What is the basic principle behind how a hydraulic brake system works?

Hydraulic brake systems use Pascal's Principle: pressure in a confined fluid is transmitted equally in all directions. Force amplification: small force on small-area piston creates pressure (P = F/A); same pressure on large-area piston creates large force (F = P × A). This allows reasonable pedal pressure to generate enormous braking force. System pressure typically 800-1500 psi during normal braking, can reach 2000 psi in emergency. Master cylinder + brake pedal: when you push the pedal, mechanical linkage compresses MASTER CYLINDER piston, which pushes brake fluid out into the brake lines. The reservoir on top of master cylinder holds extra fluid (also accommodates fluid level changes from temperature and pad wear). DUAL-CIRCUIT brakes (standard since 1967 in US): master cylinder has TWO internal chambers, each serving a separate brake circuit; typically split FRONT-REAR or DIAGONAL (left-front + right-rear together, right-front + left-rear together — diagonal split maintains some braking even if one circuit fails); if one circuit fails (leak), the other still works; you'll feel a longer pedal travel but still have some braking. BRAKE LINES: rigid steel lines for most of the run; flexible rubber hoses near wheels (allow steering and suspension movement); under high pressure during operation; can corrode (steel) or deteriorate (rubber bulging/cracking). CALIPER PISTONS: receive hydraulic pressure; push outward to press brake pads against rotors. Floating caliper has one or two pistons on one side; the caliper itself slides on pins; pad pressure on one side pulls the caliper which pulls the opposite pad against the rotor. Fixed caliper has pistons on both sides; doesn't slide; usually higher performance (track cars). Caliper sizes: typical car 40-60mm piston; performance cars 50-70mm; some race cars have multiple smaller pistons. WHEEL CYLINDERS (drum brakes): smaller pistons on each end push out shoes against drum. BRAKE FLUID: hydraulic fluid; KEY PROPERTIES: incompressible (otherwise pedal would feel spongy), high boiling point (brake heat would otherwise boil it, causing fluid to vapor-lock — gas IS compressible, leading to spongy pedal and brake failure), low freezing point, lubricates seals, compatible with rubber components. TYPES: DOT 3 (glycol-based, 401°F dry / 284°F wet boiling point); DOT 4 (446°F dry / 311°F wet, more common modern); DOT 5.1 (similar to DOT 4 but higher quality); DOT 5 (SILICONE-BASED, NOT compatible with glycol fluids; some military and classic car applications). HYGROSCOPIC: glycol fluids ABSORB MOISTURE from air over time; this lowers boiling point progressively; fluid should be flushed every 2-3 years (or per manufacturer); brake fluid turns from clear-amber to dark with age. POWER BRAKE BOOSTER: between brake pedal and master cylinder; uses ENGINE VACUUM (gasoline engines) or ELECTRIC PUMP/MOTOR (diesel, hybrid, EV) to amplify pedal force; without booster you'd need to push very hard — typically 4-8x assistance. ABS (Anti-lock Brakes): adds electronic control; sensors detect wheel speeds; computer modulates pressure rapidly via valves to prevent wheel lockup; maintains steering control during emergency braking. Stability control extends this — selective wheel braking to counteract skidding.