This simulator compares a maintained-head orifice discharge with an unfed draining tank, using the Torricelli relation and a discharge coefficient. Switch tank operating mode, adjust head, orifice diameter, tank plan area, discharge coefficient and outlet drop height, and watch the contracted jet, trajectory and cumulative collected volume respond.
• A real-time 3D cutaway workbench of the transparent head tank, maintained-head supply, sharp-edged orifice plate with a closure slide, contracted free jet, trajectory landing ruler, collection tray and a head-gauge/trial console, with home view, focus-selected-part, full-enclosure toggle, exploded view, auto-rotate, expand and show/hide labels controls. • A tank operating-mode selector (maintained head vs. unfed draining tank) plus five range controls: initial/maintained head above outlet (0.1–3 m), circular orifice diameter (10–80 mm), tank plan area (0.2–3 m²), discharge coefficient Cd (0.45–0.98) and outlet height above landing plane (0.4–2 m). • Playback controls: pause/resume, 0.1 s and 1 s step advances, four speeds, plus 'Open/close outlet' and 'Refill and reset trial' quick actions. • A Curves & measurements tab with a head chart and a discharge chart, a depth/discharge history chart, the full equation set (orifice area, Q = Cd·Ao·√(2gh), Cv/Cc split, unfed-tank recursive draining relation, ballistic range) and snapshot readouts. • An Experiments tab with four guided fixtures (maintained free jet, unfed draining tank, double the head, large hole at low head) and a Model verification bench with an independent-check run, timestamped event log and copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz with reset, and a written model-scope statement with a reference link.
Ideal exit speed from an orifice under head h is the Torricelli relation √(2gh); the simulator applies a fixed velocity coefficient Cv = 0.98 to get jet speed, then derives the contraction coefficient as Cc = Cd/Cv so that discharge coefficient Cd is never mistakenly used directly as a velocity coefficient. Discharge is then Q = Cd·Ao·√(2gh), and jet area equals Cc·Ao — deliberately separating how much the jet area contracts from how fast it actually moves.
In maintained-head mode an external supply replaces discharged volume, holding head and hence discharge constant, so the 'Double the head' experiment shows discharge and landing range both increasing by √2 relative to the 1.5 m baseline. In unfed draining mode, head and discharge decline together as stored volume drops.
With no feed, the simulator advances head using the recursive relation √h(t+Δt) = max[0, √h(t) − Cd·Ao·√(2g)·Δt/(2·Atank)], so collected volume equals exactly the tank's lost stored volume — the model conserves mass rather than integrating an idealized closed-form draining curve. The small-orifice approximation assumes the hole is small relative to head and tank area; the 'Large hole at low head' experiment deliberately violates this and the lab flags the result as approximate rather than exact.
This model excludes finite-hole integration effects, viscosity-dependent coefficients, inflow transients, jet breakup and air resistance, and the ballistic trajectory is a quasi-steady snapshot rather than a full unsteady jet solution.
Torricelli's law states that the ideal exit speed of liquid from an orifice under head h is √(2gh). The simulator applies a velocity coefficient Cv = 0.98 to this ideal speed to get the actual jet speed, and separately derives the contraction coefficient Cc = Cd/Cv from the selected discharge coefficient.
Discharge coefficient Cd combines both area contraction and velocity reduction effects. By fixing Cv = 0.98 and computing Cc = Cd/Cv, the simulator preserves Q = jet area × jet speed correctly rather than misapplying Cd as if it were a velocity coefficient alone.
Head, discharge and jet landing range all decline together as stored volume depletes. The simulator advances head with a recursive mass-conserving relation, so cumulative collected volume always equals the tank's lost stored volume in the "Unfed draining tank" experiment.
No. It assumes the orifice is small relative to head and tank area. The "Large hole at low head" experiment (80 mm orifice at 0.1 m head) deliberately violates the small-orifice criterion, and the simulator flags that result as approximate rather than presenting it as exact.