Saturday, 28 September 2019

Fluid dynamics in Borrowdale


 The two pictures above show the serenely calm waters on one side of the track near Rosthwaite.
Hard to see on this photograph, but on the other side of the track, barely 2 metres away, the flow rate was quite substantial. The pool must act as a header tank but the drop can only be maybe 10cm. I had a poke at the outflow. It might have been 30cm by maybe 5cm max. Here's a simplistic attempt at analysis using some school equations. Loss in gravitational potential energy = gain in kinetic energy. mgh=0.5mv^2. Put in h=10cm and you get v=1.4 metres per second. Volume flow rate = Av = 0.30 x 0.05 x 1.4 = 0.021 cubic metres per second. The entire volume of the header pond might be 3m x 1m x 0.05m = 0.15 cubic metres meaning that the pond would be drained in 7 seconds if there were no water flowing in. That sounds very unlikely so the calculated flow rate must be too high.