By Kate Allaway
On Monday, November 26th, thousands of dairy farmers coordinating with the European Milk Board (EMB) came to Brussels, Belgium to protest low milk prices in the European Union. EU milk is often sold below the production price, forcing small farmers out of business. In their demonstrations, which are ongoing, protestors are spraying fresh milk out of large hoses onto policemen and the European Parliament building, preventing many EU employees from getting to work.
I wanted to determine the approximate volume rate of flow out of these hoses. This is most easily accomplished using Poiseuille’s equation (Q = (πR4ΔP)/(8ηL)).
I made the following assumptions about the hose based on the pictures:
R=5 cm (0.05 m)
Δheight between ground and person holding the hose=1.5 m
I found the following values for milk:
ρ= 1030 kg/m3 (for whole milk, from http://physics.info/density/)
η= 3 mPas = 0.003 Pas (from http://physics.info/viscosity/)
First I found the ΔP:
ΔP = ρgΔh = (1030 kg/m3)(9.8m/s2)(1.5 m) = 15,000 Pa
Then plugged in to find Q:
Q = (πR4ΔP)/(8ηL) = (π(0.05 m)4(15,000 Pa))/(8(0.003 Pas)(15 m ))
Q = 0.8 m3/s
With that volume rate of flow and the number of protestors spraying milk with hoses, it is clear why many EU employees are struggling to get past the mayhem to their offices.