#### Transcript A Brief History of Planetary Science

Archimedes’ Principle Physics 202 Professor Lee Carkner Lecture 2 “Got to write a book, see, to prove you’re a philosopher. Then you get your … free official philosopher’s loofah.” --Terry Pratchett, Small Gods PAL #1 Fluids Column of water to produce 1 atm of pressure r = 1000 kg/m3 h = P/rg = 10.3 m Double diameter, pressure does not change On Mars pressure would decrease Archimedes’ Principle The fluid exerts a force on the object If you measure the buoyant force and the weight of the displaced fluid, you find: An object in a fluid is supported by a buoyant force equal to the weight of fluid it displaces Applies to objects both floating and submerged Buoyancy Will it Float? What determines if a object will sink or float? A floating object displaces fluid equal to its weight 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: Example: ice floating in water, W=rVg Vi/Vw=rw/ri rw = 1024 kg/m3 and ri = 917 kg/m3 Iceberg Ideal Fluids Steady -Incompressible -Nonviscous -Irrotational -- Real fluids are much more complicated The ideal fluid approximation is usually not very good Moving Fluids Consider a pipe of cross sectional area A with a fluid moving through it with velocity v Mass must be conserved so, If the density is constant then, Av= constant = R = volume flow rate Because the amount of fluid going in must equal the amount of fluid going out Continuity R=Av=constant is called the equation of continuity You can use it to determine the flow rates of a system of pipes Can’t lose or gain any material Continuity The Prancing Fluids How can we keep track of it all? The laws of physics must be obeyed Neither energy nor matter can be created or destroyed Bernoulli’s Equation Consider a pipe that bends up and gets wider at the far end with fluid being forced through it The work of the system due to lifting the fluid is, The work of the system due to pressure is, Wp=Fd=pAd=DpDV=-(p2-p1)DV The change in kinetic energy is, Equating work and DKE yields, p1+(1/2)rv12+rgy1=p2+(1/2)rv22+rgy2 Fluid Flow Consequences of Bernoulli’s Equation Fast moving fluids exert less pressure than slow moving fluids This is known as Bernoulli’s principle Based on conservation of energy Note that Bernoulli only holds for moving fluids Constricted Flow Bernoulli in Action Blowing between two pieces of paper Convertible top bulging out Shower curtains getting sucked into the shower Shower Physics Lift Consider a thin surface with air flowing above and below it This force is called lift If you can somehow get air to flow over an object to produce lift, what happens? December 17, 1903 Deriving Lift Consider a wing of area A, in air of density r Use Bernoulli’s equation: The difference in pressure is: pb-pt=1/2rvt2-1/2rvb2 Pressure is F/A so: L=Fb-Ft and so: If the lift is greater than the weight of the plane, you fly Summary: Fluid Basics Density =r=m/V Pressure=p=F/A On Earth the atmosphere exerts a pressure and gravity causes columns of fluid to exert pressure Pressure of column of fluid: p=p0+rgh For fluid of uniform density, pressure only depends on height Summary: Pascal and Archimedes Pascal -- pressure on one part of fluid is transmitted to every other part Hydraulic lever -- A small force applied for a large distance can be transformed into a large force over a short distance Fo=Fi(Ao/Ai) and do=di(Ai/Ao) Archimedes -- An object is buoyed up by a force equal to the weight of the fluid it displaces Must be less dense than fluid to float Summary: Moving Fluids Continuity -- the volume flow rate (R=Av) is a constant fluid moving into a narrower pipe speeds up Bernoulli p1+1/2rv12+rgy1=p2+1/2rv22+rgy2 Slow moving fluids exert more pressure than fast moving fluids