# Trouble applying water pressure analogy to electrical circuits

I am preparing a lesson plan on voltage for a class and it's been a while since I've studied electronics. I like to use analogies to help students understand concepts that are often hard to grasp.

Currently (npi), I am trying to describe how voltage is analogous to water pressure and how resistance is the obstruction of water flow. By partially covering a water hose's opening thereby creating resistance, the output water pressure increases, but the amount of water flowing is the same. The analogy, however, seems to fall apart when you consider that adding a resistor in series decreases the voltage, but the current increases. Moreover, if I connect a Y hose fitting to the water hose, creating a parallel connection, the output water pressure decreases, but in a electrical circuit the voltage is the same.

Is my understanding correct? If so, how can I explain voltage in terms of the analogy?

• Check this out: en.wikipedia.org/wiki/Hydraulic_analogy – Vladimir Cravero Jun 13 '15 at 11:28
• Where you're going wrong is that electric potential (voltage) doesn't spill out of the end of a wire into space like water does. I think for your analogy you should only talk about closed systems. For example, have a pressure source (battery) flowing into a valve (resistor) then through a flow meter. You can then say as you turn the valve there is more restriction (resistance) to the water and so the flow (current) reduces. – Jon Jun 13 '15 at 12:02
• @user148298 What you describe looks more like a current source, not a voltage source. Adding a resistor in series with a current source will increase the voltage drop, but the current will remain the same. – Ruslan Jun 13 '15 at 19:31
• I would always go for a closed circuit analogy: the central heating system is a great analogy! – Sanchises Jun 13 '15 at 20:26

First, analogies can be good for getting the basic concepts, but can only go so far. A common pitfal with the water analogy is that, unlike the air around a hose, the air around a wire is non-conduting. It can also make the requirement for closed loop current hard to grasp later. Someone holding the end of a hose and the water spilling onto the ground is a mental picture you want them NOT to have of electric circuits.

This doesn't mean the water analogy can't be useful. It can, but don't make too big a deal of it. Use it to introduce the concepts of voltage (pressure) and current (flow rate), but don't go too far with it. The details don't match well with electric circuits, so get off the water analogy once the basic concepts have been introduced.

By partially covering a water hose's opening thereby creating resistance, the output water pressure increases

NO! It seems you have yourself fallen into the water analogy too deeply. Analogies are aids in learning, not substitutes for actually knowing something.

There is no simple electric equivalent of a open-ended hose. If the hose were to continue, the pressure after the constriction would be lower than in front of it. Actually with the open-ended hose it is even lower. You can't observe pressure, only flow. You see a jet of water and erroneously assume it has high pressure. It may have high velocity, but that's not pressure.

This is yet another source of confusion from the water analogy. Water velocity (meters/second, for example) doesn't really map to anything useful in electricity. Stick to flow rate (gallons/minute), which maps to electric current flow (Amperes).

One of the big problems with the water analogy is that we intuitively know that water has momentum, even when we aren't aware we are looking at water that way. The jet of water produced by the nozzle relies on momentum. There is nothing analagous in electricity (yes, I know about electron guns, but by the time you understand those, you're way past the initial crutch of the water analogy).

• great: fallen into the water analogy too deeply could not help but imagine a * splash * sound while reading this. – Magic Smoke Jun 14 '15 at 10:25
• So the speed of the water after the point of resistance is faster, but the pressure is lower. As an experiment, if I were to point the hose at a scale. the weight reading would be lower if I squeezed the tip of the hose? I know I am still using the same analogy here. – user148298 Jun 14 '15 at 15:54
• @user: Not necessarily, but now you're measuring impulse, which is yet another quantity that doesn't map to electrical circuits. – Olin Lathrop Jun 14 '15 at 21:34
• Whoever downvoted this, it would be good to know what exactly you think is incorrect, misleading, or badly written. – Olin Lathrop Jun 14 '15 at 21:35

You are constructing the analogy improperly.. Take a tank of water and put a hose at the bottom. The pressure between the end of the hose and the surface of the water (for low flow rates) is just the difference in height between the surface of the water and the location of the hose end (called the head) times the density of the water. When the flow rate goes up, you get an effect that is fooling you: pressure develops at the points where the flow is constricted. So in your first case, with no constriction at the end of the hose, it is the length and diameter of the hose which controls the flow rate. When you put your finger on the end of the hose, two things happen: first, the flow rate is reduced - it does not remain constant. Second. you feel pressure increase at your finger, but this is not the total pressure on the water. Since the flow rate has decreased, there is less pressure drop in the hose.

Try making your analogy a different way. Take a thin-walled tank, and cut a hole in the bottom. Water will run out at a certain flow rate. Now increase the hole size, and the flow rate will increase, but there will be no change in pressure at the hole - it's still just the depth of the tank times the density of the water. It should seem pretty clear that if you double the area of the hole you'll get twice the flow rate (again, for small holes).

This is a good example of one of the pitfalls of reasoning from analogy with everyday experience - some of that experience isn't nearly as simple as it appears at first glance.

By partially covering a water hose's opening thereby creating resistance, the output water pressure increases but the amount of water flowing is the same.

The analogy is imperfect, and You've already complicated it considerably. What you have in mind is this:

The water tank has a constant pressure (voltage) and can in theory supply infinite current into a small resistance. But you have already assumed the hose has a large resistance, which will limit the current.

Further, you have assumed that the amount of resistance you can apply with your finger is small, so small that you are unable to reduce the flow of water. Effectively the combination of tank and hose of large resistance is acting as a constant current source. Replace your finger with a proper valve and you will be able reduce (and ultimately cut off) the water flow. This would be analogous to a potential divider.

For your original intention, which was a current limiting resistor, consider just a large tank of constant pressure, with a small tap connected directly to it. The flow will then depend only on the resistance of the tap.

Unfortunately the water analogy only goes so far, but it still might go far enough for your purposes.

Water pressure from, for example, an elevated tank of water, is Voltage. The thickness of the pipes is resistance. What quantity of water that flows per unit of time is current.

So the higher the tank of water is (greater potential energy due to gravity), the more water flows through the pipe per unit of time, all other things being equal. And the wider the pipe, also the more water flows per unit of time, all other things being equal.

If you put your finger over part of the end of the pipe, you're literally decreasing the diameter, so less water will flow per unit of time. If you add a Y-fitting, half the water will go through each - half the current. Don't be confused by the effect of how far water will spurt out the end of a hose if you squeeze off the end - it might squirt further, but there will still, in fact, be less water flowing out per unit of time, because you've increased the resistance to water flow.

In the parallel situation your interpretation is incorrect. The voltage stays the same in the electrical circuit because it's actually defined to be a constant voltage. That's why it's called a voltage source. You are treating the hydraulic system more like a current source. The true equivalent would be if you had a constant pressure source for the hydraulic system. Something that you can do with a very large tank of water to create pressure at the bottom of the tank. The water flowing out of the hose at the bottom of the tank would result in a very small drop in water level and would nearly the same pressure, even if you use a y-connector.