Specific Energy Calculator

At a glance:Specific energy (symbol E, unit m) is a central concept in open-channel hydraulics: the energy per unit weight of flow measured with the channel bottom as the datum. To understand it, recall total head = bed elevation (potential) + pressure head (in a free-surface channel equal to the depth y) + velocity head (v²/2g, the kinetic part). Choose the bed itself as the datum, so bed elevation is zero, and what remains — depth plus velocity head — is specific energy: E=y+v²/(2g). Term by term: y is the depth (m), the potential part; v is the section mean velocity (m/s); g=9.81 m/s²; v²/(2g) is the velocity head (m), converting kinetic energy into an equivalent water-column height. The clever part: for a given discharge Q, E vs y forms a curve with a minimum — at large depth the flow is slow and the velocity head is tiny, so E≈y rises with depth; at small depth the flow is fast and the velocity head explodes, so E is also large; between them lies a minimum depth, the critical depth yc, where the Froude number Fr=1. One specific-energy value (above the minimum) usually maps to two depths — one above critical (subcritical/tranquil) and one below (supercritical/shooting), called alternate depths. Example: depth y=0.5 m, mean velocity v=2 m/s → velocity head v²/(2g)=4/(2×9.81)=0.204 m; E=0.5+0.204≈0.704 m. That is, referenced to the bed, this flow carries about 0.704 m of water-column energy per unit weight. Uses: (1) analyse how depth changes across sluice gates, drops, humps (Parshall flumes) and contractions — by specific-energy conservation or change to find the downstream depth; (2) locate and design critical flow (flumes use critical flow); (3) with Froude number and critical depth, understand sub/supercritical transitions and hydraulic jumps. Notes: (1) specific energy is measured from the bed, excluding bed elevation — compare across different bed heights add the difference; (2) v is the section mean velocity — for non-uniform profiles use a kinetic-energy correction α (often 1.0–1.1), this tool uses α=1; (3) a given E may have no solution if below the minimum for that Q; (4) use consistent SI units (y m, v m/s, E m). In short, specific energy E=y+v²/(2g) is depth plus velocity head — the basis of open-channel water-surface profiles, critical flow and local structures.