I Fun question: Can this fish swim?

[Einey77]

Imagine a fish in a tank that is completely filled with water and closed on all sides. Can this fish swim?
Since water is extermely difficult to compress, when the fish moves its fin to propel itself forward, the water can't move anywhere, so the fish should not be able to move right?

Then I thought about the dissolved air in the water, and air can be compressed. So can the fish move if the water is saturated with air?

 

[DaveC426913]

Well, fish at the bottom of the Mariana Trench can swim, even with 11 kilometers of water on top of them.

The fact that water is (almost) incompressible does not mean it is super-viscous.

A fish will contract (or angle) its fin to make a smaller surface area in the direction of motion (like a slice pf paper on-edge). Then, when it moves its fin forward, the water molecules can flow sideways a tiny bit, out of the way of the fin. It then expands (or tilts) its fin to make a large surface aea, resutling in less water being able to escape around its perimeter. When it moves its fin backward, the now trapped water drives the fish forward.

 

[Delta2]

I think it depends also on the size of the fish, if the fish is small, and its fin is small, then as the fin and/or fish moves, the amount of water displaced is small, so the compression (if needed, not sure about that, check what DaveC says) will be also small, maybe a compression of something like 1% ratio, probably the water is compressible for such a small ratio.

 

[DaveC426913]

BTW, here is a chart of the compression of water as a function of depth.

http://www.windows2universe.org/earth/Water/density.html

 

[Einey77]

Well, fish at the bottom of the Mariana Trench can swim, even with 11 kilometers of water on top of them.

The fact that water is (almost) incompressible does not mean it is super-viscous.

A fish will contract (or angle) its fin to make a smaller surface area in the direction of motion (like a slice pf paper on-edge). Then, when it moves its fin forward, the water molecules can flow sideways a tiny bit, out of the way of the fin. It then expands (or tilts) its fin to make a large surface aea, resutling in less water being able to escape around its perimeter. When it moves its fin backward, the now trapped water drives the fish forward.

If there is no where for the water to be displaced since its a completely closed tank, then it shouldn't be able to move. I didnt think about the fish km's below though

 

[Delta2]

Well, the water doesn't seem compressible at big depths , BUT, even in big depths the water isn't constricted and "forced to be compressed" when the fish moves like it will happen when the water is fully enclosed in a tank from all sides. When the tank is firmly closed the water (as the fish moves) will be forced to be compressed as it has nowhere else to move.

 

[jbriggs444]

Water can move without changing its volume.

 

[DrGreg]

When an object moves through water, it's true that water has to move away from the region in front of the object. It's also true that water has to move towards the region behind the object. The two effects cancel each other out as far as the total volume of the water is concerned.

 

[sophiecentaur]

If there is no where for the water to be displaced since its a completely closed tank, then it shouldn't be able to move. I didnt think about the fish km's below though

Trying to take real physical occurrences to extremes will usually let you down because it can often lead to apparent paradoxes that don't actually exist.
Water is not 'displaced' in the wider sense. It is caused to circulate; if there were no friction, the water would be moving in closed loops (vortices) but, in real water, that circulatory motion dies down so the pressure on the fish's nose is less than the pressure of reaction on its tail.

 

[Chestermiller]

Water can move without changing its volume.

Yes. The fish being able to move has nothing to do with water compressibility. Even if water were totally incompressible, the fish would still be able to swim.

 

[CWatters]

Well, the water doesn't seem compressible at big depths , BUT, even in big depths the water isn't constricted and "forced to be compressed" when the fish moves like it will happen when the water is fully enclosed in a tank from all sides. When the tank is firmly closed the water (as the fish moves) will be forced to be compressed as it has nowhere else to move.

The water and the fish can just swap places. No need for the water to be compressed.

 

[DaveC426913]

The water and the fish can just swap places. No need for the water to be compressed.

The issue comes down to understanding how water can move at all if it is (ideally) incompressible.

If you had a bucket of marbles that were fully packed, you would not be able to move something through it. They cannot slide past each other - or swap places - without having at least a bit of wiggle room.

 

[Delta2]

The water and the fish can just swap places. No need for the water to be compressed.

I thought of that, but then again I thought that the swapping cannot be done (I suppose in the way that DrGreg says in Post #8) unless there is some free space for the water to move there first, or unless the water is compressible (what DaveC says more or less in post #12).

 

[A.T.]

unless there is some free space for the water to move there first

It's a continuous process.

 

[Chestermiller]

Are you saying that I can't swim under water in a fully enclosed tank? (Aside from running out of breath)

 

[jbriggs444]

I thought of that, but then again I thought that the swapping cannot be done (I suppose in the way that DrGreg says in Post #8) unless there is some free space for the water to move there first, or unless the water is compressible (what DaveC says more or less in post #12).

It is an elementary and well established experimental fact that water is a liquid (*). Please examine the definition of liquid to determine what that means.

(*) Under a wide range of conditions in which it does not solidify as "ice" or evaporate into "water vapor". Maintaining a constant volume for a quantity of existing liquid water is not a condition which is observed to cause either transition.

 

[Chestermiller]

Let's forget about how the fish is being propelled for the moment. Let's just model the fish as a sphere that is moving forward in the tank at a constant velocity. Let's imagine that we are outside the tank and we are moving with the same velocity as the fish, so that the tank appears to us to be moving backwards. What does the streamline pattern in the tank look like to us (assuming the fluid is inviscid)?

 

[Delta2]

Let's forget about how the fish is being propelled for the moment. Let's just model the fish as a sphere that is moving forward in the tank at a constant velocity. Let's imagine that we are outside the tank and we are moving with the same velocity as the fish, so that the tank appears to us to be moving backwards. What does the streamline pattern in the tank look like to us (assuming the fluid is inviscid)?

Got no clue...

Ok well, I think I get it, water is liquid, the streamlines it will make will transfer water volume from the front of the fish to the back of the fish, in a continuous way without the need for extra free space or the need for compression...

 

[Chestermiller]

Got no clue...

Ok well, I think I get it, water is liquid, the streamlines it will make will transfer water volume from the front of the fish to the back of the fish, in a continuous way without the need for extra free space or the need for compression...

The streamlines will be parallel far ahead of the fish and far behind the fish. But in the vicinity of the fish, the streamlines have to pass through the gap between the fish and the sidewalls. So they have to converge (get closer together) and the velocity will have to speed up a little (so that all the fluid passes through the gap). At the hind portion of the fish, the streamlines will have to diverge again, and the velocity will have to slow down to again match the velocities of the front and back faces of the tank.

 

[CWatters]

I thought of that, but then again I thought that the swapping cannot be done (I suppose in the way that DrGreg says in Post #8) unless there is some free space for the water to move there first, or unless the water is compressible (what DaveC says more or less in post #12).

There is space. Molecules of water are nothing like solid glass marbles. They are spaced apart and at room temperature their average speed is >1000 mph.

This (http://galileo.phys.virginia.edu/classes/304/h2o.pdf) has info on the properties of water such as the mean free path of a molecule (the average distance it can travel between collisions with another).

 

[davenn]

There is space. Molecules of water are nothing like solid glass marbles. They are spaced apart and at room temperature their average speed is >1000 mph.

?? say what ?

 

[Chestermiller]

Here is a diagram of the streamline pattern in inviscid incompressible fluid flow past a sphere, where the sphere is immersed in an infinite ocean of the fluid:

Only the region within one diameter on either side of the sphere is shown. But one will note that, even at such a short distance from the sphere, the streamlines at y = +2R and y = -2R are nearly horizontal. Further out, they become essentially indistinguishable from horizontal. So, if the side walls of the tank were at these further out locations, they would essentially coincide with the streamlines. So this picture presents an excellent representation of the streamline pattern in our tank as reckoned from the rest frame of reference of our fish (sphere). Notice how, close to the sphere, the streamlines get closer together. This also corresponds to higher down-channel flow velocities (in order for all the fluid to get past the sphere without having to be compressed). Notice also that it is not necessary to invoke a molecular approach to explain what is happening and that this flow occurs even if the fluid is perfectly incompressible.

 

[CWatters]

?? say what ?

Under "Thermal Energy" enter 20C in the first box..

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html

gives rms speed of 1425 mph.

 

[davenn]

Under "Thermal Energy" enter 20C in the first box..

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html

gives rms speed of 1425 mph.

that seems to be all relating to gas molecules, not a liquid as being discussed in this thread
help me understand how it's related to a fish swimming in water

 

[DaveC426913]

this flow occurs even if the fluid is perfectly incompressible.

This is the crux of the OP's question.

 

[CWatters]

As Dave and Chester point out a liquid doesn't have to be compressible to flow. That's the key to understanding why the fish can swim.

that seems to be all relating to gas molecules, not a liquid as being discussed in this thread
help me understand how it's related to a fish swimming in water

Look again. The calculator in that link uses data for water. The point I was making is that water molecules are not like glass marbles packed tightly together. The average size of a water molecule is about 1 Angstrom, and they vibrate rapidly moving around 2 Angstroms before colliding with each other. In effect there is lots of "space" between water molecules. See also this vid from about 7min 50...

 

[Dale]

If there is no where for the water to be displaced since its a completely closed tank, then it shouldn't be able to move.

You are mixing up two different, but related, topics. What makes something compressible or not is that a compressible material's normal deformation is proportional to its normal stress. What makes a fluid flow is that its shear deformation rate is proportional to its shear stress.

So the difference between a compressible gas and an incompressible liquid is in its behavior under normal stress. They behave the same under shear stress. So a fish in a sealed container can swim just fine, by applying shear stress to the water, as always.

 

[Chestermiller]

You are mixing up two different, but related, topics. What makes something compressible or not is that a compressible material's normal deformation is proportional to its normal stress. What makes a fluid flow is that its shear deformation rate is proportional to its shear stress.

So the difference between a compressible gas and an incompressible liquid is in its behavior under normal stress. They behave the same under shear stress. So a fish in a sealed container can swim just fine, by applying shear stress to the water, as always.

For an inviscid fluid, the stress tensor is isotropic (pure pressure), and there are no shear stresses present (either at surfaces or within the fluid). Nevertheless, the fish could still swim (if such a fluid existed).

 

[Dale]

I don't know about hypothetical fish in inviscid fluids, but real fish in real water exert shear stress on the water. This is what makes water flow around the fish. In particular, at the edge of a fin the shear stresses are highest and therefore the water flows fastest forming vortexes that are used to swim.

But I honestly don't have a good intuition for inviscid fluids. But in any case the normal deformation is not important.

 

[Chestermiller]

I don't know about hypothetical fish in inviscid fluids, but real fish in real water exert shear stress on the water. This is what makes water flow around the fish. In particular, at the edge of a fin the shear stresses are highest and therefore the water flows fastest forming vortexes that are used to swim.

Hi Dale,

Do you have a reference indicating that fish could not swim without being able to exert viscous shear stresses on the water? As a guy whose thesis area was fluid mechanics, I have trouble accepting this premise for a low viscosity fluid like water. When I swim, my hands push water backwards behind me, and the reaction force of the water pushes me forward. The water that I have pushed backwards creates a circulation flow to my sides so that, at distances away from me to the side, an equal amount of fluid flows forward so that mass is conserved. So, to me, the act of swimming is similar to being on a frozen lake and throwing a shoe; it's primarily a fluid momentum effect.

For a fish, I visualize the same kind of swimming action, with its tail forcing water backwards. Again, fluid momentum would provide the driving force. I would really be interested in seeing a reference that says that a fish could not swim in a fluid whose viscosity is insignificant.

@boneh3ad, what are your thoughts on this?

Chet

 

[DaveC426913]

You are mixing up two different, but related, topics. What makes something compressible or not is that a compressible material's normal deformation is proportional to its normal stress. What makes a fluid flow is that its shear deformation rate is proportional to its shear stress.

So the difference between a compressible gas and an incompressible liquid is in its behavior under normal stress. They behave the same under shear stress. So a fish in a sealed container can swim just fine, by applying shear stress to the water, as always.

This is good. I have not been acquainted with 'shear' stress and 'normal' stress, but now that you're described it, I can very easily understand why water can 'slide" even while being incompressible. They're two different properties.

I had been thinking of these tile puzzles:

They slide past each other easily enough but they will not compress - one tile always takes up the same area (volume).

 

[boneh3ad]

If you had a completely incompressible and inviscid flow, then I think you could make the case that a fish could not actually swim if the tank was small enough because the water would just recirculate and it would be the aquatic equivalent of a treadmill. In the real world, where viscosity will dissipate some of that energy and water actually is minutely compressible, I think a fish could swim just fine, although it would certainly get harder in the small tank because there would definitely still be some recirculation.

 

[Chestermiller]

If you had a completely incompressible and inviscid flow, then I think you could make the case that a fish could not actually swim if the tank was small enough because the water would just recirculate and it would be the aquatic equivalent of a treadmill. In the real world, where viscosity will dissipate some of that energy and water actually is minutely compressible, I think a fish could swim just fine, although it would certainly get harder in the small tank because there would definitely still be some recirculation.

What if the tank were very large in the incompressible inviscid case?

 

[DaveC426913]

If you had a completely incompressible and inviscid flow, then I think you could make the case that a fish could not actually swim if the tank was small enough because the water would just recirculate and it would be the aquatic equivalent of a treadmill.

No. The water would go to one end of the tank as the fish went to the other end - even if that end is only a few centimeters in front of its nose.

There may be some loss of efficiency due to recirculaton, but it would not prevent the fish from reaching the wall.

 

[boneh3ad]

No. The water would go to one end of the tank as the fish went to the other end - even if that end is only a few centimeters in front of its nose.

There may be some loss of efficiency due to recirculaton, but it would not prevent the fish from reaching the wall.

I am not actually sure what you are talking about, but if the flow is inviscid and incompressible (as I discussed in the statement you quoted), then there would be no such "loss of efficiency". There is no mechanism for dissipation.

The water wouldn't just go to one end of the tank either. After all, it can't go back there and just pile up; it has to go somewhere. It would be propelled backward off of the fish, it the back wall, and turn outward (stagnation point flow), then do the same when it reached the other boundaries until it came back around to the front and touched the fish. If the medium was truly incompressible (i.e. the speed of sound is infinite), then this would happen instantaneously and there is a decent chance the fish doesn't move since its potential forward velocity would be evenly matched by the oncoming flow.

The question in my mind is whether or not this is the case if you assume it starts from rest and has to accelerate to its steady speed. In that case, it's possible the fish could move before the recirculation fully sets up, but I haven't come to my own mental consensus on this yet.

What if the tank were very large in the incompressible inviscid case?

That's an interesting dilemma as far as I can tell. I am not sure that such a recirculation would necessarily be set up for an arbitrarily sized tank, so perhaps once you reach a certain size, you start instead developing vortices that form just along the back wall and the fish does swim forward. I would guess that this would be the case because certainly as the size of the tank goes to infinity, the fish can swim forward since there is no wall there to cause recirculation. it seems plausible to me, then, that for a sufficiently large tank, the actual physical situation will begin to mimic the infinite case.

 

[DaveC426913]

I am not actually sure what you are talking about, but if the flow is inviscid and incompressible (as I discussed in the statement you quoted), then there would be no such "loss of efficiency". There is no mechanism for dissipation.

I mean efficiency in the fish's movement forward. I might be slightly more difficult for the fish to move in a very small volume of water as opposed to an unbounded volume, but it will certainly be able to move.

The water wouldn't just go to one end of the tank either. After all, it can't go back there and just pile up; it has to go somewhere.

Yes. It fills the space vacated by the fish.

A one "fish-unit" volume of fish moves to one end of the tank, while a one" fish-unit" volume of water moves to the other.

 

[boneh3ad]

I mean efficiency in the fish's movement forward. I might be slightly more difficult for the fish to move in a very small volume of water as opposed to an unbounded volume, but it will certainly be able to move.Yes. It fills the space vacated by the fish.

A one "fish-unit" volume of fish moves to one end of the tank, while a one" fish-unit" volume of water moves to the other.

Except it doesn't. A fish moving doesn't just move the water behind it. It moves all of the water in front of an around it as well, so the actual "vacancy" could just as easily be argued to be out in front of the fish. Of course no such vacancy exists because this is a continuous medium, and since it is incompressible, the effects of water moving in one location are immediately felt at every other location in the fluid.

 

[DaveC426913]

Except it doesn't. A fish moving doesn't just move the water behind it. It moves all of the water in front of an around it as well, so the actual "vacancy" could just as easily be argued to be out in front of the fish.

The vacancy cannot be in front of the fish; it is the fish.

Again: A one "fish-unit" volume of fish moves to one end of the tank, while a one" fish-unit" volume of water moves to the other.

 

[boneh3ad]

The vacancy cannot be in front of the fish; it is the fish.

Again: A one "fish-unit" volume of fish moves to one end of the tank, while a one" fish-unit" volume of water moves to the other.

And that nut of fish move, and water wills in, and then the water behind that fills in, and eventually there's just a wall. So the water above and below along the wall fills that space in. Then the water along the top and bottom fills that space in. Then along the front wall. The the water in front of the fish. Now your vacancy is in front of the fish.

Of course that's not really how it all works, as it must START with the assumption that the fish moves, which is not necessarily true here. It doesn't prove that assumption at all.

Instead, the fish could flap its tail and simply propel water backward, setting up the aforementioned recirculating, and not going anywhere since that thrust would move him exactly as fast as the oncoming water stream.

 

[jbriggs444]

Instead, the fish could flap its tail and simply propel water backward, setting up the aforementioned recirculating, and not going anywhere since that thrust would move him exactly as fast as the oncoming water stream.

Newton's third law still applies, surely. If the water is propelled backward, the fish moves forward. And not just relative to the water.

 

[Chestermiller]

See this reference regarding the relative importance of viscous effects vs inertial effects in fish propulsion:

https://books.google.com/books?id=w...onepage&q=inviscid propulsion of fish&f=false

 

[Chestermiller]

Now that we have dispensed with the issue of viscous vs inertial (see my previous post), we can focus on the main issues for the inviscid case. In my judgment, there are two fluid dynamic features that need to be considered:
1. Maintaining steady movement of the fish after it has propelled itself to a certain (constant) speed
2. Propulsion (acceleration) action of the fish to generate forward thrust

Maintaining steady constant speed movement of the fish has been addressed in my post #22, where the steady inviscid solution for flow past a sphere is presented. This flow will prevail as long as the fish (sphere) is not close to the leading or trailing faces of the tank. It also illustrates DaveC436913's concept of the streamlines separating at the leading edge of the fish (to make room for the fish) and rejoining beyond the trailing edge of the fish. Note also that, for the case of inviscid flow, the drag force on the fish is zero. So, in real life, only a small forward force is required to maintain the speed against the (small) viscous drag.

So, now, the only thing left to address is generation of forward thrust. For this, imagine that the fish is held in place by an externally applied force, but that the fish is doing whatever is necessary to try to paddle forward. The question is "does the circulation flow created by this paddling create a pressure distribution on the surface of the fish (and fins) that results in (a) net forward thrust or (b) total cancellation of forward thrust?" The situation here is different from the passive case where the fish is just moving forward without any thrust. In this case, the fish itself is adding energy to the system by doing work on the water. For a very large tank, it appears to me that the backward flow in close proximity to the fish is very strong, but the return circulation from the front of the fish will be distributed over a much larger cross section of the tank, and the force of that return flow on the fish will be much less. So, I would conclude that positive forward thrust would definitely be achievable.

 

[boneh3ad]

Newton's third law still applies, surely. If the water is propelled backward, the fish moves forward. And not just relative to the water.

That is certainly a good point, and I think it does a fine job of illustrating why I need to get more sleep.