May 14 - June 11, 2007 - Redo old work, developing new equations. Final fit using simulated annealing to a set of weir data with 2682 measurements. The weirs were constructed of plywood as prismatic notches in a flume in about 380 different geometries, including base widths of 8, 16 and 32 inches, drops into headcuts of 0, 1/2 and 1 foot, and side and upstream slopes of from 0 up to as much as H:V = 6:1. Upstream bed depth had little apparent effect. The data and fitted equation show the effects of the cross-sectional area of the heacut compared to the upstream height of the water over the base of the notch. The experiment took no velocity data, but the logistic weighting functions seem to include at least some of the contraction effects, as the fitting process was insensitive to gross calculated entrance velocities, and the error residuals had no readily discernable correlation to them.
, 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