Abstract: The current calculation of the normal water depth of semi-cubic parabola-shaped channel  has such shortcomings as complex process and inadequate precision. Through transforming the basic equation of normal water depth and by introducing the dimensionless water depth and the characteristic parameter, we present an approximate formula which is obtained through successive approximation and fitting equation of normal water depth, with the minimum standard residual difference as the objective function. The formula is simple, convenient, applicable and practical. Error analysis and calculation example show that the maximum relative error is only 0.261%, which meets the requirements of engineering accuracy. This research provides a more effective approach of calculating the normal depth of semi-cubic parabolic channel.

Key words: parabolic channel, uniform flow depth, optimization and fitting, hydraulic calculation