Iterative calculation for contracted depth of horseshoe tunnel cross-section

In order to obtain the appropriate formulas for computing contracted depth of horseshoe cross-section tunnel, appropriate dimensionless parameters were introduced and mathematical transformation was made for energy equation for contracted cross-section of horseshoe cross-section tunnel. Then iterative formulas were developed for computing contracted depth for all types of horseshoe cross-sections. Critical discharges were defined and derived to determine the range of contracted depth. Numerical calculation example indicates that the iterative formulas for computing contracted depth are simple and available.