The conic-hydrometer

Here, I present different conic-hydrometer models; the elliptical-hydrometer, parabolic-hydrometer and the hyperbolic-hydrometer. The new models provide the hydrometers and the hydrometer-velocities measuring the evolving depths of the frictional fluids and their exit velocities from out lets in such longitudinally oriented conic-sectional reservoirs or mountain lakes. The conic-hydrometers are expressed as simple differential equations whose solutions are presented. These two-parameter hydro-mechanical systems are based on dynamically justified physical principles for energy dissipations through the discharge coefficient and the complementary friction. These new models are fundamentally different from the classical Torricelli-Bernoulli-law.  As the fluid surface area evolves nonlinearly with the hydraulic head in a complex manner, this becomes the game-changer characterizing the conic-hydrometers. I presented several innovative reservoir principles: The reservoir geometry intrinsically commands the hydrometer dynamics, its timing and the out let velocity. The conic reservoirs are canonically invariant under rotation and translations with the hydraulic-head rate of the reservoir profile area, a great new revelation. The elliptical-hydrometer is weakly convex, in contrast, the parabolic- and the hyperbolic-hydrometer are moderately concave, and surprisingly they overlap. The concavity-convexity and overlapping of the hydrometers are novel understanding for the conic reservoir fluid exit processes. There exists a universal hydro-mechanical principle explaining how the potential energy of the conic-reservoir system is consumed by hydro-geometric constrains in controlling the flow. The hydrometer commands the exit velocity to follow a universal conic-hydrometer-velocity rule as the parabolic-hyperbolic hydrometer velocities overlap. This is phenomenal. I construct the fundamental theorem of reservoir: the rate of change of the reservoir mass is given by the actual reservoir fluid length. The new conic-hydrometers can be applied to hydraulic, hydro-mechanical, transportation and environmental engineering problems. This includes the controlled and efficient design and emergency evacuation of the geometrically differently shaped glacial or mountain lakes, hydropower reservoirs, fluid vessels and their engineered discharges. For mountain flash flood simulation, my methods provide cost-effective, very efficient, premier solutions with hydrographs.