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?

The Problem of the Spinning Tube

Posted in Cute Problems with tags , , on November 22, 2017 by telescoper

It’s been a while since I posted a problem in the folder for cute physics problems so here’s a nice little one for you to have a go at:

A vertical cylindrical tube of height 12cm and radius 6cm, sealed at the bottom and open at the top,  is two-thirds filled with a liquid and set rotating with a constant angular velocity ω about a vertical axis.  Neglecting the surface tension of the liquid, estimate the greatest angular velocity for which the liquid does not spill over the edge of the tube.

A Cube of Resistance

Posted in Cute Problems with tags , , , on September 14, 2017 by telescoper

It has been brought to my attention that I haven’t posted any cute physics problems recently, so here’s one (which involves applying Kirchoff’s laws) that’s a bit harder than A-level standard which might be of interest to students about to begin a degree in physics this month!

The above image, produced using the advanced computer graphics facilities available at Cardiff University’s Data Innovation Research Institute, represents a cube formed of 12 wires each of which has resistance 1Ω.

What is the electrical resistance between: (i) A and G; (ii) A and H; and (iii) A and D?