@sbcglobal.net   
      
   (This entire discussion is in the context of Newtonian mechanics.)   
      
   On 7/15/22 9:44 AM, Luigi Fortunati wrote:   
   > If the water accelerates outward, it means that there is a force   
   > directed outward.   
      
   In the rotating-bucket coordinates:   
   As the bucket starts spinning you are correct -- the increasing   
   "centrifugal force" induces an increasing pressure gradient that causes   
   the fluid to increasingly rise higher for increasing radius. In a steady   
   state there is no acceleration anywhere and the net force is zero on   
   each small portion of the water -- the "centrifugal force" exactly   
   balances the horizontal fluid force induced by gravity and the   
   surrounding fluid; the radial pressure gradient causes the surface to be   
   higher for increasing radius.   
      
   In the inertial frame in which the bucket axis is at rest:   
   As the bucket starts spinning the acceleration of each small portion of   
   water is rather complicated (nonzero radial and tangential components).   
   In a steady state there is a centripetal force (directed radially   
   inward) that is different for each small portion of the water -- this   
   maintains each portion's "orbit" around the axis. For small portions of   
   the water against the wall it comes from the wall; for other portions it   
   comes from neighboring portions of the water. All other components of   
   force sum to zero for each small portion of the water; the radial   
   pressure gradient causes the surface to be higher for increasing radius.   
      
   > If the walls of the bucket do not accelerate inwards, it means that   
   > there are no forces accelerating the walls of the bucket inwards.   
      
   In the rotating-bucket coordinates:   
   in the steady state, the centripetal force on each small portion of the   
   wall equals the "centrifugal force" on it. All components of force sum   
   to zero for each small portion of the water. The centripetal force of   
   the wall is canceled by the "centrifugal force" on it. No portion of   
   bucket or water accelerates in any direction.   
      
   In the inertial frame in which the bucket axis is at rest:   
   in the steady state, the centripetal force on each small portion of the   
   wall accelerates it radially inward, maintaining its "orbit" around the   
   axis. Ditto for the wall. There is, of course, no "centrifugal force".   
      
   You should see from the above discussion that it is ESSENTIAL that you   
   specify which coordinates or frame you are discussing. Your repeated   
   failure to do that turns what you say into nonsense.   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)