§ 43. Triangular Notch (fig. 46).—Consider a lamina issuing between the depths h and h + dh. Its area, neglecting contraction, will be bdh, and the velocity at that depth is √(2gh). Hence the discharge for this lamina is
b√2gh dh.
But
B/b = H / (H − h); b = B (H − h) / H.
Hence discharge of lamina
= B(H − h) √(2gh) dh/H;
and total discharge of notch
= Q = B √(2g) ∫H0 (H − h) h1/2 dh/H
= 4⁄15 B √(2g) H3/2.
or, introducing a coefficient to allow for contraction,