Plane baffles (Denil) fishway

Geometrical characteristics

Characteristics of a plane baffles (Denil) fishway

Excerpt from Larinier, 2002¹

Hydraulic laws given by abacuses

Experiments conducted by Larinier, 2002¹ allowed to establish abacuses that link adimensional flow $Q^{*}$ :

Q^{*} = \frac{Q}{\sqrt{g} L^{2, 5}}

to upstream head $h a$ and the average water level in the pass $h$ :

Abacuses of a plane baffles (Denil) fishway for a slope of 10%

Abacuses of a plane baffles (Denil) fishway for a slope of 10% (Excerpt from Larinier, 2002¹)

Abacuses of a plane baffles (Denil) fishway for a slope of 15%

Abacuses of a plane baffles (Denil) fishway for a slope of 15% (Excerpt from Larinier, 2002¹)

Abacuses of a plane baffles (Denil) fishway for a slope of 20%

Abacuses of a plane baffles (Denil) fishway for a slope of 20% (Excerpt from Larinier, 2002¹)

To run calculations for all slopes between 8% and 22%, polynomes coefficients of abacuses above are themelves adjusted in the form of slope $S$ depending polynomes.

We thus have:

h a / L = a_{2} (S) Q^{* 2} + a_{1} (S) Q^{*} + a_{0} (S)

a_{2} (S) = 315.110 S^{2} - 115.164 S + 6.85371

a_{1} (S) = - 184.043 S^{2} + 59.7073 S - 0.530737

a_{0} (S) = 15.2115 S^{2} - 5.22606 S + 0.633654

And:

h / L = b_{2} (S) Q^{* 2} + b_{1} (S) Q^{*} + b_{0}

b_{2} (S) = 347.368 S^{2} - 130.698 S + 8.14521

b_{1} (S) = - 139.382 S^{2} + 47.2186 S + 0.0547598

b_{0} (S) = 16.7218 S^{2} - 6.09624 S + 0.834851

Calculation of $h a$ , $h$ and $Q$

We can then use those coefficients to calculate $h a$ , $h$ and $Q^{*}$ :

h a = L (a_{2} (Q^{*})^{2} + a_{1} Q^{*} + a_{0})

h = L (b_{2} (Q^{*})^{2} + b_{1} Q^{*} + b_{0})

Using the positive inverse function, depending on $h a / L$ , we get:

Q^{*} = \frac{- a_{1} + \sqrt{a_{1}^{2} - 4 a_{2} (a_{0} - h_{a} / L)}}{2 a_{2}}

And we finally have:

Q = Q^{*} \sqrt{g} L^{2, 5}

Calculation limitations of $Q^{*}$ , $h a / L$ and $h / L$ are determined based on the extremities of the abacuses curves.

Flow velocity

Flow velocity $V$ corresponds to the minimum flow speed given the flow section $A_{w}$ at the perpendicular of the baffle :

V = \frac{Q}{A_{w}}

for plane baffles fishways using the notation of the schema above, we have:

A_{w} = B \times (h - \frac{C + D}{2} \sin (45 °))

Which gives with standard proportions:

A_{w} = L (0.583 h - 0.146 L)

Upstream apron elevation $Z_{r 1}$

Z_{r 1} = Z_{d 1} - D \sin (45 ° + \arctan (S))

Minimal rake height of upstream side walls $Z_{m}$

Z_{m} = Z_{r 1} + - H_{m i n} \sin (45 ° + \arctan (S))

Larinier, M. 2002. “BAFFLE FISHWAYS.” Bulletin Français de La Pêche et de La Pisciculture, no. 364: 83–101. doi:10.1051/kmae/2002109. ↩↩↩↩↩