Egg-shaped cross section: Uniform flow direct solution and stability identification

The complexity of an egg-shaped cross section makes developing a straightforward formula to calculate the normal depth a challenging task. In this paper, the inadequacy of the power regression based model employed so far for estimating the normal depth in these conduits was presented based on the relative hydraulic sensitivity of structures. A set of precise iterative formulas for the normal depth solution was developed which facilitates the calculation of the normal depth especially using spreadsheets. Also, accurate and direct equations to determine the uniform flow depth in an egg-shaped cross section were obtained by using an alternative regression based model developed according to the concept of the relative hydraulic sensitivity. The maximum relative error associated with the proposed equations compared to the precise iterative formula results is less than 1%. In addition, to design a sewer system especially in relatively steep urban areas, direct formulas were developed to distinguish between sub- and supercritical flow regimes and to categorize the uniform flow stability condition in such channels.

► Sensitivity analysis is used to show the drawback of current direct solutions.
► An exponential regression model is developed to estimate the normal depth directly.
► Direct formulas were presented to classify the uniform flow regime and stability.