Fluid_Mechanics_0212_handout

# Fluid_Mechanics_0212_handout - Fluid Mechanics A fluid is...

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PHYS 0212 Fluid Mechanics 1 Fluid Mechanics This experiment has four parts: 2. Venturi Tube – Fluid velocity 1. Archimedes’ Principle – Why things float (or not) 3. Blood Pressure – Bernoulli’s equation 4. Diffusion and Osmosis – Fick’s law A fluid is either a liquid or a gas. Air and Water are both fluids. Force Pressure Area = F P A = 2 N Units: Pascal (Pa) m = F PA = Pressure as a function of depth in a fluid: 0 PP g h ρ =+ 0 Pressure at the top of the fluid P = Density of the fluid = Depth h = PHYS 0212 Fluid Mechanics 2 Archimedes’ Principle: Picture a cube with sides s submerged in a fluid. Force: h s s s Pressure at the top of the cube: 0 top PPg h ( ) 2 0 top top F PA P g hs == + ( ) 0 bottom PP g h s + ( ) () 2 0 bottom bottom F PAP g h s s + + Pressure at the bottom of the cube: Force: The force on a vertical side varies with the depth, but the forces on opposite sides cancel each other out. top F bottom F side F side F B bottom top F FF =− Buoyant Force: 0 x F = s 2 A ss s =×= PHYS 0212 Fluid Mechanics 3 B bottom top F ( ) 2 00 B F Pg hg s h s ρρ =+ + −− 3 B F gs gV ( ) ( ) 22 B F h s sPg h s + −+ B F gV = Though this was derived for the case of a cube but it is true for any shape of the volume. PHYS 0212 Fluid Mechanics 4 yy F ma gV mg Float Vm > Sink < mass of water displaced by the object V = mg gV Note that the buoyancy force does not depend on the depth of object in the fluid. ? Fm a = =

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PHYS 0212 Fluid Mechanics 5 mass of balloon and air volume of the balloon density of water weight > buoyant force b b bB b bb m V mg F gV mg mV ρ = = = >= > > Is it possible for a balloon filled with air to sink in water? b) No a) Yes () ( ) 3 32 3 kg 4 5 3 m 0 kg m ms 1000 0.1 m 1.013 10 Pa 11 0.01 kg 1000 9.80 4320 m 2.68 mi o b PV h gm h π  ×  =− =  == PHYS 0212 Fluid Mechanics 6 PHYS 0212 Fluid Mechanics 7 Cartesian Diver Increase the pressure at the top of the column of water and the volume of air inside the diver will decrease. Decrease the pressure at the top of the column of water and the volume of air inside the diver will increase.
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## This note was uploaded on 08/17/2008 for the course PHYS 0212 taught by Professor Naples during the Spring '08 term at Pittsburgh.

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Fluid_Mechanics_0212_handout - Fluid Mechanics A fluid is...

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