A nutty problem: a pistache installation of 3 communicating vessels. The pistache nuts are dumped in vessel 1 where the nuts are colored red. From the bottom of the first vessel, they stream to the second vessel where they are salted. Eventually they stream from the bottom of vessel 2 to vessel 3 where they are stored to be shipped. The heights in each vessel are indicated by h1, h2, h3. Which simple pistache dynamics teach you that the discharge from vessel 1 and 2 is proportional with their respective heights and with proportional constants k1,k2. tbc...

Question

anonymous · Answer

a) set up the system of DEs that describe the height of nuts in the 3 vessels and solve it.
b) starting values: 10 m vessel 1, 3 m vessel 2, 1 m vessel 3. Find the evolution of the pistache nuts throughout the vessels. Is the result after a while what you would expect?

anonymous · Answer

I know that in communicating vessels the heights are supposed to be equal if the same pressure conditions apply in each. And that discharge formule is Q=V/t with V the volume.