Illustrated Physics
physics, drawn
Concept

Centre of pressure — where it appears

The point at which the resultant of a distributed pressure acts, which moves as the loading changes and is not the centre of the area. For a vertical wall holding still water it sits a third of the way up from the base, because the pressure distribution is triangular rather than uniform.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Three vessels, one pressure. Three vessels filled to the same depth of 3 m. The pressure on each base is 29.4 kPa — identical, because pressure is set by depth — while the weight of water each holds differs by a factor of 4.7. The base of the flaring vessel carries more force than the water standing over it weighs.

The pressure that only knows depth

A litre of water and a swimming pool press equally hard on a floor at the same depth. Pressure in a still fluid is a scalar with no direction of its own, it depends on how far down and on nothing else, and the shape of the container falls out of the arithmetic entirely.

fluids · Hydrostatics Which failure comes first. The dividing line between a block that slides and one that tips over, for a horizontal push applied at the top. Sliding needs a force of μ_s times the weight; tipping needs the push's moment about the leading bottom edge to beat the weight's, which is the weight times half the width. The weight appears in both and cancels, so the boundary is the curve aspect ratio = 1/2μ_s and nothing else: not the mass, not how hard the block is pushed, and not what it is made of except through μ. At μ_s = 0.5 the dividing shape is as tall as it is wide; at μ_s = 0.2 it is 2.5 times as tall. Of the 5 objects marked, 3 sit above the line and go over rather than sliding: a paperback, standing, a full filing cabinet, a pint glass.

Slide or topple

Push a wardrobe and it goes over; push a brick and it skids. Both are held by the same friction and both are pushed by the same hand, and which of the two failures arrives first has nothing to do with how hard the push is. The floor decides it, by shifting where it pushes back.

mechanics · Free-body 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.

EquilibriumTorqueCentre of gravityCentroidCoefficient of frictionContact areaContinuumDensityFree-body diagramFree surfaceGauge pressureHydrostatic equilibrium

All concepts