## Water and Energy

Posted in Biographical, Science Politics, The Universe and Stuff with tags , , , , , on May 25, 2010 by telescoper

I’ve refrained from blogging about the fraught history of my attempts to have a new  gas boiler installed in my house. Today, however, at last I have finally succeed in getting a state-of-the-art high-efficiency condensing contraption fit for the 21st Century, which will hopefully save me a few bob in gas bills over the winter but, more importantly, actually produce hot water for more than a minute or so without switching itself off.

The chaps that did the job for me actually had to test all the radiators too, which meant switching them all up to maximum. It wasn’t quite as hot today as it was yesterday but nevertheless the inside of the house was like a Turkish bath for a while. I therefore sat outside in the Sun for a bit waiting for them to get finished and tidy everything up.

While I was sitting there I got thinking about sustainable energy and so on, and was reminded of a comment Martin Rees made in his Reith Lecture not long ago. Wanting to sound positive about renewable energy he referred to the prospect of generating significant tidal power using a Severn Barrage. Given the local relevance to Cardiff – one of the main ideas is a barrage right across the Severn Estuary from Cardiff to Weston-super-Mare -so he presumably thought he was on safe ground mentioning it. In fact there was a lot of uneasy shuffling in seats at that point and the question session at the end generated some tersely sceptical comments. Many locals are not at all happy about the possible environmental impact of the Severn Barrage. That, and the cost – probably in excess of £20 billion – has to be set against the fact that such a barrage could in principle generate 2GW average power from an entirely renewable source. This would reduce our dependence on fossil fuels and increase our energy security too. The resources probably aren’t available right now given the parlous state of the public finances, but I’m glad that the Welsh Assembly Government is backing serious study of the various options. It may be that it won’t be long before we’re forced to think about it anyway. The Wikipedia page on the various proposals for a Severn Barrage is very comprehensive, so I won’t rehearse the arguments here. In any case, I’m no engineer and can’t comment on the specifics of the technology required to construct, e.g., a tidal-stream generator. However, I have to say that I find the idea pretty compelling, provided ways can be found to mitigate its environmental impact.

For a start it’s instructive to look at turbine-generated power. Wind turbines  are cropping up around the British isles, either individually or in wind farms. A  typical wind turbine can generate about 1MW in favourable weather conditions, but it needs an awful lot of them to produce anything like the power of a conventional power station. They’re also relatively unpredictable so can’t be relied upon on their own for continuous power generation. The power $P$ available from a wind turbine is given roughly by

$P \simeq \frac{1}{2} \epsilon \rho A v^3$

where $v$ is the wind speed, $A$ is the area of the turbine, $\rho$ is the density of air, which is about 1.2 kg per cubic metre, and $\epsilon$ is the efficiency with which the turbine converts the kinetic energy of the air into useable electricity.

The same formula would apply to a turbine placed in water, immediately showing the advantage of tidal power.  For comparable efficiencies and sizes the ratio of power generated in a tidal-stream turbine to a wind turbine would be

$\frac{P_{t}}{P_{w}}\simeq \frac{\rho_{t}}{\rho_{w}} \left( \frac{v_{t}}{v_{w}}\right)^{3}$

The speed of the water in a tidal stream can be comparable to the airspeed in a moderate wind, in which case the term in brackets doesn’t matter and it’s just the ratio of the densities of water and air that counts, and that’s a large number! Of course wind speed can sometimes be larger than the fastest tidal current, but wind turbines don’t work efficiently in such conditions and in any case it isn’t the $v$ which provides the killer factor. The density of sea water is about 1025 kg per cubic metre, a thousand times greater than that of air. To get the same energy output from air as from a tidal stream you would need to have winds blowing steadily ten times the velocity of the stream, which would be about 80 knots for the Severn. More than breezy!

Not all proposals for the Severn Barrage involve tidal stream turbines. Some exploit the gravitational potential energy rather than the kinetic energy of the water by exploiting the vertical rise and fall during a tidal cycle rather than the horizontal flow. The energy to be exploited in, for example, a tidal basin of area $A$  would go as

$E \simeq \frac{1}{2} \epsilon A\rho gh^{2}$

where $h$ is the vertical tidal range, about 8 metres for the Severn Estuary, and $g$ is the acceleration due to gravity. The average power generated would be found by dividing this amount of energy by 12 hours, the time between successive high tides. It remains to be seen whether tidal basin or lagoon based on this principle emerges as competitive.

Another thing that struck me doodling these things on the back of an envelope in the garden is that this sort of thing is what we should be getting physics students to think about. I’m quite ashamed to admit that we don’t…