Waterline — Canal Lock Laboratory

RIVER CAM · CAM 01

Willowmere Lock

Stone chamber · Upper reach · North bank

● READY TO OPERATE↗ ORBIT CAMERA

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MISSION · RAISE THE BOAT

Close the lower gate, balance the chamber to the upper reach, then release the boat safely.

WATER LEVEL · 0.80 m | DRAG TO ORBIT

03 / Lockmaster controls

DECISION WINDOW · ENERGY STRATEGY

When the gust arrives, choose how to spend pump energy. Boost closes the time gap; conserve favours efficiency.

Chamber level · m

vs. time

Live solver Ideal fill

Flow rate · m³/s

in / out

Net flow Zero line

04 / Field notes

A lock is a water elevator. The chamber level changes until it matches the next reach. Your job is to move the boat without opening a gate against a large head difference.

FIXED STEP 1/120 sMODEL OPEN CHANNEL

THE SCIENCE / EQUATIONS, ASSUMPTIONS & MODEL LIMITS

Hydraulic flow

Q = Cᵈ · A · a · √(2g · |Δh|) · sign(Δh)

Q is volumetric flow (m³/s), Cᵈ is a discharge coefficient, A is the gate aperture area (m²), a is the opening fraction, and Δh is the water-head difference (m).

dh/dt = (Qᵢₙ + Qₚᵤₘₚ − Qₗₑₐₖ) / Aₗₒ꜀ₖ

The chamber level is integrated by a fixed-step solver at 120 Hz. The dashed graph is an analytic, idealised fill curve for a constant upstream head and gate opening.

h(t) = H − [√(H − h₀) − (k·t/2)]²

Buoyancy & pressure

Fᵦ = ρ · g · Vᵈᶦˢᵖˡᵃᶜᵉᵈ

Archimedes' principle: a floating hull displaces a volume of water whose weight balances the vessel mass. The displayed draft uses a vertical-sided waterplane approximation:

draft ≈ mᵥₑₛₛₑₗ / (ρ · Aʷᵃᵗₑᵣₚˡᵃⁿᵉ)p = ρ · g · d

Gauge pressure increases with depth below the free surface. Fresh water density is treated as 1000 kg/m³ and g as 9.81 m/s².

Assumptions & simplifications

Water is incompressible and treated as fresh water of uniform density. The gate law is an approximate orifice equation; real lock hydraulics include submerged jets, changing discharge coefficients, turbulence, wall friction and complex transients.

The boat is a simplified box-hull with constant waterplane area. Mooring is a one-dimensional spring-damper approximation; wind loading is approximate. Pump efficiency is assumed to be 70% for the energy KPI.

Visual water waves are decorative and do not feed back into the hydraulic solver. No claim is made that this is a design or navigation tool.

Placeholder for project credits and further reading.

WATERLINE / Canal Lock