Control the flow. Watch time rise.
Torricelli: water leaves an orifice at v = √(2 g h) (energy: ½v² = g h). The flow is Q = Cd a √(2 g h); the cylinder level rises by dy/dt = Q / A.
The problem: in an open reservoir dh/dt = −Q/Ar so the head falls and the clock slows. Ctesibius' idea (and this regulator) keeps h constant with a float valve: then Q is constant and the level is linear in time, y = Q t / A, so equal marks mean equal minutes.
Temperature: viscosity of water changes by ~45 % between 40 °C and 10 °C. For a tiny orifice the discharge coefficient depends on Reynolds number; here Cd = 0.62 (1 − 3/√Re), Re = v d / ν, an illustrative correlation, not a measured one. Real clepsydrae also suffered from evaporation, dirt and valve wear, which are not modelled. The float valve is modelled as a small proportional sag h = hset − Q/K.
Not modelled: surface tension at the nozzle, air bubbles, thermal expansion of brass and glass. Virtual toy for learning: numbers are realistic in size, not a design for a working instrument.