Rotura de Presas

1. ASYMPTOTIC SOLUTION FOR DAM-BREAK PROBLEM3
Discussion by Mohammad Akram Gill,2
M. ASCE
Hunt's paper is an interesting contribution on the dam break problem.
This discussion is confined to the direct solution of Eq. 21. Hunt pre-
sented a parametric solution (Eq. 27), which is correct and complete when
considered together with his Eqs. 14 and 21. Equation 21 can be inte-
grated, however, directly, as explained here.
Let T = 3t/i for the sake of simplicity. Equation 21 can now be written
as
3dxs =
IdT
1 +
d ~ !
T1
Also set xs/T2
= 0, so that Eq. 35 now becomes
3Tl — I = 4V1 + 6 - 4 - 66
Now let VI + 6 = <
t
> with the result that Eq. 36 reduces to
ifdif AT
1 + 2<|
> - 3c|>2
3T
after separating the variables. Equation 37 is solved to give
T4/3
(l - 4>)(1 + 3ct>)1/3
= Constant
Reverting to original variables gives
3
•t~ + X, t + 3 x.+ t Constant
(35)
(36)
(37)
(38)
(39)
Using the initial condition xs = 1 at t = 0 determines the constant giving
t + 3 -xlxs+ -t] = 3 (40)
3 3
If now Vh = —1+ -i xs + (- t (41)
is substituted in Eq. 40 and xs is eliminated, Hunt's result (Eq. 27) is
recovered.
"January, 1982, by Bruce Hunt (Paper 16801).
2
Prof. of Hydr. Engrg., Water Resources and Environmental Engrg. Dept., Ah-
madu Bello Univ., Zaria, Nigeria.
633
J. Hydraul. Eng. 1983.109:633-633.
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