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:

• plane baffles (Denil) fishway;
• "Fatou" baffle fishway;
• superactive baffles fishway;
• mixed / chevron baffles fishway.

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

$$L_w=(Z_1-Z_2){\displaystyle \frac{\sqrt{1+S^2}}{S}}$$

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:

$$L_S=\lceil (L_w-ϵ)/P\rceil \times P$$

With $ϵ$ = 1 mm to leave a margin before adding an extra baffle.

Horizontal projection of the pass length $L_h$ thus equals:

$$L_h={\displaystyle \frac{L_S}{\sqrt{1+S^2}}}$$

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:

$$Z_{r2}=Z_{r1}-{\displaystyle \frac{L_S\times S}{\sqrt{1+S^2}}}$$

$$Z_{d2}=Z_{r2}+Z_{d1}-Z_{r1}$$