Accurate gradually varied flow model for water surface profile in circular channels

The paper presents an accurate approximation of the Froude number (F) for circular channels which is part of the gradually varied flow (GVF) equation. The proposed approximation is developed using optimization technique to minimize the relative error between the exact and estimated values, resulting in a maximum error of 0.6% compared with 14% for the existing approximate method. The approximate F is used in the governing GVF equation to develop an exact analytical solution of this equation using the concept of simplest partial fractions. A comparison of the proposed and approximate solutions for backwater length shows that the error of the existing approximate solution could reach up to 30% for large normal flow depths.