Rotating Vessel

Forced-vortex free-surface simulation

Created by DIT Gillesania

Tank & Fluid

Tank shape Diameter D (m) Height H (m) Liquid depth h₀ (m) Gravity g (m/s²) Liquid ρ = 1000 kg/m³ · SG = 1.000

Rotation

Ramp-up (s) Ramp-down (s) Playback ×

Controls

Angular speed ω (target) = 0.000 rad/s

Tank Top

Closed lid Ceiling opening ⌀ (m) radius = 0.050 m

View

Display Tank opacity 0.15

Readouts

StateREST ω current0.0 RPM (0.00 rad/s) ω target0.0 RPM (0.00 rad/s) Mean depth hₘ— m Center depth h_c— m Wall depth h_w— m Max elevation— m Δh (wall − center)— m Initial volume V₀— L Remaining volume— L Spilled volume0.00 L Spilled %0.00% Overflowno Dry centerno Dry radius r_dry— m Final resting depth— m Max bottom pressure0.00 kPa

Worked Solution

Live-updates as parameters change.

Physics

Symbols: D = tank diameter, H = tank height, h₀ = initial water depth, ω = angular speed, ρ = fluid density, g = gravity, P = pressure.

Free surface at steady rotation:

z(r) = C + ω²r² / (2g)

Fully wetted: hₘ = V / (πR²), Δh = ω²R² / (2g)

Volume is conserved except when liquid spills over the rim, which is permanent.