Three vessels, one pressure
At its defaults it draws 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.
pressure-depth is one function in lib/figures/fluids.js —
matter that will not hold a shape, and the forces in it. Everything below came out
of it during this build, at parameters taken from the essays rather than invented for this
page. A figure here is the figure a reader meets in an essay, and if the generator changes,
this page changes with it.
At its defaults
Drawn even though every essay passes options, because a default nothing exercises is a trap for the next essay to call this with none — which has happened here twice.
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.
Force multiplied, distance paid
The options are the ones Force multiplied, and nothing gained passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Two pistons on one body of fluid, of areas in the ratio 16 to 1. A force of 200 N on the small one holds 3.20 kN on the large one, and pushing the small piston 16 cm raises the large one by 10.0 mm. The two products are the same number: nothing is gained except the shape of the bargain.
Force multiplied, distance paid
The options are the ones Force multiplied, and nothing gained passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Two pistons on one body of fluid, of areas in the ratio 100 to 1. A force of 150 N on the small one holds 15.00 kN on the large one, and pushing the small piston 25 cm raises the large one by 2.5 mm. The two products are the same number: nothing is gained except the shape of the bargain.
Force multiplied, distance paid
The options are the ones Force multiplied, and nothing gained passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Two pistons on one body of fluid, of areas in the ratio 100 to 1. A force of 200 N on the small one holds 20.00 kN on the large one, and pushing the small piston 30 cm raises the large one by 3.0 mm. The two products are the same number: nothing is gained except the shape of the bargain.
Pressure against depth in one column
The options are the ones The block the water does not lift passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
A column of water with the gauge pressure marked at four depths. Each is the weight of the water above one square metre, so the numbers are in proportion to the depth and to nothing else.
Three vessels, one pressure
The options are the ones The block the water does not lift passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
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.
What checks it
physicscheck asserts something about pressure-depth that
could fail — it draws it and measures the result against a value reached some other
way.
Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
Force multiplied, and nothing gained
A push on a small piston becomes a much larger push on a large one, in the ratio of their areas, with no machinery in between except the liquid. What the liquid will not do is give anything away — the distances shrink by the same factor the forces grow by, and the product is untouched.
FluidsThe block the water does not lift
A block bedded flat on the bottom of a tank, with no water underneath it, feels no upthrust at all. It is fully submerged, Archimedes' principle is not suspended, and it presses on the floor with more than its own weight — because buoyancy is not something a fluid has, it is what the bottom face is doing, and a face the water cannot reach does nothing.
FluidsThe depth past which it must sink
A body carrying a pocket of gas can be trimmed to hang motionless in water at exactly one depth. Push it a little deeper and it does not come back — the gas compresses, the buoyancy falls, and the equilibrium turns out to have been balanced on its point.
FluidsThe height a siphon cannot pass
A siphon will not lift water more than about ten metres, and the usual explanation for the limit is also given as the explanation for the mechanism. It cannot be both. A siphon runs in a vacuum, with degassed water, over a crown no atmosphere could support.
FluidsThe 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.
FluidsThe push that has no direction
That the pressure at a point in a still fluid is the same whichever way the surface faces is not a definition. It is a theorem, and its proof is an argument about how two kinds of force scale with size — which is also the exact statement of when it stops being true.
FluidsThe surface a spin decides
Spin a dish of liquid and its surface settles into a paraboloid — exactly, with nothing about the liquid in the shape. A parabola of that form has a focal length of g over twice the spin rate squared, so a bucket of mercury turning at twenty revolutions a minute is a telescope mirror figured by a clock instead of by grinding.