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Model checks
The science
What is modelled
Water falls from a flume into the buckets of an overshot wheel and turns it. The power available is the weight of water per second times the fall height, reduced by an overall efficiency. A large wooden gear on the wheel shaft drives a small pinion, trading torque for speed so the millstone turns faster than the wheel.
Equations
P_hyd = ρ g Q H, P_shaft = η·P_hyd, τ = P_shaft/ω. Gears: ω_stone = ω_wheel·(36/9) = 4 ω_wheel, τ_stone = τ/4 (ideal). Bucket fill: f = Q / (N·n·V_b) with N buckets and n revolutions per second.
Honest simplifications
A steady-flow engineering calculation, not a site measurement: efficiency is a slider rather than a function of bucket design, wheel speed does not feed back on efficiency, gear mesh losses are ignored, and the bucket count and capacity are illustrative.
Built-in checks
The two power formulas against each other, power conservation through the gear train, and a discrete bucket simulation that accounts for every litre poured.