An exploratory approach to teaching gradually varied flow

An innovative approach to teaching the principles of gradually varied flow is presented in the larger context of water resource engineering. The paper illustrates an approach to gradually varied flow (GVF) by directly tracking the “deposits” and “withdrawals” of mechanical energy to a channel and then using this balance to show that certain evolutions on the specific energy diagram are precluded, and others permitted, under steady flow. Based on this well known approach, but now applying second law of thermodynamics, students are encouraged to first explore, and then critique, an innovative approach for GVF calculation. This “trial” approach minimizes the total input of mechanical energy to the channel and, perhaps surprisingly, succeeds in calculating water surface profile under both in sub- and supercritical regimes, and even captures the hydraulic jump in a single pass calculation. However, students are challenged to understand both the power and the limitations of this formulation. The overall educational thrust is not to present yet another method of computing flow profiles; rather, the goal is to help students establish a more complete understanding of the computational constraints and options, and how these manipulations must always reflect the underlying physics.