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Baffle fishways (or baffle fishways) calculation formulas

For calculation of:

  • upstream head \(ha\);
  • water level in the pass \(h\);
  • flow \(Q\);
  • flow velocity \(V\);
  • upstream apron elevation \(Z_{r1}\);
  • minimal rake height of upstream side walls \(Z_m\)

Refer to the formulas specific to each baffle fishway type:

Upstream water elevation \(Z_1\)

\[Z_{1} = Z_{d1} + h_a\]

With \(Z_{d1}\) the spilling elevation of the first upstream baffle, \(h_a\) the upstream head.

Pass length

Pass length along a water line parallel to the pass slope \(L_w\) equals

\[L_w = (Z_1 - Z_2)\dfrac{\sqrt{1 + S^2}}{S}\]

with \(Z_1\) and \(Z_2\) the upstream and downstream water elevations, \(S\) the slope.

Pass length along the slope \(L_S\) must be a multiple of the length between two baffles \(P\) rounded to the greater integer:

\[L_S = \lceil (L_w - \epsilon) / P \rceil \times P \]

With \(\epsilon\) = 1 mm to leave a margin before adding an extra baffle.

Horizontal projection of the pass length \(L_h\) thus equals:

\[L_h = \dfrac{L_S}{\sqrt{1 + S^2}} \]

Number of baffles \(N_b\)

For plane and Fatou types:

\[N_b = L_S / P + 1\]

For superactive and mixed types:

\[N_b = L_S / P\]

Downstream apron \(Z_{r2}\) and spilling \(Z_{d2}\) elevations:

\[Z_{r2} = Z_{r1} - \dfrac{L_S \times S}{\sqrt{1 + S^2}}\]
\[Z_{d2} = Z_{r2} + Z_{d1} - Z_{r1}\]