OBSERVATION CONTRACT
Jurin gives the equilibrium height
For a circular tube, h = 2γ cosθ / (ρgr). A wetting liquid (θ<90°) rises, θ=90° gives zero, and θ>90° gives depression.
OBSERVATION CHAMBER / ACTIVE
Capillary Rise Observatory
Observe Jurin-law capillary rise or depression as surface tension balances hydrostatic pressure in a deterministic tube model.
structure / capillary balance
Observation Model
ROUTE 83 / FLUID / CAPILLARY
JURIN LAW / CAPILLARY TUBE
Read the rise from the meniscus
Change the tube and fluid values. The chamber shows the equilibrium height and a deterministic second-order damped relaxation for teaching.
Target height
Current height
Canvas 2D is unavailable. The DOM values below remain available.
- Height
- 0.000 m
- Contact angle
- 0°
- Radius
- 0.50 mm
Focus the Canvas for Space/P play or pause, S step, R reset, and 1–4 presets. Pointer focus is supported.
READY
- Target height
- 0.000 m
- Current height
- 0.000 m
- Contact angle
- 0°
- Tube radius
- 0.50 mm
READOUTS
The height in SI units
- Raw Jurin target (unbounded)
- 0.000 m
- Raw-clamped target (±2.00 m)
- 0.000 m
- Displayed target (±0.350 m)
- 0.000 m
- Current response
- 0.000 m
- Response velocity
- 0.000 m/s
- Model time
- 0.00 s
- Canvas pixels
- 1200 × 720
finite
Observation report
Generate a report after changing the observation state.
SELF-TEST
Deterministic acceptance values
Known Jurin values, signs, clamp limits, monotonicity, convergence, and finite state are checked at load and on demand.
| TEST | RESULT | DETAIL |
|---|
The response is a deterministic second-order damped relaxation for teaching. It is not a real fluid transient or a measurement.
WHAT TO WATCH
Radius and angle change the sign
- NARROW makes the magnitude larger because height is proportional to 1/r.
- POOR WETTING moves θ above 90° and makes the level fall below the reservoir.
- Change γ, ρ, or g and compare the finite target with the damped current response.
MODEL SCOPE
A bounded teaching response
The displayed CURRENT is a deterministic, fixed-step second-order damped relaxation toward the displayed TARGET. It shows the approach; it does not claim a Navier–Stokes transient.
Open the formula and limits
h = 2γ cosθ / (ρgr)
x″ + 12x′ + 36(x − target) = 0
unbounded raw target · raw-clamped target ±2.00 m · displayed target ±0.350 m · radius > 0 · all values finite
Inputs use SI units internally. The UI shows radius in millimetres, while height and response velocity use metres and metres per second.
OBSERVATION POLICY
This observatory runs a deterministic Jurin-law surface-balance model with a damped visual response in your browser. Inputs, target/current levels, calculations, reports, and images stay local. It does not measure visitors, liquids, materials, or bulk fluid flow.
Route
This chamber belongs to Structures & Symmetries.
STRUCTURE Back to Structures & Symmetries Route.