Standard horseshoe cross section geometry
Gary P. Merkley
Biological and Irrigation Engineering Department,
Utah State University, Logan, UT 84322-4105, USA
Accepted 1 July 2004
The standard horseshoe cross section is found in many tunnels for open-channel and pressurized
conduit water conveyance. The exact geometric relationships for this cross section are needed for
hydraulic analysis and mathematical modeling purposes because look-up tables of numerically
approximated values are typically as slow, or slower, when implemented in computer programs.
Implicit solutions of the unsteady hydraulic equations require exact, analytical partial derivatives of
some of the relationships, both for accuracy and numerical stability. The equations for cross-sectional
area, wetted perimeter, top width, and depth to area centroid are presented as functions of the depth of
water in standard horseshoe sections, in addition to the partial derivatives of wetted perimeter with
respect to water depth, and depth to area centroid with respect to water depth. Sample unsteady-ﬂow
simulation results for a horseshoe cross section are compared to those of a comparably sized circular
# 2004 Elsevier B.V. All rights reserved.
Keywords: Horseshoe cross section; Open-channel ﬂow; Hydraulic modeling; Hydraulic equations; Tunnels
Hydraulic modeling of irrigation conveyance systems is becoming more common as
water management becomes more important, gate automation is considered, and
infrastructure modiﬁcations are planned. Dozens of irrigation canals have tunnels with
horseshoe cross sections, and the capability for their hydraulic analysis is an important part
Agricultural Water Management 71 (2005) 61–70
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0378-3774/$ – see front matter # 2004 Elsevier B.V. All rights reserved.