Invent an oscillating water circuit?

Question

Much has been said about the mathematical analogies between certain mechanical and electrical systems. See the following for example:

http://www.swarthmore.edu/NatSci/echeeve1/Ref/Analogs/ElectricalMechanicalAnalogs.html

"LCR" circuits lead to differential equations that result in oscillatory behavior---the three essential components in electric circuilts being the inductor (L), capacitor (C), and resistor (R). They have their mechanica analogues.

Water flow dynamics share some analogies as well with such mechanical and electrical circuits, such as resistance through a pipe or constriction. Given a high tank of water and a lower place for water to drain to, can a "water circuit" be devised, involving no moving mechanical parts, that can result in oscillatory behavior, per the same kind of differential equations? Would it be possible to make a school science project to induce water, in flowing from a high to a low place, to oscillate?

Answer 1

A very incomplete answer: an oscillating circuit requires both a capacitor and an inductance. If water pressure is the analogue of electrical potential, then an open upward-pointing tube would be analogous to a capacitor.  I don't know what would be analogous to an inductance, and hope someone can tell you.

Answer 2

This requires more thought.  Quick answer:

Obviously, as previously stated, it is easy to make a capacitor.

Water in piping is both an inductor and a resistor.  It is the momentum in water that acts as an inductor.

It is easy to add more resistance to a water system.  Have to think about how to add more inductance.

Note: One of your problems in circuit design is that resistance varies with v^2 so you will have problems with the differential equations.  I.e., frequency may be dependent on flow rate.

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Battery:  Use a venturi meter or pitot tube for power.  Just get the difference between static head and dynamic head to power the system.

Inductor:  Piping in general.  But here you are looking for momentum.  Best way to do this is a big fat piece of pipe.  But in general, it is just the amount of fluid in the system.

Capacitor:  Just one of those open ended piping tube things where the level can vary.  Again, the bigger the pipe, the more capacitance.

Resistor:   The piping in general, but you could put it a throttling globe valve.

[Sorry, got waylaid thinking about one of Alex's insolvables ;-).

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Ok,

Capacitance =  A *ρ g h = Ch

velocity = Volume system/ average cross sectional area

Indunctance:

I = L  ÃÂ dv/dt  (This is conservation of momentum.)

Resistance =  R v²

Pressure =  Voltage = Static - Dynamic head

..............

Forget resistance for a moment:

L  ÃÂ dv/dt  + C h = Constant

L' d²h/dt²  + C h = C

Note L ∝ L'

This is the equation for simple harmonic motion

Now the R is screwy because you will have both dynamic head and dyanamic head loss both of which relate to v².  The overall equation will be:

L' d²h/dt²  + R (dh/dt)²  + C h

I'd just run a pipe from the static end of a flow meter through a fat pipe (inductor)  attach to a standpipe going up  (capacitator) followed by a flow restrictrive devise (Resistor) such as a throttle valve, or better yet simply a smooth constriction which widens out afterwards so there is minimal loss of head.  Finally run it back to the dyanamic end of the flow meter.

Answer 3

The tides of Earth ;)

Answer 4

This happens with some taps. Have you ever noticed when turning the water at a certain flow rate, usually slow, that there is a loud squealing noise? It sounds a bit like electronic feed-back. Changing the flow rate usually stops the noise.

I don't know what causes it. There could be some air in the line to store potential energy, and the momentum of the water is the inertia.

For a school project attach a vertical pipe in a "T" to a horizontal pipe where the main flow occurs. If the flow is just right it could cause an oscillation in the vertical pipe a bit like blowing across a flute. But blowing across a flute doesn't always cause an oscillation. You would have to just the flow, and angle, and opening.

A much simpler way to produce a water oscillator is to put some water in a U-tube and give it a bump, or put some water in a bowl and shake it.

But you want it to be powered by flowing water. I think a U-tube with an opening at the bottom sealed to the pipe with the flowing water should work reliably.

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I don't get your reference to a time machine. I'll look at the differential equations and get back to you.