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The velocity of water, v (m/s), discharged from a cylindrical tank through a long pipe can be computed
as
0 =2gH tanh
✓
2gH
22 t)
where g = 9.81 m/s2, H = initial head (m), L = pipe length (m), and t = elapsed time (s).
a. Graphically determine the head needed to achieve v = 5 m/s, in 2.5 s for 4 m-long pipe
b. Determine the head for v = 3.5 – 6.5 m/s (at 0.5 m/s increments) and times of 1.5 to 3.5 s (at
0.5 s increments) via the bisection method with stopping criteria of 0.1% 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?
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