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Hydraulics of flow over rectangular labyrinth weirs

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Abstract

Laboratory experiments were carried out to study the hydraulics of flow over rectangular labyrinth weirs in both free and submerged flow conditions. In order to study the effects of approach velocity and rectangular pool dimensions, nine weir models with different pool lengths a, widths b, and discharge were tested. The length-to-width aspect ratio a/b was varied from 0.25 to 3. The discharge coefficients of rectangular labyrinth weirs were compared with the discharge coefficients of linear sharp-crested weirs of the same channel width B and weir height P. It was found that the discharge coefficients decreased with increasing the approach velocity and the pool aspect ratio. Semi-empirical formulations were developed to predict the discharge over rectangular labyrinth weirs in free flow condition. A critical approach velocity was introduced to evaluate the advantages of the rectangular labyrinth weirs over sharp-crested weirs. It was found that rectangular labyrinth weirs are hydraulically more efficient than sharp-crested weirs for ho/P ≤ 0.4 where ho is the water head over the crest of the weir in free flow condition. Performance of rectangular labyrinth weirs in submerged flow condition were investigated. Experimental data indicated that rectangular labyrinth weirs are more sensitive than the linear sharp-crested weirs in submerged flow condition. Having the same headwater in submerged flow condition, flow over rectangular labyrinth were 10% and 20% less than linear sharp-crested weirs for pool aspect ratios of a/b ≥ 1 and a/b < 1, respectively.

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Abbreviations

a :

Length of the pool (m)

b :

Width of the pool (m)

B :

Channel width (m)

C d :

Discharge coefficient in free flow condition (based on B)

C L :

Discharge coefficient in free flow condition (based on L)

F :

Froude number

g :

Acceleration due to gravity (m/s2)

h o :

(piezometric) head on the weir in free flow condition (m)

h :

(piezometric) head on the weir in submerged flow condition (m)

H o :

Total head on the weir in free flow condition (m)

H :

Total head on the weir in submerged flow condition (m)

L :

Crest length of the weir (m)

L e :

Effective crest length of the weir (m)

n :

Exponent

P :

Weir height (m)

Q :

Discharge (l/s)

Q f :

Discharge in free flow condition (l/s)

Q s :

Discharge in submerged flow condition (l/s)

R :

Reynolds number

t :

Tailwater depth above the crest (m)

t/h :

Submergence

(t/h)*:

Submergence at modular limit

x :

Horizontal distance between the first wave trough to the downstream edge of the weir (m)

y :

Vertical distance between the first wave trough to the weir crest (m)

α :

Apex angle of labyrinth weirs (°)

υ :

Kinematic viscosity of water (m2/s)

ψ :

Discharge reduction factor

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Acknowledgements

The study presented here was partially supported by the NSERC-Discovery Grant no. 421785.

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Authors and Affiliations

  1. Department of Civil Engineering, Lakehead University, Thunder Bay, ON, P7B 5E1, Canada

    Amir H. Azimi & Sara Seyed Hakim

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  1. Amir H. Azimi
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  2. Sara Seyed Hakim
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Correspondence to Amir H. Azimi.

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Communicated by G. Merkley.

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Azimi, A.H., Hakim, S.S. Hydraulics of flow over rectangular labyrinth weirs. Irrig Sci 37, 183–193 (2019). https://doi.org/10.1007/s00271-018-0616-6

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