**A 6% Fit to Experimental Prismatic
Weir Data**
#### Summary:

**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 ft^{3}/s

b = bottom width of gap in plywood breach, ft

g = acceleration of gravity, 32.174 ft/s^{2}

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

D_{1} = 0.46342, D_{2} = 0.32459, D_{3}
= -0.16306, D_{4} = 0.51441, D_{5} = 8.6838,

D_{6} = -0.10813, D_{7} = 0.73077, D_{8}
= 0.50789, D_{9} = 2.5213, D_{10} = 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

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