mino.mobi / tide / pressure & gravity

Pressure & gravity vs radius · the centrifugal barometer

The smallest honest model of the cylinder's air. Give it a radius, a spin, and how much air is inside (its non-spinning pressure) — it draws gravity g(r)=ω²r and the isothermal pressure profile P(r)=P_axis·e^{S(r/R)²} from the axis out to the rim. ↩ tide

Cylinder

radius R8.00 km

spin Ω0.299 rpm

rim speed — · one turn every — · Ω = — rad/s

Air

non-spinning pressure P₀101.3 kPa

temperature20.0 °C

gas

P₀ means…

gravity g(r) = ω²r — axis (left) → rim (right)

pressure P(r) — the air pools at the rim

—

profile number S

= Mω²R²/2RT = v²_rim/2c² · rim/axis ratio = e^S

Gravity

at the rim—

1 g radius—

rim speed—

Pressure

on the axis—

at the rim—

rim ÷ axis—

axis below rim—

area-mean—

air per metre—

At the cursor

radius— hover a plot

gravity—

pressure—