Abstract:

In order to get the explicit calculation formula of conjugate depth for semi-cubic, square, and cubic parabolic-shaped channels, the jump equations of the three parabola-shaped channels were transformed identically and the relationships between the dimensionless water depth x before jump and the dimensionless water depth y after jump were obtained according to the property that the critical depth was between the pre-jump depth and the post-jump depth. Their iterative formulas were further obtained respectively. Hence, a set of explicit calculation formulas of conjugate depth for semi-cubic, square, and cubic parabolic-shaped channels were obtained by fitting the iterative initial value through excel in common engineering scope. Finally, example and error analysis shows that the absolute value of maximum relative error of dimensionless water depth x before jump was 0.25%, 0.17%, and 0.31% respectively for the semi-cubic, square, and cubic parabolic-shaped channel, and that of dimensionless water depth y after jump was respectively -0.23%, -0.29%, and 0.39%. The formulas were convenient and highly accurate with clear physical meaning and wide application scope.

Key words: semi-cubic parabola-shaped channel, square parabola-shaped channel, cubic parabola-shaped channel, conjugate depth, explicit calculation formula