Fluids and Hydraulics: Practice Questions & Explanations

Pascal's principle: pressure applied to a confined fluid is transmitted equally throughout the fluid. Pressure = Force / Area. In a hydraulic system, pressure is the same in both pistons; force differs based on area. P = F/A is constant: F₁/A₁ = F₂/A₂. Calculation: F₁/A₁ = 100/2 = 50 psi. F₂ = P × A₂ = 50 × 20 = 1000 lbs. The larger piston multiplies force by the area ratio (10:1 in this case). Trade-off: distance moved is reduced by the same ratio. If small piston moves 10 inches, large piston moves 1 inch (volume is conserved: A₁ × d₁ = A₂ × d₂). Work in = work out (ignoring friction): 100 lbs × 10 in = 1000 lbs × 1 in = 1000 in-lbs. Real-world applications: hydraulic brakes (small force at pedal → large force at brake pad), hydraulic lifts (small pump pressure → lift heavy vehicles), hydraulic presses, excavator arms. Mechanical advantage of hydraulic system = A₂/A₁ (area ratio). Pneumatic systems work similarly but with compressed gas (less common in ASVAB). Fluid properties relevant to ASVAB MC: density, pressure increases with depth (P = ρgh in a fluid column), buoyancy (Archimedes' principle: buoyant force = weight of fluid displaced), incompressibility of liquids (vs compressibility of gases).

Archimedes' principle (3rd century BC): a body fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. An object floats when the buoyant force equals its weight. A solid block of steel has density ~7,850 kg/m³, much denser than water (1,000 kg/m³); it sinks. But a steel SHIP is mostly hollow — its overall average density (steel + air inside + cargo) is LESS than water. As the ship sits in water, it displaces water; the buoyant force pushes up. The ship sinks deeper until enough water is displaced for the buoyant force to equal the ship's total weight. Then it floats in equilibrium. Loading more cargo: ship displaces more water (sits lower), buoyant force increases, equilibrium maintained until maximum capacity. Plimsoll line (load line): marking on ships indicating the maximum safe loading depth. Variables affecting buoyancy: (1) Fluid density — same object floats higher in dense water (salt water) than in fresh water; ships displace less salt water for the same buoyant force (which is why ships have different load lines for fresh and salt water); (2) Object density — less dense objects float higher or float entirely; (3) Object shape — shape affects how much fluid is displaced (a flat steel sheet sinks; the same steel formed into a bowl shape floats). Submarines control buoyancy by changing internal volume (ballast tanks fill with water to sink, empty to rise). Hot air balloons use the same principle in air (warm air less dense than cold air → buoyancy). Hydrometers measure fluid density by how deep they sink.

States of matter properties: SOLID — fixed shape and volume; particles vibrate in place; strong intermolecular forces; nearly incompressible. LIQUID — fixed volume, no fixed shape (takes container shape); particles flow past each other; moderate intermolecular forces; nearly incompressible (compressible by only ~5% even under extreme pressure). GAS — no fixed shape OR volume; expands to fill any container; particles move freely with weak interactions; highly compressible (volume changes significantly with pressure). PLASMA — ionized gas, fourth state. Implications for ASVAB MC: (1) HYDRAULIC systems use liquids precisely BECAUSE they're incompressible — pressure transmits efficiently; (2) PNEUMATIC systems use compressed gas, providing spring-like behavior and energy storage; (3) Gas laws: pressure × volume = constant at constant temperature (Boyle's Law); volume increases with temperature (Charles' Law); pressure increases with temperature in fixed volume (Gay-Lussac's Law); combined: PV/T = constant. (4) Fluid (both liquid and gas) physics: pressure increases with depth (P = ρgh); buoyancy works in both; flow rate × area = constant (continuity equation); Bernoulli's principle relates pressure to velocity (faster flow = lower pressure — explains airplane lift, perfume atomizers, carburetors). Density: solids generally densest, liquids next, gases least dense; exceptions exist (mercury liquid denser than many solids; some solids less dense than liquid water like ice — which is why ice floats).

Bernoulli's principle (Daniel Bernoulli, 1738): for a flowing fluid, faster flow = lower pressure. Conversely, slower flow = higher pressure. This is a consequence of conservation of energy in flowing fluids: kinetic energy (motion) + pressure energy + gravitational potential energy = constant. Faster motion → more kinetic energy → less pressure energy. Real-world examples: (1) AIRPLANE LIFT — wings shaped so air moves faster over the top (curved upper surface) than the bottom (flat or less curved); faster top = lower pressure above; slower bottom = higher pressure below; net upward force = lift; (2) CARBURETORS / SPRAY BOTTLES — fast air stream through a venturi (narrowed section) creates low pressure that draws up fuel/liquid; (3) BASEBALL CURVES — spinning ball drags air faster on one side, creating pressure difference and curving the trajectory; (4) ROOFS LIFTED OFF IN STORMS — high winds over roof create low pressure above; interior pressure stays normal; pressure difference can push roof off; (5) SHOWER CURTAIN PULLED INWARD — running water creates low pressure inside the shower; (6) CHIMNEYS — fast wind across the top pulls smoke up. Venturi effect: narrow section in a pipe causes fluid to speed up (continuity equation: A₁v₁ = A₂v₂); speeding up causes pressure to drop (Bernoulli). Pitot tubes measure airspeed by measuring this pressure difference. Despite being central to aerodynamics, Bernoulli's principle is often misunderstood — it applies to ideal flow along streamlines without friction, viscosity, or compressibility effects; real aerodynamics combines Bernoulli with other effects. ASVAB MC tests the basic concept.

Pressure in a fluid increases with depth at a predictable rate. P = ρgh, where ρ is fluid density, g is gravity, h is depth. For water: ρ = 1000 kg/m³, g = 9.8 m/s². Pressure increase per meter of depth = 1000 × 9.8 = 9800 Pa per meter ≈ 9.8 kPa/m ≈ 1.4 psi/m. So 33 feet (10 meters) ≈ 14 psi pressure increase, or about 1 atmosphere (atm ≈ 14.7 psi at sea level). Total pressure at depth = atmospheric pressure (at surface) + water pressure (due to depth). At 33 feet depth: total pressure ≈ 2 atm (1 atm air + 1 atm water). At 66 feet: 3 atm. At 99 feet: 4 atm. This affects scuba diving in important ways: (1) GAS COMPRESSION — at 33 feet, lungs and gas spaces compress to half their surface volume per Boyle's Law; at 99 feet, to one-fourth; (2) BREATHING — divers need pressurized gas equal to surrounding water pressure to inflate lungs; modern regulators automatically adjust; (3) NITROGEN ABSORPTION — at higher pressure, more nitrogen dissolves in tissues (Henry's Law); ascending too fast releases nitrogen as bubbles (decompression sickness, 'the bends'); divers ascend slowly with decompression stops on deep dives; (4) OXYGEN TOXICITY — at high pressure, even normal-percentage oxygen becomes toxic (~6 atm); deep divers use special gas mixtures; (5) NITROGEN NARCOSIS — at depth, nitrogen affects the central nervous system; called 'rapture of the deep'; reversible upon ascent. Salt water is slightly denser than fresh water, so pressure increases slightly faster (about 33 feet per atm in salt water, 34 feet per atm in fresh). Atmospheric pressure at sea level: 1 atm = 14.7 psi = 101 kPa. Decreases with altitude (about 0.3 psi per 1000 ft elevation).

PASCAL'S PRINCIPLE: In a closed fluid system, pressure is transmitted equally in all directions. Pressure = Force ÷ Area. Small piston: P = 10N ÷ 2cm² = 5 N/cm². Same pressure at large piston: Force = P × Area = 5 N/cm² × 20 cm² = 100 N. MECHANICAL ADVANTAGE = large area ÷ small area = 20/2 = 10. Input force × MA = Output force: 10N × 10 = 100N. Hydraulic systems are used in: car brakes (small pedal force → large caliper force); hydraulic jacks; heavy machinery. As with all mechanical advantage: the large piston moves 10× less distance than the small piston moves.

A steel SHIP floats because its hollow SHAPE DISPLACES a large volume of water, creating an upward BUOYANT FORCE equal to the ship's weight (Archimedes' principle); a solid steel BOLT displaces very little water, so its buoyant force is less than its weight, and it sinks. ASVAB Mechanical Comprehension tests buoyancy. BUOYANT FORCE = weight of displaced fluid; an object floats if it displaces water weighing as much as the object. The ship's shape (enclosing air, displacing much water) makes its average density less than water, while the compact bolt is denser. The buoyancy/displacement principle is commonly tested.

Pascal's principle states that pressure applied to a confined (enclosed) fluid is transmitted equally and undiminished in all directions throughout the fluid. This is the basis of hydraulic systems: a small force applied to a small piston creates pressure that acts on a larger piston, producing a larger force — which is how hydraulic jacks, car brakes, and lifts multiply force. Because liquids are nearly incompressible, they transmit pressure efficiently. Understanding that confined fluids transmit pressure equally in all directions, and how this enables hydraulic force multiplication, is central to the fluids topic.

In a hydraulic system, pressure (force per unit area) is transmitted equally through the fluid (Pascal's principle). Since pressure equals force divided by area, the same pressure acting on a larger piston area produces a larger force: F = pressure × area. So a small force on a small-area piston creates a pressure that, when applied to a large-area piston, yields a much greater force. The tradeoff is distance — the large piston moves a smaller distance than the small piston travels, conserving work/energy. This force-multiplication principle underlies hydraulic jacks, presses, and brakes.

An object feels lighter in water because the water exerts an upward buoyant force on it. According to Archimedes' principle, this buoyant force equals the weight of the fluid the object displaces. The buoyant force partially counteracts gravity, so the object's apparent weight is reduced. If the buoyant force equals or exceeds the object's weight, the object floats; if it's less, the object sinks but still feels lighter than in air. Understanding buoyancy — the upward force from a fluid that makes submerged objects feel lighter — is part of the fluids topic.