WRITE THE MATLAB CODE FOR THIS:

The velocity of water, $v(\frac{m}{s}),$ discharged from a cylindrical tank through a long pipe can be computed

as

$v=\sqrt[\phantom{2}]{2gH}tanh(\frac{\sqrt[\phantom{2}]{2gH}}{2L}t)$

where $g=9\mathrm{.}81\frac{m}{s^2},H=$ initial head $(m),L=$ pipe length $(m),$ and $t=$ elapsed time $(s).$

a$.$ Graphically determine the head needed to achieve $v=5\frac{m}{s},$ in $2\mathrm{.}5s$ for $6m-$long pipe.

b$.$ Determine the head for $v=4-7\frac{m}{s}($at $0\mathrm{.}5\frac{m}{s}$ increments$)$ and times of $2$ to $4s($at $0\mathrm{.}5s$

increments$)$ via the bisection method with stopping criteria of $0\mathrm{.}1\%$ estimated relative error.

c$.$ Perform the same series of solutions with the Regula Falsi method where you choose the same

starting points and convergence tolerance.

d$.$ Which numerical method converged faster?