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Capacitance of a hydraulic capacitor model 1

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cmb042

cmb042

Geotechnical
Apr 28, 2008
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I was trying to explain how a capacitor works to someone who considered themselves a "mechanical". I used the hydraulic model of a hollow metal sphere with a rubber bladder separating it in half and a port connected to each half, both halves filled with water.

Voltage is pressure
Current is water flow
What is capacitance?

Maybe the model breaks down when it comes to capacitance. The best I could come up with at the time was capacitance is the stiffness of the bladder. The more elastic the bladder, the more flow produced to by a specific pressure. But now I think there is a flaw here but I can't quite put my finger on it.

What would charge be in the hydraulic model? Volume of the water? Mass of the water? Should you use a compressible fluid instead of water?
 
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I prefer to think of water pressure as being sort-of like voltage. ;-) Current flow is sometimes more like the reverse flow of bubbles in a water pipe.

You're on the right track. Capacitance is how much charge (litres of water) can be held for a given, or per unit of, voltage (pressure).

 
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Your hydraulic capacitor model is right on track, I've used the same analogy before. The larger the diameter of your sphere, the more capacitance. The elasticity would be more on the line of the voltage rating.
You can demonstrate DC and AC characteristics quite nicely. Draw a big open tank full of water (the ground) then draw a centrifugal pump with the suction in the tank. Draw a discharge pipe with a little turbine in it with the discharge going back into the tank. Draw a handle on the pump and show how as you crank the pump, the turbine will turn.
Now put your hydraulic capacitor in the circuit and show how when you first start cranking the pump, the turbine will turn momentarily but will stop when the bladder finally stretches to its limit.
Now replace the pump with a piston that you can move back and forth with a lever and put another piston where the turbine was and show that as you move the drive piston back and forth, the other piston will also move back and forth even though the water is only sloshing back and forth in the pipe.
You can demonstrate a diode with a check valve. For the pièce de résistance, you can arrange 4 check valves and show how a diode bridge converts pulsating water flow into a continuous (unidirectional) flow.
It's a fun exercise with children and adults that don't understand electrical concepts.
I'm not trying to be pedantic, I'd be quite happy for someone with a good understanding of chemistry to use real world examples to educate me :)

Charlie

Charlie Gill
--
 
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Try hydraulic accumulator.

A closed tank that is filled with fluid to system pressure, as system pressure drops, the accumulator starts to discharge back into system in an attempt to maintain system pressure.

Flow into the accumulator mimics the charge on a Cap, At the start, flow is high. As it fills, and pressure is built, flow decreases until accum. pressure & system pressure equalize.

That discharge pressure drops as fluid follows out of the accumulator, much like a cap does



Ed
 
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I think everone is saying the same thing but it may not be clear. The bladder is a good capacitor analogy but water should be considered incompressible and the fluid on the other side of the bladder should be a compressible gas, as in a hydraulic accumulator.
 
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So what is capacitance then? The area of the rubber layer as Charlie says doesn't make sense to me. Regardless of the bladder size, wouldn't a given pressure displace the same amount of water?

I tried to demonstrate the model using a circuit in the lab. A driver outputted 10V sq pulses through a coupling capacitor that had 80V DC on the other side. The pulse goes through, but then goes negative at the falling edge before asymptotically returning to zero. Increasing the capacitance reduced the how far negative the trailing edge went. I explained this as the bladder being stiffer having more capacitance so 10V of pressure pushed out less current, so it took less to return to 80V. After wards I thought, that is not right, more capacitance should produce more current.
 
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Capicitance (electrical) is the amount of charge (i.e. number of charge carriers) that can be stored/discharged per unit voltage.

So, the fluid equivalent of capacitance would be the volume displaced per unit pressure.

To be a linear "fluid capacitor", the hydraulic accumulator would either be isothermal, or perhaps not use gas pressure, but a piston acted on by a linear spring.
 
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I think a better hydraulic analogue would be a U-tube manometer half-filled with mercury.

Provided you don't pressurise it to the point where all the mercury ends up in one limb, you get an increasing hydrostatic head as you pump more and more water into it.

The analogy to capacitance would be the cross-section of this reservoir tube.

A.
 
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Electricity as a compressible fluid and capacitors as simple containers is a cleaner analogy.

It also works better when the maximum pressure (voltage) is exceeded - instead of running into a piston or bladder limit (not realistic), it is at ever increasing risk of exploding (very realistic).

And it lays the mental foundation for the stray capacitance of normal conductors.

 
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"So to increase the capacitance one would reduce the spring constant of your piston accumulator?"

Umm...yeah.

"Electricity as a compressible fluid and capacitors as simple containers is a cleaner analogy"

Except that compressible fluids behave non-linearly, e.g. P~V^k. Then again, all fluids have flow ~ dp^2, so the analogy quickly falls apart (when compared to linear circuit theory) anyway.

But, to each their own. The analogy should only be taken so far, I think we could all agree.

"And it lays the mental foundation for the stray capacitance of normal conductors."

Err...well...that's a stretch. Stray capacitance in conductors is a function of their spacing to adjacent conductors of differing voltages. Stray capacitance in compressible fluid-conveying tubes is a function of their size alone. Back to my 2nd para above - the analogies only hold so far, and then...somebody's gonna lose an eye. ;)
 
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I never did understand hydraulics... ;-)


"...analogies only hold so far..."

Have you ever heard the expression, "It's turtles all the way down"?

Well, I hate to break it to you: It's analogies all the way down.
 
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Unit capacitance, measured in Farad, is the measure of the charge that can be held at 1 volt (C=Q/V). This can also be read as the measure of the charge needed to create 1 volt of pressure.

Therefore, hydraulic equivalent of capacitance would be the amount of water needed to develop a unit pressure or the amount of water that can be held at one unit of pressure.

The two spheres with rubber membrane analogy comes close to explaining a capacitor in a DC circuit, but presents difficulty in explaining propagation of ac current, which is a bit different than DC. A capacitor behaves differently when applied AC voltage vs. DC voltage. In fact they have opposite effects. A capacitor is seen as a short circuit by a AC voltage source, while it is open circuit to a DC voltage source. So you would need two different models for each.

Also AC electrical current is a electromagnetic wave and cannot be entirely explained using a particle model.

I would think, the capacitor in an AC circuit is more akin to a holding tank (expansion tank or a balloon) in a hydraulic circuit. (I won't mind this being corrected).






Rafiq Bulsara
 
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I think it works fine for AC. It blocks steady state pressures, and the flow out is derivative of the pressure. If you increase and decrease the pressure in cycles like AC, it passes through the hydraulic model.

You can even say take a wave pool, take a section cut of it, and place the hydraulic model underneath it with one inlet at a gap in the floor of the pool and the other into the ocean or the water table or whatever you want to make ground. As a wave passes over the gap in the floor the pressure increases and stretches the bladder lowering the height of the wave. Then as the wave passes the bladder returns to its original position more slowly, spreading out the wave. Attenuation, RC filter.
 
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