Abstract: In view that the calculation of energy dissipation bucket for high dam is very complicated, the influence of centrifugal force of bottom arc on the contraction of water depth is considered in giving basic equations of energy dissipation based on the theory of dimensionlessness, the basic theory of hydraulics and the derivation of mathematical theory. Equations of the contracted water depth at the bottom of bucket and the downstream conjugate water depth are given respectively by using the Cardan formula of simple cubic equation. Moreover, MatLab software is used to calculate the relationship among conjugate water depth and dimensionless discharge per unit width, dimensionless total head and bucket angle. Calculation and comparison on engineering examples proves that the proposed equations for bottom contracted water depth and downstream conjugate depth are accurate, reliable and convenient to be applied to practical project.

Key words: roller bucket of high dam, energy dissipation calculation, MatLab, bottom contraction water depth, conjugate water depth after jump