As depicted in Fig. P5.15, the velocity of water, y (m/s), discharged from a cylindrical tank through a long pipe can be computed as

where g = 9.81 m/s2, H = initial head (m), L = pipe length (m), and t = elapsed time (s). Determine the head needed to achieve v = 5 m/s in 2.5 s for a 4-m-long pipe (a) graphically, (b) by bisection, and (c) with false position. Employ initial guesses of xl = 0 and xu = 2 m with a stopping criterion of Es = 1%. Check you results.

V2gH v = V2gH tanh 2L