Water and Energy

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…

14 Responses to “Water and Energy”

  1. […] This post was mentioned on Twitter by Sherry Driedger and Chattertrap Climate, Peter Coles. Peter Coles said: Water and Energy: http://wp.me/pko9D-1yg […]

  2. Rhodri Evans Says:

    Peter – very interesting blog. Yes it is shameful that we don’t get our physics students thinking about sustainable forms of energy generation more. I should put you in touch with Jim Poole at the environment agency (where Maggie happens to work). I’ve chatted to him about sustainability before at some length. Apparently he gives a lecture to the first year engineering students each year and told me last year that he was keen to do something similar to the physics students. It would be great to set up. He’s the EA’s expert on sustainability including the proposed Severn barrage.

  3. telescoper Says:


    That’s a great idea! One first-year lecture wouldn’t do everything I’d like to do, but it would be a start!


  4. Bryn Jones Says:

    This is, of course, the kind of analysis that can be carried out in physics tutorials to give students examples of scientific reasoning beyond the scope of the material covered in their lecture modules.

    On the issue of the role of physics in understanding human interaction with the environment specifically, I recall Mike Disney arguing when the Cardiff physics department was aiming to recruit a new chair in the mid 1990s that it should advertise a chair in environmental physics.

    Peter will remember that the Nottingham physics degree course had a module in environmental physics at one time (a frst-year module if I recall correctly).

  5. telescoper Says:


    We’ve just advertised a chair and several lectureships in physics and group in an area generally related to environmental physics could well be what comes out of that. Also the AIG is trying to move into earth sensing instrumentation instead of space astronomy, which would also be a move in that direction.

    Yes, I do remember the environmental physics module at Nottingham. I don’t know whether it’s still going but it was a good idea. I felt that it would be better a bit later on, though, when the students knew a bit more physics. We’re currently doing a course review here and I’ll be pushing for an environmental physics module, but it would probably be an option. I’d have no problem putting this kind of thing alongside nuclear (fission and fusion) in a general module on energy, for example, but these require quite a lot of advanced physics to do properly.

    However, I think we could easily generate problems for exercise classes generally that look at issues like this. It doesn’t have to be done in a separate module, but could instead be embedded more throughout the syllabus.


  6. S Jones Says:

    It’s becoming pretty famous now, but should mention the book

    Sustainable Energy without the Hot Air by David Mackay

    which is available for free at the website

    Mackay is a professor of physics at Cambridge University and in the last third of the book gets into the nitty gritty of the physics of how much energy can be produced by solar, geothermal etc.

    Would get my vote to be on any reading list for a course teaching energy to phys students.

  7. Bryn Jones Says:

    I wasn’t aware that David Mackay’s book was available online. Many thanks to S. Jones for pointing this out.

  8. telescoper Says:

    Indeed. Mike Edmunds showed me David Mackay’s book on the way back from the RAS Club the other night. I thought it looked really good, but I promptly forgot about it. Thanks to Jones the reminder for the, er, reminder.

  9. S Jones Says:

    I’m a huge fan of this book. I particularly like how he puts all units into
    kilowatt hours
    kilowatt hours per day
    kilowatt hours per day per person

    One of the tragedies of getting to grips with sustainable energy is that for historical reasons it has so many units. A lot of books and reports would be much simpler but for the kwh per year, calories, kcals, BTUs, exajoules, mega tonne of oil equivalent (Mtoe), quads, metres cubed of gas that one must wade through.

    Some things that would be as plain as day it we just had one unit require several pages of calculations to discover.

    – how does all the heat pumped out by all the power stations, chimneys and campfires in the world compare to the heat being trapped by the greenhouse effect caused by those activities? Mackay solves this in a paragraph (its about 10% – the CO2 is far more important)

    – does it take more energy to cook a meal than is contained in it? Yes, sometimes. My dinner of chicken, potato and veg was 500calories or 0.6kwh but it took 0.8kwh to cook. Makes me wonder why I bothered.

  10. telescoper Says:

    You mean he doesn’t use natural units?

  11. S Jones Says:

    lol – I predicted that was coming!

    Having read


  12. Anton Garrett Says:

    Yes Dave MacKay’s book is full of excellent back-of-envelope physics about energy and human needs. His aim is to get politicians and laymen thinking quantitatively about these issues, because adjectives like big and huge are not useful when comparing energy needs and sources.

  13. Rhodri Evans Says:

    Peter – I will email Jim Poole forthwith and try to set up a lunch-time meeting for the three of us….

  14. […] about the cost of HS2, which had earlier been estimated at a mere £30 billion, reminded me of an old post about renewable energy, and specifically the proposed Severn Barrage, which has an estimated cost somewhere between £10 […]

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