Hydraulic Engineering · Bottom Intake

Tyrolean Weir
discharge calculator

Method
Frank–Mosonyi (classical)
Version
1.0 · 2026

Sizes the trash rack of a Tyrolean (bottom) intake for a target diversion discharge in a mountain stream. Implements the classical design equation Q = c · μ · b · L · √(2gh) with rack-shape coefficient c, bar-shape discharge coefficient μ, and inclination factor k tabulated per Mosonyi. Adjust inputs to compute required rack length, water capture ratio, and rack-bar geometry.

Flow rate routed through the rack to the headworks.
Gap between adjacent bars.
Centre-to-centre of bars.
Typically 15°–30°.
Clogging allowance, 1.5–2.0.
Discharge coefficient based on bar profile (Noseda).
Computing...
Required rack length (with safety factor)
m
qUnit discharge
m²/s
h_cCritical depth
m
hInitial water depth
m
kInclination factor
cRack shape coeff.
a/dVoid ratio
nBar count
bars
BCollection canal width
m
Q TO PENSTOCK hc β L x = 0 x = L approach channel collection gallery bypass q(L) Tyrolean weir · longitudinal section FLOW ARRIVES AT CRITICAL DEPTH · DROPS THROUGH BARS INTO GALLERY · ANY EXCESS BYPASSES

Method & assumptions

For engineering reference

Governing equation

The classical Frank–Mosonyi formulation treats the rack as a submerged weir with discharge dependent on initial water depth, void fraction, bar shape, and rack inclination:

Q = c · μ · b · L · √(2g · h)
where c = 0.6 · cos3/2(β) · (a/d) is the rack shape coefficient, μ the bar-shape discharge coefficient (Noseda), b the rack width, L the rack length, and h = k · hcrit the initial water depth at the rack head. Critical depth hcrit = (q²/g)1/3.

Inclination factor k

Per Mosonyi's tabulation, k decreases from 1.000 at β = 0° to roughly 0.75 at β = 36°. The calculator linearly interpolates between tabulated values. Typical Tyrolean weirs are inclined 15°–30° to promote self-cleaning by gravity-driven sediment transport along the rack.

Discharge coefficient μ

Bar shape strongly affects intake efficiency. μ ≈ 0.50 for sharp-edged rectangular bars rises to ~0.95 for streamlined oval profiles. Round-edged rectangular bars (the standard fabricated profile) sit at roughly 0.65 and are the default here. These coefficients trace to Noseda's experiments and are reported in Mosonyi's High-Head Power Plants.

Safety factor

The hydraulic rack length is multiplied by SF = 1.5 to 2.0 to allow for clogging from cobbles, leaves, branches, or organic debris — particularly important in glacier-fed and forested catchments. Without this margin, design discharge is not delivered whenever the rack partially blocks. Drobir, Kienberger and Krouzecky (1999) recommend the upper end of this range for unattended remote installations.

What this calculator does not do

This is a first-pass design tool, not a substitute for engineering judgement or physical modelling. It does not compute: sediment-transport effects on rack capacity, the collecting gallery longitudinal profile, energy dissipation downstream, structural design of the bars and supports, scour protection at the toe, ice and frazil-ice handling, or the hydraulic behaviour at flood discharges substantially exceeding the design value. For projects above roughly 5 m³/s diversion or in highly variable catchments, supplement with CFD (FLOW-3D, OpenFOAM) or a physical model (TU Vienna, EPFL-LCH, University of Innsbruck).

Collection canal sizing

The canal width B is shown for reference as B = L · cos(β), per Mosonyi's guideline that the canal should approximately match the projected horizontal length of the rack. The canal depth should be set so a freeboard of at least 0.10–0.20 m is maintained at design flow.

  1. Mosonyi, E. (1991). High-Head Power Plants, Vol. 2/A, 3rd ed. Akadémiai Kiadó, Budapest. — Standard design reference.
  2. Frank, J. (1956). "Hydraulische Untersuchungen für das Tiroler Wehr." Der Bauingenieur, 31(3), 96–101.
  3. Drobir, H., Kienberger, V., & Krouzecky, N. (1999). "The Wetted Rack Length of the Tyrolean Weir." XXVIII IAHR Congress, Graz.
  4. Brunella, S., Hager, W. H., & Minor, H.-E. (2003). "Hydraulics of Bottom Rack Intake." J. Hydraulic Eng., 129(1), 2–10.
  5. Noseda, G. (1956). "Correnti permanenti con portata progressivamente decrescente, defluenti su griglie di fondo." L'Energia Elettrica, 33(6), 565–581.
  6. Castillo, L. G. et al. (2016). "Bottom Intake Systems: Performance and Design." Universidad Politécnica de Cartagena.