The velocity of water (m/s) discharged from a cylindrical tank through a long pipe can be computed as:

where = 9.81 (m/s2), = initial head (m), = pipe length (m), and = elapsed time(s). We would like to find needed to achieve = 5m/s in = 2.5s for = 4m.

(i) Plot the function with Python between 0 and 2 (use a step of 0.1)

(ii) Find with a stopping criterion of

(iii) Plot root estimate (y axis) vs iteration number (x axis) of the results from the four methods in the same chart for a meaningful visual comparison of the convergence.

v=2gHtanh2L2gHt