Physics & Monitoring Dr Rishi Mehra

Question Describe the laws governing the behaviour of fluids (gases and liquids)

Daltons Law Daltons Law of partial pressures John Dalton : Pressure = Force per area = N / m In a mixture of gases (e.g. air), each gas exerts a pressure that it would if it occupied the volume alone This pressure = Partial pressure Sum of partial pressures = total pressure

Daltons Law For example - Total atmospheric pressure = 760mmHg - Partial pressures - pO2 = 760 x 21% = 159 mmHg - pCO2 = 760 x 0.04% = 0.3 mmHg - pN2 = 760 x 78% = 592 mmHg - pArgon = 760 x 0.94% = 7 mmHg

Gas molecular theory Gas molecular theory: - If sufficient heat applied to a solid, increased kinetic energy of each molecule - Increased energy results in breakdown of molecular lattice - Liquid is formed

Gas molecular theory If energy added to a liquid, each molecule gains more kinetic energy Some molecules are able to overcome Van der Waals forces and become gaseous At boiling point, all molecules begin to transfer to the gaseous phase

Gas molecular theory At this time, they collide with each other and walls of the container Hence exert a force over an area ‘ ie pressure ’ – units = N/M More commonly pressure referenced to atmospheres or mmHg Hence if temperature increased, more kinetic energy and higher pressure

Gas molecular theory Likewise, decreased temperature and lower kinetic energy Hence drop in partial pressure

Henry’s Law Applies to gaseous phase in contact with a liquid in a closed environment: Amount of gas dissolved in liquid is proportional to partial pressure of gas above liquid

Henry’s Law Changing pressure: Doubling pressure doubles concentration Concentration proportional to partial pressure

Henry’s Law Constant = solubility coefficient - Varies with individual gas - Varies with temperature Solubility coefficient increases with drop in temperature

Gas Law No 1: Boyle’s Law Robert Boyle: 1627 – 1691 Pressure x Volume = Constant Hence inverse relationship between pressure and volume of a perfect gas if temperature kept constant E.g. halving volume causes doubling of pressure

Gas Law No 2: Charles’ Law Jaques Charles Volume / Temperature = Constant Describes relationship between volume and temperature of a perfect gas at constant pressure Hence doubling temperature causes doubling of volume (Pressure kept constant)

Gas Law No 3: Pressure / Temperature = Constant For a container maintained at constant volume, absolute pressure of a gas varies directly with absolute temperature Hence increase in temperature causes increase in pressure

Avagadro’s hypothesis Count Amadeo Avagadro : Equal volumes of gases and the same temperature and pressure contain equal amounts of molecules One mole of any gas as STP occupies 22.4 litres

Laminar Flow Higher velocity of flow of a gas or liquid in the centre of a cylinder

Laminar Flow

Hagen-Poiseuille Law Q = flow Delta P = pressure gradient r = radius n = viscosity l = length

Hagen-Poiseuille Law Valid for laminar flow only Predictor of whether flow will be laminar = Reynold’s Number R=radius V=mean velocity ρ = density η = viscosity Re > 1500 = Non- laminar flow

Non-laminar flow: