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Sluice, head and cargo
Sluice flow follows Q = Cd A g sqrt(2 g H); the wheel and drivetrain convert part of rho g Q H into cable force. The cable force must beat the gravity imbalance of the two trolleys plus rolling and drag.
Operation
Model checks
The science
What is modelled
Two trolleys on a common cable: when one rises the other falls, so only the difference of their weights along the slope loads the drive. Water from a head tank passes a sluice, turns a wheel, and the drivetrain pulls the cable. A governor tapers the drive as the cable approaches its speed limit.
Equations
- Sluice flow:
Q = Cd A gate sqrt(2 g H). - Water power
P = rho g Q H; shaft powerP x eta_wheel x eta_drive; drive forcemin(F_max, P_shaft / v_rated)times the governor factor. - Net force
F_drive - (mA - mB) g sin(theta) - mu (mA + mB) g cos(theta) - c vover the total mass plus an equivalent inertia.
Checks run in the page
- Sluice flow against the orifice formula.
- Shaft power against the efficiency chain.
- Stall when gravity imbalance beats the available force.
- Terminal speed against bisection on the force balance.
Honest simplifications
A reduced-order teaching model: constant efficiencies, a single rolling coefficient, no cable stretch, no wheel-speed dynamics and no real site geometry. Time is compressed so a haul takes under a minute. Not an engineering or safety tool.
What to try
- Press Heavy uphill load: the net force at rest is negative and nothing moves.
- Press Balanced loads and watch the cable speed settle where drive meets resistance.
- Open the sluice and raise the head: shaft power grows as H to the power 1.5.