A tank of section A is fed with a constant flow rate Qo of a liquid of density and viscosity. The tank has a drain pipe of diameter D and length L>>D (see figure) that has a valve. When the height of liquid in the tank is hot, the drain pipe valve is opened and, keeping feeding the tank with the constant flow rate Qo, the liquid begins to come out from the deposit. Assuming that in the movement of the liquid in the drain pipe viscous forces dominate, it is requested: www ww a) Differential equation that determines the evolution of the height h(t) of the liquid in the bear deposit b) Final height hf that the liquid acquires in the tank. >What condition should you check? What so that at the end of the process there is liquid left in the tank? c) Integrate the equation in section a). Write the order of magnitude of time How long does it take to reach the final height hf? d) Conditions that must be verified so that, as has been assumed, the forces viscous are dominant in (v = 10-6 m/s) and that L = 10 m, make use of one the movement. Assuming the liquid is water www www of these conditions together with the one obtained for Qo in section b) and give a limit value in relation to which the diameter of the duct should be much smaller.