# 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:

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