Pressure and Hydraulics

Hydraulics is the one machine in this subtest that multiplies force without any visible lever or gear, and the reason is worth understanding rather than memorizing.

Pressure

Pressure = force / area.

Units are pounds per square inch (psi) or pascals.

The same force over a smaller area is more pressure, which is why:

• A sharp knife cuts and a blunt one does not. Same push, far less area.
• Snowshoes stop you sinking. Same weight, far more area, less pressure on the snow.
• A woman's stiletto heel puts more pressure on a floor than an elephant's foot, despite the enormous difference in weight.

That last example is the one questions like, because it separates force from pressure cleanly.

A 200-pound force acts on 4 square inches.

200 divided by 4 is 50 psi.

What force does 30 psi exert on a 12-square-inch piston?

30 times 12 is 360 pounds.

Pascal's principle

Pressure applied to a confined fluid is transmitted undiminished to every part of the fluid and to the walls of its container.

Two consequences that make hydraulics possible:

The pressure is the same everywhere, so a small piston and a large piston in the same system feel identical pressure.

Force depends on area, so the large piston, feeling the same pressure over a larger area, produces a larger force.

Liquids are essentially incompressible, which is why hydraulic systems use oil rather than air. A gas would compress and the motion would be spongy rather than immediate - which is exactly what air in a brake line feels like, and why brakes are bled.

The hydraulic press

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Mechanical advantage = large piston area / small piston area.

In the figure: 4 square inches over 1 square inch is an advantage of 4. A 10-pound push gives 40 pounds of lift.

Work it through with pressure to see why:

• Pressure from the small piston: 10 pounds over 1 square inch is 10 psi.
• That 10 psi acts everywhere, including on the large piston.
• Force on the large piston: 10 psi times 4 square inches is 40 pounds.

Nothing is created. The small piston travels 4 inches while the large one rises 1 inch, which is what the caption says and what keeps the work equal: 10 times 4 is 40, and 40 times 1 is 40.

A jack has a 1-inch diameter input piston and a 4-inch diameter output piston. What is its advantage?

Not 4. The diameter ratio is 4, so the area ratio is 4 squared, which is 16.

Where hydraulics is used

Brakes are the clearest case of Pascal's principle at work: one pedal, one master cylinder, and equal pressure delivered to four wheels through the lines.

A pneumatic system uses gas instead of liquid. It is lighter and tolerates leaks better, and it is springy because gas compresses - which is fine for an air tool and wrong for a brake.

The parts of a hydraulic system

Hydraulics work because liquid is nearly incompressible, so a push at one end arrives at the other almost instantly.

A single-acting cylinder pushes in one direction only and returns by a spring or the load; a double-acting cylinder is powered both ways.

The fluid needed is the cylinder's area times its stroke. A 3-square-inch piston extending 12 inches needs 36 cubic inches. More force from the same cylinder means more pressure.

Air in a hydraulic line is the enemy, because air compresses: the brake pedal goes spongy. Bleeding a brake system removes that trapped air. Water in the fluid is also harmful, causing corrosion, and overheated fluid thins and leaks past the seals.

Pneumatics

Pneumatics use a gas - compressed air - where hydraulics use a liquid. Air is light, clean and quick to exhaust, so pneumatics suit light, fast tools such as an air-powered impact wrench or a nail gun. Because air compresses, a pneumatic cylinder is springier under a sudden load. Compressed air is stored in a receiver tank, and a regulator delivers a steady working pressure. A tank feels warm right after filling because compressing a gas heats it.

For a sealed gas at a constant temperature, pressure and volume are inversely related: a 2-cubic-foot container at 30 psi expanded to 6 cubic feet - three times the volume - drops to 10 psi.

Pressure in a fluid at rest

Pressure increases with depth, because more fluid is stacked above.

It does not depend on the container's shape, only on the depth. Two vessels of very different shapes filled to the same level have the same pressure at the bottom, which surprises people and is asked.

Pressure acts equally in all directions at a given point, not just downward.

Atmospheric pressure at sea level is about 14.7 psi, and it falls with altitude.

What you can skip

Across the 116 questions on this topic in our bank:

• Fluid flow principles. Bernoulli's principle, the venturi and the siphon never appear on this topic.
• Metric pressure. Pascals come up once as a unit; kilopascals never. The calculations are in pounds and square inches.
• Gauge against absolute pressure never appears.

Where people lose points

Using diameters instead of areas for a hydraulic advantage.

Thinking a hydraulic system creates energy. The small piston moves further.

Saying pressure depends on the container's shape. Depth only.

Confusing force with pressure. Pressure has an area in its denominator.

Using a gas where an incompressible fluid is needed.

Thinking pressure in a fluid acts only downward.

Work one in under a minute

A hydraulic jack has an input piston of 2 square inches and an output piston of 30 square inches. What force on the input lifts a 1,500-pound car, and how far must the input move to raise it 1 inch?

Advantage: 30 over 2 is 15.

Force: 1,500 divided by 15 is 100 pounds.

Distance: the input moves 15 times as far, so 15 inches for 1 inch of lift.

Check the work: 100 times 15 is 1,500; 1,500 times 1 is 1,500. Equal. And 15 inches per inch of lift is why a jack handle is pumped many times.

Where this leads

Pressure and density together are what buoyancy is about, and hydraulic braking is the mechanism behind the brakes lesson.