The original simple equation can be used if

m = μ (1 + αu2/2gh)3/2

or very approximately, since u2/2gh is small,

m = μ (1 + 3⁄2αu2/2gh).

(3)

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