Volume v,(t) Valve Volume v(1) Valve Glyn James, Modern Engineering Mathematics 3rd ed Figure 1: Cylindrical Tanks Two cylindrical water tanks are connected as shown in Figure 1. Initially there are 250 litres in the top tank and 50 litres in the bottom tank. At time t = 0 the valve between the two tanks are opened. The flowrate through each of these valves is proportional to the volume of the water in the tank immediately in the valve. The differential equations of volume for both tanks are denoted as follows: dv dt dv dt = -0.1v +0.12 0.1v+cosh t = Find the time taken for the volume of the water in the top tank to reach 20% of its starting value.