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 R _{1} through this the hole for a pressure difference p_{1} is made using a particular fluid. What can be predicted for a fluid of twice the density and one-third the viscosity?*

As usual, answers through the comments box please!

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