(USING MATLAB)

Hipatia is a little girl, very curious and restless. Every morning she brings lemonade to her school in a big bottle. Tired of getting up so early, she wants to optimize the filling of lemonade into her bottle and for this she wants to know what to use: whether to invest in a funnel (cone) or simply use a plastic cup (cylinder) with a hole in the bottom.With your savings, she (he) has hired you to help her decide the best option. However, Hypatia is incredulous; if you give her a solution, she will not be convinced until she sees with her own eyes what is most convenient. convenient. Since Hypatia is still small, showing her a graph of the liquid level versus time in each of the containers would be fruitless. the level of the liquid versus time in each of the containers would be fruitless. So the best option is to make a video showing the two types of containers (cone and cylinder). (cone and cylinder) being emptied, so that it will be evident which is the better choice.

Make a video of a conical tank and a cylindrical tank of the same volume being emptied through a small hole (of the same radius) located at the bottom of the containers (of course, you do not have to recreate the same small hole (of the same radius) that is located at the bottom of the containers (of course, you do not have to recreate this situation this situation in reality but in a simulation).

Using matlab

Propose a model using differential equations for the emptying of each of the tanks. For your model, consider the following: the emptying/filling of a tank containing a volume of liquid V, can be modeled by the following differential equation: = - , where is the rate of change of the liquid volume (the derivative of the volume with respect to time); is the liquid inflow into the tank; and is the liquid outflow from the tank. If the tank has a hole through which liquid flows out, then. = , where is the area of the hole and the velocity at which the liquid exits. This velocity obeys Torricelli's law. HINT 1: According to Torricelli's law, the velocity of the liquid flowing out of a hole at the bottom of a tank is the same as the velocity of a liquid flowing out of a hole at the bottom of a tank. is the same velocity that a particle falling freely (in a vacuum) from the level of the liquid to the place where the liquid is of the liquid to the place where the orifice is located.

Hint 2: To determine the height of the water at each instant of time you can use a Matlab ODE solver. Hint 3: You can use Matlab's cylinder function to plot both the cylinder and the cone. To give you to get an idea of how this function works, it is recommended to use Matlab's help. Hint 4: Before making the drawings it is convenient to fix the axes and the view (if this is not done, in each plot Matlab will optimize the view and in the video you will see abrupt transitions), for example with the following command lines. commands: figure() xlim([-2,2]) %fixes the x-axis of the figure Page 5 of 5 ylim([-2,2]) %set y-axis of the figure zlim([0,10]) %set the z-axis of the figure view(60,30) %set the perspective of the figure Hint 5: To delete a figure without deleting the axes, use command: cla Hint 6: calculate the height of the water in time intervals of equal length, so that your simulation will run in "real time".