## Bullshit on the Internet

You see a lot of bullshit on the internet. Some of it genuine scams, some of it well-intentioned but ultimately misguided.

Well, here’s something I’m not quite sure what to make of: the Eco-Cooler.

The video demonstrates a design of “air conditioning” requiring no electricity: instead just relying on the flow of air through bottles. It’s one of those things where at first glance (at least if you watch their explanation) it looks plausible, then you think about it a bit more and go “wait, what?”

Their snazzy video explains… blow on your hand with your lips pursed and it feels cooler than if you have your mouth wide open.

That, they say, is how their cooler works.

Air blows through a bottle, it gets compressed, and that cools it down. A nice idea, but unfortunately thermodynamics and fluid mechanics don’t work like that.

Let’s look at the first example – air blown through pursed lips. Why does it feel colder? The answer is simply that it’s faster. Faster fluids transfer more heat, because they keep replacing the warm air around you. On a cold day, you warm up a small “bubble” of air around you. When the wind blows, it blows that away and suddenly you’re surrounded by cold air again. The faster that wind, the less of a “bubble” of warm air you can maintain and the colder you feel. But the air you’re blowing on your hand isn’t any colder because you’ve blown it through pursed lips.

## Refrigeration Basics

So what about “the bottle neck compresses and cools the air”? This seems like a massive misunderstanding of how a refrigeration cycle works. So let’s start there.

The way conventional air-conditioning works is that it takes some working fluid (1) and compresses it (2), using a pump. The pressure increases and, crucially, the volume decreases. The same amount of heat* in a smaller space is going to get hotter. If you dump this heat somewhere (3) and bring the compressed fluid down to ambient temperature, it now has less heat than it started with. This is what’s happening in the compressor outdoors when you have an air con system and why it blows out hot air. Since the now cool-ish fluid is still compressed, you can expand it again. When you do, that same amount of heat* spreads out across a larger volume, and so you end up colder than you started. This is what’s happening indoors where the cold air comes out.
(*Actually the heat changes a bit because of the work done on or by the fluid, but that’s unnecessary complication and isn’t crucial to understand the general idea. I thought I should say it anyway for the sake of intellectual honesty.)

So is that what’s happening here? No. The key thing to note about a refrigeration (or air-conditioning) system is that no heat is destroyed. The inside’s made colder at the expense of hot air being blown out of the compressor. So, if this eco-cooler does indeed cool air, where does the heat go?

Could we potentially make this work if we extracted some heat at the bottle neck, and dissipated that to the outside environment?

## Flow Analysis

Enter everyone’s favourite often-misused equation of fluid mechanics: Bernoulli.

Bernoulli’s principle is simply a statement that along a streamline, energy is conserved. This means that anywhere along the flow, $\frac{v^2}{2}+\frac{p}{\rho}$ is the same. As air travels through one of the bottles, it will indeed have to speed up as it enters the mouth, because of conservation of mass and therefore volume (subsonic air flow is essentially incompressible). By Bernoulli, this causes pressure to decrease and therefore, according to the ideal gas law, the temperature to change slightly.

How much does the temperature change? Let’s say air enters at 5m/s. That’s a fair breeze. Looking at a drinks bottle, i’d guess the mouth is about 1/5 the diameter of the bottle, so the air has to accelerate to 25 times its starting speed to get through. Let’s also assume an air density of 1.2kg/m³ and ignore the obvious ludicrousness of air travelling through a bottle neck at 125m/s (in reality viscosity would mean a lot more energy gets turned to heat).
Plugging the numbers in, the gauge pressure in the mouth is:
$\rho \left(\frac{v_1^2}{2}-\frac{v_2^2}{2} \right) = 1.2 \left(\frac{5^2}{2}-\frac{125^2}{2} \right) = -9.4kPa$

From the ideal gas equation, air at 45 degrees will be around 110kPa:
$P=\rho \overline{R}T=1.2 \times 287\times(45+273)=109.5kPa$

Taking off the gauge pressure and doing the same in reverse gives a temperature of 18 degrees. The air in the mouth is actually colder! This isn’t what we want for a refrigeration cycle at all — if anything this colder air would absorb heat from the environment and be even hotter than it started when it leaves the mouth and returns to atmospheric pressure. We’ve made a very shitty heat pump.

## What is this thing?

So if this isn’t actually going to do any refrigeration, what is it? And why does it cool the building by 5 degrees as they claim in the video?

My guess is that their test is unfair or unrepresentative. Perhaps they were comparing no ventilation with this, rather than comparing this with… well, just a window. Just the circulation of cooler air from outside is going to help to some extent, but no more than an open window. But they don’t seem to have any information beyond what’s in the video.

I struggle to work out what the motivation is here. Initially it seems like a solar-freakin-roadways sort of thing: well-intentioned but fatally flawed. But although there’s nothing being sold here, the video does mention two sponsors, so perhaps this is just a publicity stunt for them?

They seem to have a website which is under construction at the moment, so perhaps we’ll find out soon…