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?
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
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