## A problem of fluid flowing through a hole

Posted in Cute Problems with tags , , , , on December 19, 2017 by telescoper

I’m sure you’re all already as bored of Christmas as I am so I thought I’d do you all a favour by giving you something interested to do to distract you from the yuletide tedium,
The cute problem of the water tank I posted a while ago seemed to provide a diversion for many – although only about 10% of respondents go it right – so here’s a similar one. It’s not multiple choice so you will have to write your answers to the two parts in the comments box. As a hint, I’ll  say that this is from some notes on dimensional analysis, and it’s one of the harder problems I have in that file!

An incompressible fluid flows through a small hole of diameter d in a thin plane metal sheet. The volume flow rate R depends on d, on the fluid viscosity η and density ρ, and on the pressure difference p between the two sides of the she

(a) Find the most general possible relationship between the quantities  R, d, η,  ρ, and p.

(b) Measurement of the flow rate R1  through this the hole for a pressure difference p1 is made using a particular fluid. What can be predicted for a fluid of twice the density and one-third the viscosity?

## Christmas Lunch Report

Posted in Biographical with tags , on December 19, 2017 by telescoper

Well, yesterday’s annual Christmas Lunch for the School of Physics & Astronomy at Cardiff University went very well, with only the one member of staff having to be taken to hospital in an ambulance.

Prior to that we had the traditional meal at Aberdare Hall, following by the traditional pool competition at the Mackintosh Hotel, and the traditional karaoke upstairs in the Flute and Tankard. I got home about 2am, whereupon I remembered that Monday nights are when I have to put the rubbish out.

These occasions are a reminder of the true Christmas message of depravity and excess which, in my opinion, is increasingly lost by the regrettable encroachment of too much crass religion.

After the lunch, our Head of School gave an inspirational speech to the assembled throng in which he summed up our feelings for the festive season by quoting George Bernard Shaw:

Christmas is forced on a reluctant and disgusted nation by the shopkeepers and the press: on its own merits it would wither and shrivel in the fiery breath of universal hatred; and anyone who looked back to it would be turned into a pillar of greasy sausages.

Happy Christmas!