Water in a glass

A scientist is someone who sees the world around them and wonders how it is like it is.

Even though I've been a scientist for most of my life, it still surprises me that so many interesting problems can arise from something as simple as a glass of carbonated water. Here are three that have occurred to me during the last week.

1. An economics problem: why is Sainsbury's own-brand carbonated water cheaper than their own-brand still water (by around 10%)? Surely, the carbonation process requires more input of energy and materials, so it should be more expensive.
2. A physics problem: when the bubbles rise they clearly accelerate, but is the acceleration constant, or is there a significant change of force with depth, resulting in non-negligible variable acceleration?
3. A mathematics problem: what is the relationship between the volume of water in the glass and the angle by which the glass can be tipped before the water spills? This would, of course, be the same regardless of the nature of the liquid in the glass, providing surface tension is ignored. I am assuming that the glass is a frustum of a right circular cone.
   

The economics question doesn't really interest me, although the answer might.

The physics problem could probably be answered with a bit of thought and some back-of-an envelope calculations and might make a useful diversion when stuck invigilating internal examinations next week.

It is the mathematics problem that has really gripped me. Despite appearing fairly straightforward initially, it turns out to be really quite complex, requiring a determination of volume of a conic section. There are 2 cases to consider:

a) a fairly full glass, where the liquid forms an eliptical section of the frustum;



b) a fairly empty glass, where the liquid forms a section of the frustrum in the form of a elipse segment (the base of the glass constituting the chord).



Finding the air/liquid contact area would be straight forward, but extending to the volume seems to be quite tricky. A volumes of revolution approach will not work as the volume section has no cylindrical symmetry. The internet doesn't seem to be very helpful, but then I might not be constructing a suitable search as the sections I'm interested in might have a "proper" name. My next stop will be my Euclid, although I don't hold out much hope.

Any suggestions would be most gratefully received.

Of course, being a scientist I could just be a bit empirical about this: I could go and get some data and then see if I can find a relationship. Maybe that should be my next stop ...

Halcyon days ...

... are here again.

There is a short period in a teacher's year when examination classes have departed for study leave and internal examinations and reports are not yet threatening, so that workload eases for just a couple of weeks. This calm is perhaps the best time of year - time to relax, reflect and generally reorganise one's life.

"Oh, come on," I hear you exclaim, "what about those long summer holidays?". Somehow, they never seem to be the treat that you think they'll be. There's always something to be doing, either domestic chores or the planning that you hope will ease the burden of the new academic year; somehow several weeks of "free" time are never so greatly enjoyed as a rare work-free weekend.

I'm hoping to finish The Daffodil Affair (Michael Innes) and Nature's Chemicals (Richard Firn) and there's a fern to plant out (once I've dug up an the remains of old ornamental current tree) - photos to follow.

A day out in London

On Wednesday, I had a day out in London. Such excursions are always a somewhat mixed experience because whilst I enjoy the things I visit, I find London a fairly miserable palce to travel around and the people less than friendly. This was actually my second London visit in two weeks, having attended my sister's graduation in the Albert Hall last week.

My aims for the day were two-fold. Firstly, I needed a minor repair to my Howarth oboe (I play an S20), which meant leaving it at their shop in Chiltern Street and then collecting it in the afternoon. Secondly, I wanted to research the medicinal/cosmetic uses of a particular fern species. I was pleased to gain access to two important libraries - the Lindley library (Royal Horticultural Society) in Vincent Square and the Botany Library at the Natural History Museum. This was time well spent and I returned with 7 A4 sides of notes. Both libraries were welcoming and friendly (not a universal experience, as visitors to some of Oxford's libraries will know only too well) and I was pleased to be given access to material that otherwise would be difficult for me to read. One of the things I most miss about Oxford is not having ready access to good library facilities; to adapt Kenneth Graham - there's simply nothing half so much worth doing as simply reading around in libraries.

Getting around proved easy in the morning, but difficult in the afternoon, mainly because the police had elected to shut park lane (N) for no obvious reason. I ended up walking from Hyde Park corner to Howarth (near Marylbone) and then back to Waterloo. Fortunately this did take me down Charing Cross Road and I was able to buy some sheet music from Foyles.

I really don't know how people can stand to commute into London every day.

Giant molecules

I recently reviewed Walter Gratzer's book Giant Molecules - from Nylon to nanotubes (OUP, 2009) for Education in Chemistry.

You can read the review here.

The Secret Agent

I finished Conrad's The Secret Agent during my time away over Christmas, which included two quite long train journeys.

Currently reading (start of Christmas holidays)

Hugo: Les Miserables (in English translation!)
Conrad: The Secret Agent
Lewycka: A Short History of Tractors in Ukranian

Barke et al.: Misconceptions in Chemistry
Rhiordan and Hoddeson: Crystal Fire

... and also a book that I'm reviewing.

Campion update: I've read the two war-time novels
Traitor's Purse (see previous post)
Coroner's Pidgin

I don't think I'll finish all of the series in 2009!

Following a few days of cold weather I found some interested ice crystals outside my front door this morning. Unfortunately we were in a hurry to get to church, but I managed to get the following photographs later in the day. The ruler is 20 cm for comparison.































I think they have formed by vapour deposition from the cold damp air. This is essentially a process of diffusion-limited aggregation, similar to the growth of zinc or silver crystals under electrodeposition, which is the usual chemical fractal demonstration. The delicate fingers would be called "dendrites".



I thought they were pretty cool - such intricate and elegant beauty produced, quite literally, out of the air.