Fluids Physics 202 Professor Vogel (Professor Carkner’s notes, ed) Lecture 19

Fluids  A fluid is a substance that can flow  A liquid or a gas  A fluid has no internal structure  Since a fluid can flow, any individual piece of the fluid can be hard to keep track of  Mass and force are often not useful  The important quantities of a fluid are density and pressure

Density  The density (  ) of a fluid is the mass per unit volume for an arbitrary volume element  Density can vary with temperature or pressure  but, liquids are much less compressible than gases  The SI unit of density is kg/m 3  Air ~1.21 kg/m 3  Water ~1000 kg/m 3  Rock ~3000 kg/m 3  Metal ~8000 kg/m 3

Pressure  Pressure is defined as the force per unit area P=  F/  A  The SI unit of pressure is the pascal (Pa), a newton per square meter  An important practical unit of pressure is the atmosphere, the pressure of the Earth’s atmosphere at sea level 1 atm = 1.01 X 10 5 Pa = 14.7 psi  For solving problems, you almost always need to use pascals (not atmospheres)

Pascal’s Principle  Pressure applied to an enclosed fluid is transmitted to every portion of the fluid and the container  Pascal’s principle is the basis for the hydraulic lever  Consider a U-shaped tube:  If you apply a pressure at one end, the same pressure is felt at the other end  But what if the other end of the tube is thicker?

A Hydraulic Jack

Hydraulic Jack  Since the pressures are the same and the areas are different, the force on the other end is larger (from P=F/A)  But energy must be conserved:  W=Fd, so if the force is greater at the other end the displacement must be less  A person can lift a car with a hydraulic jack, but ratcheting the jack 3 feet may only move the car an inch

Archimedes’ Principle  What happens if you put an object in a fluid?  The fluid exerts a force on the object  Called the buoyant force  The object will also displace fluid  If you measure the buoyant force and the weight of the displaced fluid, you find:  An object in a fluid experiences an upward buoyant force equal to the weight of fluid it displaces  This is Archimedes’ principle  Applies to objects both floating and submerged

Buoyancy

Will it Float?  What determines if a object will sink or float?  Density  An object less dense than the fluid will float  A floating object displaces fluid equal to its weight  An object denser than the fluid will sink  A sinking object displaces fluid equal to its volume

Floating  How will an object float?  The denser the object, the lower it will float, or:  The volume of fluid displaced is proportional to the ratio of the densities  Example: ice floating in water, W=  Vg  i V i g=  w V w g V i /V w =  w /  i V w =V i (  i /  w )  w = 1024 kg/m 3 and  i = 917 kg/m 3 V w =0.89 V i

Iceberg