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