Closure to “Explicit Solution for the Specific Flow Depths in Partially Filled Pipes” by Mohamed Elhakeem and Ahmed Sattar

Abstract

The discusser presented other forms of equations for explicit solution of the critical and normal depths in partially filled pipes. He believes that the equation of Swamee (1993) for the prediction of the critical depth is preferable than that of the authors because of its simplicity and applicability range. Simplicity of a regression equation is often measured in terms of the number of input parameters, coefficients, and mathematical operations. If we compare the equation of the authors to the equation of Swamee (1993), we can see that both have one input parameter and four coefficients, and require four mathematical operations. Thus, from the writers’ viewpoint, they have the same level of simplicity. Regarding the extended range of the Swamee (1993) equation for yc/dyc/d to 1.0 compared to 0.98 by the authors, this is of little importance because the equations are limited to partially filled pipes where yc/dyc/d must be less than 1.0. The discusser also suggested two modified versions of the Swamee’s (1993) equation of higher accuracy, but the formulations were relatively complex. His equations have one input parameter and six coefficients, and require seven mathematical operations. From the writers’ viewpoint, the accuracy of 1.46% of either the equation in the original paper or the equation of Swamee (1993) is quite sufficient for most engineering practices, but if higher accuracy is required then the equations suggested by the discusser can be used.