Recently I noticed someone filling a kettle for tea by running the both hot and cold taps full open. That generated a lot of questions in my mind. Not that I asked him any of them, it's much more fun to speculate online. My final conclusion was that perhaps he thought he was saving time. If so he probably hadn't even thought about it. It may be that this is another case where our instinctive behaviour is wrong, or at least misses the complexity of a problem. However, to first settle the matter for myself I recorded the video shown below. Watch for yourself and see that whether I run hot only, cold only, or hot and cold together, it takes pretty close to 21 seconds to fill the bowl.
Hot Water in Your Tea, So What?
Ok, let's back up a bit before explaining the video. Most tea drinkers that I've ever heard mention taps are emphatic that they want NO water from the hot water tap in their kettle. In fact, I had approximately this conversation at work a few years ago (I don't claim to remember the exact words, but this genrally gives the idea):
Me: why are you dumping the kettle? I just filled and boiled it.
Tea Drinker: Did you user cold water? Some people put water in from the hot tap.
Me: Yes, I used cold water.
Tea Drinker: did you dump out any water that was in the kettle first, in case some of it was from the hot water tap?
Tea Drinker: Did you run the cold water a few seconds to get any hot water out of the pipe?
Tea Drinker: That's why.
So in case you're not a tea drinker, or not one of those tea drinkers, here's the deal: tea generally has a mildish flavor, hence tea drinkers are more likely than coffee drinkers to notice the taste of water from the hot tap. It is also just plain not advised to drink or cook with water from the hot tap due to all extra stuff in it. With a quick Google search you can pull up lots of pages explaining why. The biggest reason cited is the lead content of water from the hot tap. For example, here is a NY Times article. Similarly, here is a page from the EPA on the same topic. In general other stuff also gets in, and I think it is those that most affect the flavor.
Back to the Tap Question
The above section shows why it stands out to me anytime I see someone fill a kettle from the hot tap. There are people who either don't know or don't care. I expect using the hot tap to save time getting the kettle to boil.
So why would anyone use a mixture of hot and cold? All I can come up with is to save time filling the kettle. If you think about it one way, it makes perfect sense. For my video, if the cold half fills the bowl in 10 seconds and the hot half fills the bowl in 10 seconds, then by running both at the same time shouldn't I expect the whole bowl to fill in 10 seconds rather than 20?
That is one way to think about it, and there are cases where it is the correct way. For example, if the hot and cold taps led to different spouts then the flow would be largely independent. So yes, the time should be approximately halved - other than whatever overall lowering of the pressure might occur by having both taps on. What is more correct for the tap in the video is to realize that a hot water and cold water pipe meet then the water from both goes though a pipe of the same diameter up to the spout. So, the flow through the third pipe is determined by the water pressure where the hot and cold meet. Now if both are wide open providing the maximum pressure they can at that point, and that pressure is the same (as seen by the equal filling times individually) then that pressure is not affected by whether one or the other or both taps are open. If the pipe after the joining point was larger than the other two then it would be more similar to the two tap case, and the flow could be higher with both on.
In Physics we have several situations that get described in similar terms: pressure or potential difference across a resistance of some kind leading to flow of something:
Fluids: Pressure differences cause water or other fluids to flow. This is the one case we can readily watch and learn from directly. It provides the basic vocabulary, refering to the flow as "current".
Electric Circuits: Pressure differences across a resistance causes electrons (or "holes" in another way of looking at it) to flow.
Thermal: Temperature differences causes thermal energy to flow ("heat").
Understanding any of these gives insight into the others. However, one may have to work a bit to get the analogous aspects correct. In Physics classes we talk about this in the most detail for electric circuits. In a quick attempt to compare flow to an electric circuit one might have thought that the taps behave like "Voltage" sources and thus opening the tap wider is increasing the "voltage". Below I show the first two obvious electric circuits to try to fit to the water tap system using this idea. On the left, a parallel connection, on the right a series connection.
Parallel: The appeal to this connection is that if you pull apart the piping and look at it, the hot and cold water taps are clearly connected to each other this way. However, this simple analogy has at least one glaring flaw, in this electric circuit the hot and cold voltages would be forced to be equal, they could not be varied independently.
Series: This allows independent hot and cold voltage, but doesn't produce distinct hot and cold current contributions.
To resolve the problem we need to realize that thinking about the taps as potential is wrong, rather it is better to think of them as variable resistances which are being fed from a common voltage. That is, the water supply provides a constant pressure at the wall where it enters. The pipes have some internal resistance to the flow, so if all taps were wide open the current would not be infinite, it would be some maximum of "I=V/Rinternal". The pipes splits into two contributions - one straight to the tap, one going through the hot water heater. Then there are two distinct water current, one heated and one not. The taps are
variable resistances. The variation spans from "infinite" resistance when closed to some small value(compared to the pipe internal resistance) when wide open. The hot an cold pipe systems will also have some internal resistance. So a better, if somewhat more complicated, electrical analogy would look like this:
In this analogy, the key issue for what will happen when both sets of taps are opened full simultaneously will depend on the relative size of the cold and hot pipe resistance compared to the common pipe resistance. In the case where they are relatively small, one gets what is found in the video, opening both full yields the flow given by the common pipe resistance. In the reverse scenario, the water flow would add.