As shown in Fig. P5.4, the velocity of water, (m/s), discharged from a cylindrical tank through a long pipe can be computed as where

As shown in Fig. P5.4, the velocity of water, υ (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). Develop a MATLAB script that

(a) plots the function f(H) versus H for H = 0 to 4 m (make sure to label the plot) and

(b) uses LastNameBisect with initial guesses of x_l = 0 and x_u = 4 m to determine the initial head needed to achieve υ = 5 m/s in 2.5 s for a 4-m long pipe. In addition, use Ead = 0.0000001. Also, set format long in your script so you display 15 significant digits for your results.

Figure P5.4:

 
 

v = /2gH tanh 2gH 2L