A Question of Bores
I was at a lengthy meeting this morning so naturally there popped into my mind the subject of bores. The most prominent of these that will be familiar to British folk is the Severn Bore, but they happen in a variety of locations, including Morecambe Bay (which is in the Midlands):
As you can see, a bore consists of a steep wavefront that travels a long distance without disruption, and is one manifestation of a more general phenomenon called a hydraulic jump; in a coordinate frame that moves with the wavefront, a bore is basically identical to a stationary hydraulic jump.
Anyway, I while ago I decided to set an examination question about this, which I reproduce here in severely edited form for your amusement and edification; you can click on it to make it larger if you have difficulty reading the question. With the examination season over I’m sure there are many people out there missing the opportunity to grapple with physics problems! Or perhaps not…
If you need hints, I suggest first working out how the pressure P varies with depth and then using the result to work out to work out the balance of forces either side of the discontinuity. Then deploy Bernoulli’s theorem and Bob’s your uncle!
P.S. For another hint, try the yellow pages:Follow @telescoper