Fluids class
I learn about as much in Fluids class as a crackhead learns from smoking crack.
There's gonna be a test next time, you got me if we've actually done anything that he could test us on.
Today, I was contemplating the similarities between electrical circuits and hydrostatic fluid systems.
Assuming the fluid is inviscid, and there is no friction, what measure in fluids is analogous to Voltage? Current? Resistance? Capacitance? Inductance?
Can you make systems in fluids which are analogous to things like, say, a battery? A transistor? A diode?
If I had to name something that related to voltage, it would have to be pressure.
As for current, I think I'd go with volumetric flow. And resistance would have to be something like inverse cross-sectional area, or something. Gotta love constants!
Let's say you have an arbitrarily small pipe. If you apply constant pressure at one end of the pipe, then the water will flow out of the other side at a constant rate by volume. Simple. Now, increase the size of the pipe. If the same pressure is applied at the end of the pipe, there will be a larger amount of water coming out of the other end. And, neglecting fudge factors, this volume per unit time of water will vary proportionally with the size of the pipe. Thus, as you decrease resistance due to pipe size (~the inverse of cross-sectional area), you increase the volume of water coming through the pipe for given pressure.
If you have the small pipe, and increase the pressure at the end, more water will come out of the other end of the pipe. Flow rate is proportional to pressure.
V=IR
Pressure=(constant)(flow rate)(1/cross-sectional area)
To make a "Battery," you want something that can store fluid energy in such a way that a constant pressure will come out. However, some kinds of batteries discharge differently. If you've got a lead-acid battery like a car battery it's mostly going to lose voltage as it discharges. So, it can be modeled by a cylinder with a spigot at the bottom. Depending how tall the column of water, the pressure at the spigot will be either low or high. Depending on the diameter of the cylinder, the "Battery" will either last a long time or not so long. As water drains out, the pressure will decrease linearly because the container is a cylinder. In any case, the volume of water in the column corresponds to the current rating on the battery and the height corresponds to the voltage.
If you're trying to model a lithium-ion battery, it gets a little more complicated. I showed my idea above in a simplified manner. Since the voltages of these kinds of batteries are meant to stay relatively constant as the battery discharges, the top of the column must be much larger than the bottom. This way, the water draining out at the spigot will not affect the height of the column as much at first. Of course, once the column starts getting closer to the bottom, it will drain much faster and correspond to a rapid voltage drop. The cone-shape may not actually be an accurate model of the battery, but a more accurate shape can be derived by bench-testing the battery, watching the voltage as the battery discharges at a constant current. Sudden drops equate to sudden decreases in column diameter... well, that may be a little off but fairly close.
As far as other components? Well... the diode is easy.. just get a check valve. Once you have a certain threshold pressure going the wrong way in the check valve, no flow will be allowed.
Transistor? Hmm.. I'd have to think about that for a little while. Something that can allow large flow in response to a small pressure....
What else... capacitors and inductors. Hmmm. A "capacitor" would need to be able to provide relatively instantaneous flow, at a relatively infinite flow rate. Also, it would have to block flow in one configuration (series) and allow it in another. Essentially, it must resist a change in pressure. If you start with a pressurized pipe, which has a certain flow rate, you could simulate a parallel capacitance by feeding the pipe through a large reservior. The reservior would fill up as water flowed through it, to the point where the pressure head in the reservoir was equal to the applied pressure. If the applied pressure was removed flow would continue but pressure would drop off as the reservior emptied. Bam. But that idea doesn't quite work with parallel.
Inductors? Any ideas? I am done rambling now so maybe I'll think on it.
There's gonna be a test next time, you got me if we've actually done anything that he could test us on.
Today, I was contemplating the similarities between electrical circuits and hydrostatic fluid systems.
Assuming the fluid is inviscid, and there is no friction, what measure in fluids is analogous to Voltage? Current? Resistance? Capacitance? Inductance?
Can you make systems in fluids which are analogous to things like, say, a battery? A transistor? A diode?
If I had to name something that related to voltage, it would have to be pressure.
As for current, I think I'd go with volumetric flow. And resistance would have to be something like inverse cross-sectional area, or something. Gotta love constants!
Let's say you have an arbitrarily small pipe. If you apply constant pressure at one end of the pipe, then the water will flow out of the other side at a constant rate by volume. Simple. Now, increase the size of the pipe. If the same pressure is applied at the end of the pipe, there will be a larger amount of water coming out of the other end. And, neglecting fudge factors, this volume per unit time of water will vary proportionally with the size of the pipe. Thus, as you decrease resistance due to pipe size (~the inverse of cross-sectional area), you increase the volume of water coming through the pipe for given pressure.
If you have the small pipe, and increase the pressure at the end, more water will come out of the other end of the pipe. Flow rate is proportional to pressure.
V=IR
Pressure=(constant)(flow rate)(1/cross-sectional area)
To make a "Battery," you want something that can store fluid energy in such a way that a constant pressure will come out. However, some kinds of batteries discharge differently. If you've got a lead-acid battery like a car battery it's mostly going to lose voltage as it discharges. So, it can be modeled by a cylinder with a spigot at the bottom. Depending how tall the column of water, the pressure at the spigot will be either low or high. Depending on the diameter of the cylinder, the "Battery" will either last a long time or not so long. As water drains out, the pressure will decrease linearly because the container is a cylinder. In any case, the volume of water in the column corresponds to the current rating on the battery and the height corresponds to the voltage.
If you're trying to model a lithium-ion battery, it gets a little more complicated. I showed my idea above in a simplified manner. Since the voltages of these kinds of batteries are meant to stay relatively constant as the battery discharges, the top of the column must be much larger than the bottom. This way, the water draining out at the spigot will not affect the height of the column as much at first. Of course, once the column starts getting closer to the bottom, it will drain much faster and correspond to a rapid voltage drop. The cone-shape may not actually be an accurate model of the battery, but a more accurate shape can be derived by bench-testing the battery, watching the voltage as the battery discharges at a constant current. Sudden drops equate to sudden decreases in column diameter... well, that may be a little off but fairly close.
As far as other components? Well... the diode is easy.. just get a check valve. Once you have a certain threshold pressure going the wrong way in the check valve, no flow will be allowed.
Transistor? Hmm.. I'd have to think about that for a little while. Something that can allow large flow in response to a small pressure....
What else... capacitors and inductors. Hmmm. A "capacitor" would need to be able to provide relatively instantaneous flow, at a relatively infinite flow rate. Also, it would have to block flow in one configuration (series) and allow it in another. Essentially, it must resist a change in pressure. If you start with a pressurized pipe, which has a certain flow rate, you could simulate a parallel capacitance by feeding the pipe through a large reservior. The reservior would fill up as water flowed through it, to the point where the pressure head in the reservoir was equal to the applied pressure. If the applied pressure was removed flow would continue but pressure would drop off as the reservior emptied. Bam. But that idea doesn't quite work with parallel.
Inductors? Any ideas? I am done rambling now so maybe I'll think on it.
posted by james at 5/26/2005 07:19:00 PM
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4 Comments:
An inductor could be something like a passive pump with a flywheel similar to a turbocharger. As fluid flows through it, the pump speeds up to match the speed of the flow.. if you cut pressure the fluid will flow for a second afterwards as the flywheel spins down.. resisting the change in flow rate.
Your average hydrostatic drive on a Bobcat, Dozer, Excavator, etc behaves essentially just like a variable-speed electric motor. I'm not sure how they meter the pressure, it'd be funny if it was like PWM. But if you try to juice it too much and the Engine can't source the pressure you'll stall your shit out, just like if you try to run a motor too hard it'll fry your battery!
Like when I tried to jump the diesel mercedes with one of those "battery buddy" jump packs. There goes the magic smoke!
To clarify, the specific property I'm thinking of that makes the two similar is the fact the max torque is achieved at 1 RPM
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