The fluid
The medium that carries all this power is engineered liquid, and the syllabus lists what makes a hydraulic fluid good at the job:
Thermal stability — the fluid is worked hard and runs hot; it must keep its properties instead of breaking down.
Corrosiveness — as low as possible: the fluid lives inside precision pumps, valves and actuators it must not attack, though some types remain aggressive to paint and seals, part of the reason a hydraulic leak is a maintenance item.
Flashpoint and flammability — a high flashpoint (the temperature at which vapour first ignites from a flame), because fine mist escaping a high-pressure leak near hot components is a fire scenario the fluid itself must resist.
Volatility — low: a fluid that evaporates or vaporises easily forms vapour where the system needs unbroken liquid.
Viscosity — right across the whole temperature range: thin enough to flow at altitude cold, thick enough to lubricate and seal when hot.
Two families provide these properties, and they are a naming pair worth keeping apart:
mineral fluids — petroleum-based, used in light aircraft and many smaller systems;
synthetic fluids — chemically manufactured, fire-resistant, the standard in transport aeroplanes precisely because of the flammability requirement above.
Three handling rules follow. Different types of hydraulic fluid cannot be mixed: their chemistry differs, and each system's seals are compatible with its own fluid only, so a mix can destroy both the fluid's properties and the seals. Hydraulic fluids are irritating to skin and eyes, which matters to anyone near a leak or a servicing point. And the property the whole machine relies on: at the pressures being considered, hydraulic fluid is considered incompressible. Push fluid in at one end and the same volume must move at the other, immediately: that is why a hydraulic system transmits force and motion stiffly and instantly, where a gas, springy and compressible, could not.
What a hydraulic system is
The working principle of a hydraulic system is Pascal's law made continuous: a reservoir holds the fluid, a pump raises its pressure, lines and valves route the pressurised fluid to where work is wanted, an actuator (a piston in a cylinder, or a hydraulic motor) turns the pressure back into force and motion, and the spent fluid returns to the reservoir to go around again. The pump replaces the pressing hand of the two-cylinder picture, and the selector valves decide which large piston (a gear's, a flap's or a brake's) is connected to the pressure at this moment; the components themselves are the next lesson's inventory.
System types
Around that principle, systems differ in three independent ways. First, in whether they have a pump at all:
Passive systems (no pressure pump) — the operator's own force, applied to a master cylinder (a small cylinder the pedal or lever drives directly), is the only pressure source: the simple brake system of a light aircraft. Pressure exists only while the pedal is pressed.
Active systems (with a pressure pump) — a pump, driven by an engine or electrically, maintains system pressure independent of the pilot's muscles: every transport-aeroplane system.
Second, in when the pump pressurises the system:
Constant-pressure systems — the system is held at its working pressure the whole time, so full force is available the instant any service is selected: the transport-aeroplane arrangement.
Pressurised on demand — the pump runs, or is driven, only when a service is actually operated (an electric pump that starts when the gear lever moves): lighter and simpler, at the price of waiting for pressure to build.
Third, in how hard the fluid is squeezed. Hydraulic systems are classified as low pressure, typically up to 2,000 psi, or high pressure, typically 3,000 psi or higher; a high-pressure system typically operates at 3,000 psi, and on some aircraft 4,000 to 5,000 psi is used (the highest figures on the newest large transports, which shrink their plumbing further). A low-pressure system works exactly like the high-pressure one: pump, regulator or relief valve to cap the pressure, selector, actuator, return; only the numbers are smaller, which suits the modest forces of a light aircraft's gear and flaps.
Why push the pressure up at all? Because force is pressure times area, a high-pressure system makes the same force with a smaller actuator, so actuators, lines and the fluid quantity all shrink, and with them the weight. The disadvantages are the price of the squeeze: every seal, fitting and line must hold the higher pressure, leaks are more violent and escape as ignitable mist, and the components cost more to make and maintain. Transport aviation judged the trade long ago: the weight saving wins, and 3,000 psi became the standard.
Hydraulics or mechanics
The syllabus asks the comparison directly: why actuate hydraulically rather than by rods, cables and screws? For force, weight and size: a compact actuator fed by thin flexible lines produces forces no reasonable mechanical linkage could, the lines route through the airframe far more easily than push-rods, and for large forces the hydraulic installation is lighter and smaller than mechanism strong enough to do the same job. The costs are the fluid itself (leaks, servicing, fire properties) and the system's dependence on pressure being available, which is why the redundancy of the first lesson returns here with two or three independent systems. Purely mechanical actuation keeps the advantage only where forces are small and simplicity rules.
The result is the list of what hydraulics actually does on a transport aeroplane: primary flight controls, landing gear extension and retraction, wheel brakes, nose-wheel steering, flaps and slats, spoilers and speed brakes, thrust reversers, and heavy doors. Every one of those systems reappears in its own module; each time, the muscle behind it is this one.