Chapter 2: Pressure

2.1 Pressure in Liquids

• Liquid pressure at depth h: P = hρg (derived from P = F/A and ρ = m/V). (p.40)
• S.I. unit of pressure is pascal: 1 Pa = 1 N m⁻². (p.41)
• Liquid pressure increases with depth and density; it does not depend on mass, volume or surface area. (p.41)
• Cross-sectional area and shape of a column do not affect liquid pressure. (p.44)
• Points at the same level in a static liquid have the same pressure; pressure acts in all directions. (p.44)
• Two immiscible liquids in a U-tube: h₁ρ₁ = h₂ρ₂. (p.45)
• Actual pressure in a liquid = hρg + P_atm. (p.45)
• Applications: siphon, intravenous liquid bag placed high, thicker dam wall at the base, water tank on top of a house. (p.47)

2.2 Atmospheric Pressure

• Atmospheric pressure is the pressure due to the weight of the layer of air acting on the earth's surface. (p.49)
• Mercury barometer: P_atm = 760 mm Hg; Torricelli's experiment was in 1643. (p.50)
• P_atm = hρg = 0.76 × 1.36 × 10⁴ × 9.81 ≈ 101 396 Pa. (p.51)
• Fortin barometer: high accuracy (±0.1 mm Hg), not portable. Aneroid barometer: portable, direct reading, lower accuracy (±1 mm Hg). (p.51)
• Units of pressure: pascal (Pa), m H₂O, millibar (1 mbar = 1 hPa), mm Hg. (p.52)
• At high altitude: lower atmospheric pressure and lower oxygen percentage; effects on humans include faster breathing, dehydration and inability to think clearly. (p.54)
• At extreme depth: pressure increases by 1 atmosphere for every 10 m; body tissues absorb excess nitrogen, and bubbles form if ascent is too rapid. (p.55)

2.3 Gas Pressure

• A manometer measures gas pressure; P_gas = h + P_atm (in the same unit). (p.56)
• Mercury manometer: P = h + P_atm in cm Hg; convert with P = hρg. Pressure does not depend on tube diameter. (p.58)

2.4 Pascal's Principle

• Pascal's principle: pressure applied on an enclosed fluid is transmitted uniformly in all directions in the fluid. (p.60)
• Hydraulic system: F₁/A₁ = F₂/A₂; force multiplier = A₂/A₁. (p.62)
• Applications of Pascal's principle: hydraulic brake and hydraulic jack. (p.63)

2.5 Archimedes' Principle

• Buoyant force arises from the pressure difference between the lower and upper surfaces of an immersed object. (p.67)
• Archimedes' principle: an object partially or fully immersed in a fluid experiences a buoyant force equal to the weight of fluid displaced; F_B = ρVg. (p.67)
• Buoyant force = weight of liquid displaced = apparent loss in weight. (p.69)
• W = F_B: stationary; W > F_B: sinks with acceleration; W < F_B: rises with acceleration. (p.70)
• A floating ship: weight of ship = buoyant force = weight of water displaced. (p.71)
• A hydrometer floats lower in a less dense liquid and measures liquid density. (p.71)
• Submarine ballast tanks work like a Cartesian diver: more water in the tank increases weight so it sinks. (p.74)
• Hot air balloon rises when heated air makes the weight less than the buoyant force. (p.75)

2.6 Bernoulli's Principle

• Bernoulli's principle: when the velocity of a fluid increases, the pressure in the fluid decreases, and vice versa. (p.80)
• In a Venturi tube, a narrower cross-section gives higher velocity and lower pressure. (p.80)
• Lift force on an aerofoil: faster air above gives low pressure, slower air below gives high pressure, so a resultant force acts upwards. (p.82)
• Angle of attack also adds to lift through Newton's Third Law. (p.82)
• Applications: Bunsen burner, downforce on racing cars, curved path of a football, aerofoil of an aeroplane. (p.83)