Some equation variables used:

Q = measured breach flow, cfs or ft³/s

Q(hat) = calculated breach flow, estimate of Q, cfs or ft³/s

b = bottom width of gap in plywood breach, ft

g = acceleration of gravity, 32.174 ft/s²

he = height above the verge of the breach (b) of water upstream, ft

hh = depth of headcut below verge of breach (at b), ft

hu = depth of upstream flow bed below verge of breach (at b), ft

ms = slope of the side of the trapezoidal breach cut, horizontal to vertical, dimensionless

mu = slope of the upstream side of the plywood dam, H:V, dimensionless

C_# or D_# = equation parameters (coefficients), mostly dimensionless

r = ratio of heads or areas, dimensionless

w = weighting function between two forms of estimated flow, usually w(r), dimensionless

np = number of points (measurements) of Q, b, he, hh, hu, mu, ms in data set

 

Some trial equations used:

, mean relative error

, with

Q(hat) = calculated breach flow, cfs or ft³/s

b = bottom width of gap in plywood breach, ft

g = acceleration of gravity, 32.174 ft/s²

he = height above the verge of the breach (b) of water upstream, ft

hh = depth of headcut below verge of breach (b), ft

ms = slope of the side of the trapezoidal breach cut, horizontal to vertical, dimensionless

mu = slope of the upstream side of the plywood dam, H:V, dimensionless

D₁ = 0.46342, D₂ = 0.32459, D₃ = -0.16306, D₄ = 0.51441, D₅ = 8.6838,

D₆ = -0.10813, D₇ = 0.73077, D₈ = 0.50789, D₉ = 2.5213, D₁₀ = 0.38428

mean absolute error = 0.08304 CFS

standard deviation of absolute error = 0.13877 CFS

mean relative error = 4.91%, std dev of relative error = 5.94%

Calculated in Fortran simulated annealing program, simanh9.for, with input data file, weirdat3.prn

Plotted results in Lotus 1-2-3 file, jn1107a.123:

Qh = calculated flow, cfs

June 11 to *, 2007 -- Testing new equations based on fitting segmented curves to weighting function.

Consider FITD6:

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This page was designed by Donald L. Baker copyright © 2007