Fluids, Pressure, Buoyancy Review question: Young's modulus Two materials have the same cross sectional area A. Their Young's moduli are different. The material with the larger modulus will be: (a) stretchier. (b) stiffer. (c) depends on F Fluids and pressure Some definitions first... Fluid: A collection of particles that flows Liquid: a fluid that is incompressible (or nearly so) Gas: a fluid that is compressible Pressure Force per unit area (a scalar) Useful for understanding fluids and how they behave Describing a fluid Since a fluid does not have well defined boundaries like a solid, we need variables that describe a fluid at any point in the volume it occupies Use density instead of mass p = m/V Mass divided by volume Use pressure instead of force p = F/A Force divided by area over which force acts Force is perpendicular to the surface, wherever fluid touches it Measuring pressure Unlike force, pressure is a scalar (no directionality) Pressure pushes perpendicularly to any surface, whatever the orientation (yes, fluids exert pressure upward too!) Units SI: pascals 1 Pa = 1 Torr: after Evangelista Torricelli. 1 torr = 1 mmHg US: pounds per square inch, psi Conversions 1 atm = 1.01 x 10^5 Pa = 760 torr = 14.7 psi A standard atmosphere (1 atm) is the atmospheric pressure at sea level Pressure and Buoyancy The net force magnitude of F2 pushing up and F1 pushing down is called the “buoyant force” F(B): = F2 F1. Evidently, F(B) = mg. In other words: the buoyant force equals the weight of the displaced fluid E mg F Archimedes Principle The magnitude of the buoyant force on an object is equal to the weight of the fluid displaced by the object Buoyancy Example: Floating Think of a block of wood, floating in water In static equilibrium, so FB = Fg FB = mdisplacedf luidg Fg = mwoodg mf luid = mwood A floating body displaces its own weight's worth of fluid (which may be less than its own volume)