Drag is not the problem. Momentum conservation is. You have persistently failed to recognize this.my dollar says when the spheres are filled with water, the modification that the drag equation causes to momentum equation describing the frictionless push off scenario is the spring needs slightly more force to achieve the same acceleration of the 2 tanks, and the outer tank still moves to the right, and the inner tank to the left as shown.
This is the drag equation for steady movement in a large body of a fluid. It doesn't apply if the body is accelerated. It doesn't apply if the body is occupying a non-negligible fraction of a filled enclosed container...., this drag term can be reduced via:
You have not specified what scenario this question applies to.Do you deny changing only the shape of the inner sphere without changing its mass will affect the force required from the spring for a given acceleration?
Tweaks of the fish bowl setup have one of two results; either... the inventor of the overbalanced wheel who knows that he's just one additional complication from making it work.
I get that now. It's easy to forget the incompressable and rigid constraints.You are falling into the same trap as @metastable. The ball does not move, even if the fish hits the side.
The gotcha is that if the fish comes to an abrupt stop then so does the water. Any momentum transferred from fish to wall is matched by an opposite momentum transferred from water to wall.
Subject to background assumptions of rigid wall, incompressible fluid, etc.
Irrelevant. All that matters is that it is a flow that does not result in a shift of the center of mass. There are many possible flow fields with that property. Almost none of them move the molecules in front to a position behind. Most put a different set behind.-it hasn’t been shown conclusively by your proof @jbriggs444 that the very same water atoms which were in front of the fish end up behind the fish
The fish gets more than the tank. Because the tank gets none. But the water gets more than the fish, because it has to move much more rapidly.In asymmetrical mass interactions (Such as a push off between two different mass skaters), The lighter body obtains more of the kinetic energy relative to the ground. In the diagram above The fish could weigh 1000 kg, with the outer tank just slightly larger so the outer tank and water only weighs 100 kg. In a push off between 1000 kg fish and 100 kg water/tank, according to the momentum equation, which gets more kinetic energy relative to ground initially during the internal push off?
I'm not sure that infinitely incompressible water is a realistic scenario worth discussion, unless we're leaving the land of reality altogether (akin to the infinitely rigid rod in relativity).Are you able to prove a fish can swim normally in “incompressible water?”
What if we're not 100% sure? Does it make sense to talk about infinitely incompressible water and infinitely rigid tanks?So are we 100% sure the fish’s normal swimming ability doesn’t rely entirely on water’s slight compressibility?
We can be 100% sure that in the limit as compressibility decreases toward zero, fish's normal swimming ability is unimpaired.So are we 100% sure the fish’s normal swimming ability doesn’t rely entirely on water’s slight compressibility?
What point are you trying to make here?If it can’t be proved that a fish can swim in 100% incompressible water, then it can’t be proved the other methods of locomotion involving the fish swimming around will work either... Can it?
If you want 100% certainty in anything, try religion instead of physics.So are we 100% sure...
Compressibility reduces the propulsion efficiency in a fluid, so it doesn't help. We use the incompressibility limit, just like we use the rigid body limit, where appropriate.... the fish’s normal swimming ability doesn’t rely entirely on water’s slight compressibility?
The physics of incompressible flow are well accepted. If you want to call that approximation into question, please start another thread.If it can’t be proven a fish can move its nose forward through 100% incompressible fluid, the realism of any scenario modeling a fish swimming in such a fluid is called into question.
I along with others have already agreed several times in this thread that if you want to discard the assumptions of incompressibility and rigidity then the problem of propulsion by the fish becomes trivial.@jbriggs444 would you infer that if the water has even slight compressibility (as it does, see: http://sites.bsyse.wsu.edu/joan/teaching/bsyse558/W2/Lec5Stu.pdf ), it can at least temporarily shift the outer glass ball slightly by pushing directly off the glass, regardless of whether the ball is floating in space, water or resting on a ground with or without friction between the ball and the contact point with ground?