Illustrated Physics
physics, drawn
Concept

Second moment of area — where it appears

The sum of each element of a shape's area times the square of its distance from an axis, a property of the shape alone. It decides how stiff a beam is in bending and how far below a submerged surface's centroid the water's resultant push acts.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A heeled hull, and the couple it makes. A rectangular hull of beam 3 m heeled 18°, with the waterline solved so that it displaces the same volume it did upright. The centre of buoyancy has moved 0.244 m to the low side, and weight and buoyancy now act along two lines 0.059 m apart — a couple that turns the hull back upright.

Why a ship comes back upright

Whether a floating body rights itself or rolls over is not decided by its weight, its density or how deep it sits. It is decided by the shape of the slice the water cuts through it, and the number that settles it can be worked out before the vessel is built.

fluids · Buoyancy The level at which a hinged gate swings open. The height of the centre of pressure on a vertical gate, as a fraction of its height H, against the depth of water above the gate's bottom (solid), approaching the centroid at half the height (dotted) as the water deepens; the dashed lines are hinges at 0.3H, 0.4H, 0.45H. A gate hinged on a horizontal axis and resting against a sill on the downstream side is held shut while the centre of pressure is below its hinge and swung open the moment it passes above. A hinge at 0.3H opens when the water is 0.90H deep, before it reaches the gate's top; at 0.4H, at 1.33H; at 0.45H, at 2.17H. A hinge at or above the centroid never opens at any depth, and the opening level grows steeply as the hinge approaches it — the setting is a choice of hinge position, made once, with no mechanism, sensor or power.

The floodgate that opens at a chosen depth

Hang a flat gate on a horizontal hinge across a channel and it can be made to stay shut while the water rises, press harder against its seat for a while, and then swing open on its own at one particular level — with no float, no motor and no sensor, only the position of the hinge. The trick is that the water's push on a submerged surface acts below the surface's middle by an amount that shrinks as the water deepens, so the point the push acts at climbs as the flood rises. Put the hinge on that climb and the gate opens where the climb crosses it.

fluids · Hydrostatics

Named alongside it

The objects these essays reach for when they reach for this one.

EquilibriumBuoyancyCentre of gravityCentre of pressureCentroidHydrostatic pressureMetacentreRighting momentStabilityTorqueUpliftWaterplane

All concepts