Rate of water falling from a vertical tank:

Here, k is a constant of the cross-sectional area of the tank and discharge hole, with the shape of the drain hole. Water depth is measured in y meters and time in t seconds. If k = 0.1, the depth of water is 3 meters at the beginning, and how long will the tank be empty:

a)analytical

b)Calculate numerically using the Euler, Heun, and Runge Kutta methods. Write a computer program for the solution and show all of the results in a table and graph of y (t). You can take 5 seconds as a time step.

dy dt k