# What corresponds to a resistor in the hydraulic analogy to current?

In the hydraulic analogy to electrical current, pressure is voltage, water moving is the current, but what is a resistor? I've heard that a resistor corresponds to a constriction in the pipe, but a series of constrictions is not additive like a series of resistors, right? Can anyone give or cite a better example of the hydraulic analog to a resistor?

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This comes up all the time when you teach physiology to engineers, and reduce the cardiovascular system to an electrical model! – Scott Seidman Apr 23 '14 at 23:54
It's all about looking at the differential equations, and shifting things around until you see the analogues. This also holds for mechanical systems, thermal systems, etc. (and shows why every engineer should understand the relationships between Laplace Xforms and diff eqs!) – Scott Seidman Apr 24 '14 at 0:17

In basic physics concepts, which relate to fluid movement, the cross-sectional area of the pipe/medium/whatever the fluid flows through determines the flow rate, for the given pressure.

As you say, if pressure is "voltage", and velocity of water is "current" (or the movement of electron charge in electricity, Coulombs per second), then indeed the restriction of the current is given by the "pipe" that it moves through. More pressure (voltage) will induce more water movement (current) through the given aperture's cross sectional area (effectively resistance).

edit: I should mention that pressure drops along the length of pipes, and that if the pipe is not 'full' of water, then it's quite more complicated to work out the area of water moving through it. The velocity of water and the "flow rate" are also a little bit different, you should try to find a few simple equations for whatever application you are doing. There are some online calculators you can use, in most cases.

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You could apply the same input pressure to a pipe system full of water, and have varying sized "collars" along the system which would create different flow rates along the system - but obviously the final complete input/output must be equal, just like Ohm's/Kirchoff's laws in an electrical system. Can't get water/energy out of nowhere! – KyranF Apr 23 '14 at 23:24
I'd specifically like to see you address my claim that two constrictions (e.g., of equal diameter) in series in a pipe do not produce a greater total "resistance" than a single one. Another example: Let's say an interstate goes from three lanes to one, then widens back to three lanes, then goes back to one lane. Those two constrictions do not slow down traffic anymore than a single one would. – BlueBomber Apr 23 '14 at 23:34
inside the system (be it road, or pipe) the input/output flow rate must be equal (conservation of energy, mass, water, etc). The velocity at each section though, created by barriers or adjustments as you say, can be different. They cannot be so wildly different that the laws of conservation are broken though. For example a road system analogy doesnt work in terms of water, because the 1 lane section would make cars go 100 miles per hour, but when they get to the 3 lane area they would all drop down to ~ 33 miles per hour. Does that make sense?? @BlueBomber – KyranF Apr 23 '14 at 23:37
@BlueBomber -- yes, the two constrictions do cause more resistance than a single one. – Scott Seidman Apr 23 '14 at 23:53
The total input/output flow rate will be negatively affected by ANY resistance in the path of the fluid, and of course the resistant of the pipe itself (the wall/friction resistance) which is why Length can also be a major factor in pressure loss – KyranF Apr 23 '14 at 23:55

Water analogies are always fun. I've always considered a resistor like a big, porous sponge obstructing the pipe :)

One place the use of water analogies breaks down is that there is no variable "speed" of current flow. If you are talking about energy transfer, then the velocity is simply the speed of light (in whatever medium you're using). If, instead, you are talking about electron movement, it's so slow that it becomes insignificant. The actual electron drift in a 1-mm thick copper conductor is on the order of one millimeter per second!

The other place it breaks down is that there is no inertia of current. You can add inductance, however, to bring about a similar effect.

There's an excellent example of this analog. Check out this Youtube of a Ram Pump. It's a neat, old technology that many people have never seen. It turns out that it's exactly the same as a boost converter! You use a diode instead of a one-way valve, a capacitor instead of the pressure tank, a MOSFET instead of the oscillating valve, and add inductance to make the inertia work out.

Have fun :)

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