I have an issue with momentum propagation in fluids. Say you have a syringe in a tank of water, located on a frictionless plane/in outer space. The syringe is filled with water, just like the rest of the tank, but the water in the syringe is dyed. The syringe is mounted to the side of the tank. For the purpose of the scenario the dye does not change the density of water in the syringe to be higher than water outside. You plunge the syringe, releasing its contents as a stream. This action creates a recoil, pushing the syringe/tank in one direction. The dyed water travels in the opposite direction, carrying momentum. I have considered this scenario, and it shows my lack of understanding of fluid dynamics. How is momentum carried through water? It is not displacement of water ie, momentum will be carried at a rate different than the plume of dyed water. Since the tank is full (ie no air pockets) displacement of water would carry no net momentum in the tank. This is simply p=mv If you have a volume of water travelling in the x direction, it will displace an equal volume of water in the tank (since we are dealing with an incompressible fluid), hence an equal volume of water will be travelling in the -x direction. No net momentum is carried. So then, how is momentum carried? I think the only option is that it propagates as a wave of stationary water molecules vibrating back and forth. But this still leaves some unanswered questions- As this wave propagates through the incompressible fluid, the fluid's center of mass is not shifting (afaik). At the end of this exchange you will still only have a tank of water ie no change in center of mass.. So it is different than throwing a ball on a space ship.
The dyed water travels in the same direction as the push on the syringe/tank. The recoil force is on the finger that pushes the syringe. You first need a good grasp of solid dynamics. I think you're biting off way more than you can chew in this scenario. It's certainly more than I can chew, at least.
In Engg no object is frictionless. You are refering to a "submerged jet". The energy is transfered by a jet via mass transport or convection current. A submerged starts diffusining immidiately and its cross section goes on increasing till all its kinetic energy is lost.
I have modified the scenario below so it is simpler. I never fully understood the value of a solid foundation. Please Register or Log in to view the hidden image! Right, a flowing fluid will also encounter friction which will decrease the kinetic energy of the jet. Convection cannot transfer momentum because it is transferred in loops. Its like taking a barrel full of water and swirling it. The momentum in the x direction will be equal to the momentum in the -x direction. Also, I don't think all of its kinetic energy is lost, or it would be unable to carry any momentum, right? A submerged jet describes the scenario very well. Its more interesting if we change the scenario to a submarine in a tank of fluid in outer space. The submarine propels itself using submerged jets. The submarine is made of specialized materials so that each part is exactly the same density as the fluid. IE the submarine can move around freely inside of the tank without changing the center of mass of this system. Think about how waves and currents will behave in such a tank due to the submarine's movement. -the center of mass of this tank never changes -all the currents/waves must cancel themselves out if momentum is conserved. Technically, the submarine doesn't have to create any waves/currents since it is of the same density as the water and so momentum is conserved no matter what it's velocity is (referring back to the fact that water is displaced in the direction opposite of motion). But, this quickly becomes a problem when the submarine starts to push against a wall in this tank. In this situation the tank will immediately feel a force in the x direction, while the jet will transfer force in the -x direction only at the speed at which the wave/current travels. What prevents the tank from accelerating ??
Ok, maybe the submarine is confusing. Say you have a slingshot inside of the tank, whose projectile is the same density as the fluid. You fire this projectile, feeling a recoil, which is transferred to the tank since you are propping yourself against it. The projectile experiences friction, and stops moving before reaching the opposite wall. At this point, what is carrying it's momentum?
This is the final iteration of my quandary- In this metal tank, in outer space, you have a compressed spring. At each end of this spring you have a projectile which is the same density as the fluid in the tank. After this spring expands, each projectile has the same speed but opposite directions. Each has momentum, but there is no net momentum. Lets say these projectiles travel 20 cm before coming to a complete halt due to friction. Now, say our tank is 3 meters long in the direction parallel to the motion of our projectiles. The spring starts 50 cm from one end. Thus, one projectile stops 30 cm from its 'target' wall. The other stops 230 cm from its 'target' wall. As these two projectiles come to a halt, their momentum is transferred to the fluid, creating a shock wave. It is completely logical that both shock waves travel at the same velocity, given that they are produced by identical projectiles which are accelerated equally. Naturally, the closer wall will come in contact with its shock wave first. This is the only reason the tank would feel a force due to the spring. So, it experiences a force first in this direction. Only after the equal and opposite shock wave reaches the other side of the wall will an equal and opposite force be felt. If this tank experiences first a force in one direction, then a force in the other direction, shouldn't its center of mass shift? Its like putting a force on a car, first in one direction, then an equal and opposite force in the other direction. The car, in the end, will carry no momentum, but it will shift its center of mass. Something I'm still thinking about is the compressibility of the fluid.
No, as there's no external force acting on it. It's no different to an astronaut using a little jet to push himself about, he moves his centre of mass about but only because he's also moving the centre of mass of the gas exhaust in the opposite direction, overall the system is unchanged. Your example can be simplified by just considering three balls connected via two springs of different strength (so it goes O----O----O), ie different spring constants, hanging in space. If you held the two ends and someone then pushed the central one to the side (so you get O-------O--O) and then both of you let go at the same time you'll see the system judder about, both the ends moving back and fore and at a casual glance it might seem like its moving but its only moving about its centre of mass, the centre of mass's motion is unchanged. The shock waves in your example are now just compressions and extensions in the springs, which are much easier to understand and model. Compressibility has nothing to do with it, it doesn't change the law of conservation of momentum, it just makes the motion of the projectiles more complicated. Have you decided to move from complaining about how you don't understand momentum in electrodynamics to now complaining about how you don't understand momentum in fluid mechanics? Rather than biting off more than you can chew by going to areas of physics which are extremely complicated (especially if you can't do any vector calculus) why not start at the basics and work your way up to the complicated stuff? Or do you plan to be perpetually wasting your own time by skipping the basics and then finding you don't understand anything?
No, I am not done with electrodynamics, but I don't plan to get bogged down with just one idea when I could get bogged down with a dozen. Please Register or Log in to view the hidden image! Thats right, you will release the balls and the springs will exert forces and so the masses will start jittering. Your example is convincing at first, but it is not analogous to mine. It would be more accurate if there were no masses, just massive springs because its the water which is both the gyrator and the massive object. The main difference is that in my example there is no difference in densities (assuming no compressibility). For our purpose the metal tank can be the same density as the fluid, the projectiles and the spring. Due to this there cannot be any jittering at all. The object must remain completely stationary ie it will appear as if nothing has happened inside. But, you will agree that the shockwaves carry momentum (the two projectiles did, so if momentum is conserved there is a momentum carrier present in the liquid), and you will also agree that one shockwave strikes its opposing wall before the equal and opposite shockwave strikes its opposing wall (they are both created by an equal and opposite force so they propagate at the same speed). Yet, there cannot be any jittering at all. I just don't see it happening. Do the shockwaves just bounce off the walls, and then cancel when they meet again? If so, why on earth (or space) do they not transfer momentum to their walls at the same time they bounce? Imagine now that instead of a liquid filled tank it is a mirror tank, filled with vacuum and with perfect mirrors at opposite sides. Now you create a burst of two photons perpendicular to these mirrors (travelling in opposite directions with equal momentum), they will bounce around for all of infinity. If this burst of light is initiated closer to one mirror than the other, then the mirror tank will jitter around. Still, the center of mass remains the same because the photons do have some mass and they can counter the external jittering of the tank by altering its internal mass composition. This is not possible in the case of the metal tank filled with fluid, because that tank has a uniform density. Its because of this that I think compressibility is actually an important issue.
The centre of mass of the tank itself (ie not including the fluid) will shift. But, the centre of mass of the fluid will shift as well - the shock wave is a region of higher density. The net result is that the centre of mass of the tank+fluid doesn't shift. The compressibility of the fluid is directly related to the speed of the shock wave. In a hypothetical perfectly incompressible fluid there will be no shock wave - any force will be transferred through the fluid instantly, just like a through a rigid rod.
Submerged jet sets up convection currents in its the fluid in its vicinity and its energy is shedded that way. In addition, velocity across the cross section is never the same, ranging from highest at center and lowest at the outer surface. So it loses energy by friction within itself. Most spectular jets are due to volcanic erruptions. A high speed issues and diffuses, creating a mushroom cloud. Energy of gases at the point of issuance is high, but that of the cloud is nearly dissipated. Car esxhausts, jet engine exhaust etc are other example.
Thats right, when a shockwave (its actually called a compression wave) travels through any medium its center of mass changes, moving in the same direction as the wave. Please Register or Log in to view the hidden image!
Actually the masses are useful to include because they can be viewed as playing the role of the tank, which is something you forget in your next part : In a perfectly incompressible system with a tank which is perfectly rigid then you'd not have been able to inject the syringe anyway because you can't add to the already filled tank. If the tank is open at the top (whatever that means in the depths of space...) then you are just adding material to the tank and you add its momentum. When the wave front (a shock wave is something different to do with large changes in pressure or density or some other quantity) hits the tank wall and is reflected it imparts momentum into the tank wall. The momentum carried as waves in the wall, rather than the water, which then spread back through the tank walls until the wave from each side reaches one another and mixes. Momentum is conserved, its now both in the water and in the tank, including the tank walls. If you make the simplification 'the walls are perfectly rigid' then you make an unphysical restriction as perfectly rigid things have infinite wave propagation speeds and you have to be careful how you account for things to be consistent. The denser something is usually the faster the wave speed. The speed of sound in air is about 330m/s (at sea level and normal temperatures). In water its something like 2000m/s. In steel its more than 5000m/s! (there abouts, its been a long time since I read that statistic but the orders of magnitude are about right). Do the shockwaves just bounce off the walls, and then cancel when they meet again? If so, why on earth (or space) do they not transfer momentum to their walls at the same time they bounce? The photons in an empty tank and the bullets in a tank of water will behave in the same qualitative way, although the tank of water will judder in a more complex manner because the momentum spreads out throughout the medium rather than being carried by just two small objects in the vacuum case. Spreading out doesn't mean it goes away.
The idea is that the syringe of water is already in the tank - plunging it does not change the volume of the system. In a perfectly incompressible system momentum will be transferred instantaneously to the walls. A possibly interesting theoretical question is - how on earth is momentum carried in a perfectly incompressible fluid? I think it is impossible due to convection currents. From what I have considered the momentum in the walls will also have to be carried by compression waves, much like in the fluid. Except in the wall the waves are a result of covalent bonds while in the fluid its a kinetic interaction of molecules. ... are you saying someone has already made a set of rules for perfectly rigid systems?? Its not impossible to consider this system without the tank, just a blob of water in space. Lets pretend it doesn't boil ... at any rate, it becomes even more complicated because the blob will judder around and its impossible to imagine how without using a computer simulation. Please Register or Log in to view the hidden image! Yes. I am satisfied ... for now. Please Register or Log in to view the hidden image!
An incompressible fluid can still flow, it can still carry momentum. Making the assumption of incompressibility is a common thing in fluid mechanics because it vastly simplifies the Navier-Stokes equations. By assuming \(\nabla \cdot \mathbf{u} = 0\) you can simplify the continuity equation. It just means the amount of material leaving a region must be exactly balanced by the amount entering. How the material's constituents communicate is largely irrelevant unless you're considering extremely small scale fluids like capillaries. A perfectly rigid object is in contradiction with special relativity as it would allow you to communicate faster than light. Light speed limits the speed a physical disturbance can move so any hypothetical material with a speed of sound higher than the speed of light in a vacuum is physically impossible (assuming relativity of course). You can determine how a perfectly rigid body would behave by considering a deformable body and then changing the relevant parameters in such a way as to reduce its deformability to zero. For instance the wave equation is \(\frac{1}{v^{2}}\partial_{t}^{2}f = \Delta f\) (\(\Delta\) is the Laplacian). The v is the speed of 'sound' in the system and if you consider \(v \to \infty\) you remove time dependency as the left hand side is made zero so you go from a wave-like system to an harmonic one, \(\Delta f = 0\) (there can still be time dependency but its decoupled from the spatial). Speak for yourself.
I WILL BE GOD DAMNED submitted october 24th (four days ago) . . . and no its not my video Please Register or Log in to view the hidden image!
There are no dates on this guys' website .. and the vid was uploaded four days ago. Methinks plagiarism. :geek: UPDATE: Elliot has a video up on youtube from summer 2008 - so he came up with the idea first.. i still like the idea Please Register or Log in to view the hidden image!
I still can't see how momentum travels in the fluid. Compression could theoretically account for change of the fluid's center of mass. BUT, fluids are generally incompressible! You just couldn't get the required compression with such a small amount of energy. http://en.wikipedia.org/wiki/Properties_of_water#Compressibility it is a very low compressibility! I don't know how to set up the math, but I hypothesize that one could easily make a scenario which shows that water simply cannot compress so much reacting to my hypothetical submarine. And if compressibility isn't the issue, then there cannot be a change in center of mass! As momentum travels through a fluid, it's center of mass does not change significantly.
I watched the video. My first thought, of course, is going to be with the conservation of momentum; the fact that the demonstration works is due to the static friction of the wheels beneath the entire assembly. If you've ever "scooted a rolling chair" without touching the ground you'll know what I mean. IOW, put this "ram mass engine" in frictionless space and it will do nothing.
Yes, that seems to be an issue. It would be a lot more convincing if the fan was attached directly to the inside of the chamber. Theoretically that should work as well. Still, it doesn't help resolve my fluid momentum problem.. :-S Water is practically incompressible. Check Momentum can't travel faster than light. Check So during the time momentum propagates inside the tank, the momentum is 'hidden'.
