m = [mu](1 + [alpha]u²/2gh)^(3/2)
or very approximately, since u²/2gh is small,
m = [mu](1 + (3/2)[alpha]u²/2gh). (3)
[Illustration: FIG. 52.]
Now if p is the height of the weir crest above the bottom of the canal
(fig. 52), u = Q/l(p + h). Replacing Q by its value in (1)
u²/2gh = Q²/{2ghl²(p + h)²} = m²{h/(p + h)}², (4)
so that (3) may be written
m = [mu][1 + k{h/(p + h)}²]. (5)
Gaugings were made with weirs of 0.75, 0.50, 0.35, and 0.24 metres
height above the canal bottom and the results compared with those of
the standard weir taken at the same time. The discussion of the
results leads to the following values of m in the general equation
(1):--
m = [mu](1 + 2.5u²/2gh)
= [mu][1 + 0.55 {h/(p + h)}²].