Lecture 2 Fluids Pressure Bouyancy Bernoulli

Lecture 2 Fluids Pressure Bouyancy Bernoulli - 1 Physics...

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Unformatted text preview: 1 Physics 213 Waves, Fluids and Thermal Physics Summer 2007 Lecturer: Mike Kagan (mak411@psu.edu, 322 Whitmore) Today’s Discussion: Fluids Pressure and Pascal’s principle Bouyancy, Archimedes principle Bernoulli’s equation 2 Fluids. Description. Fluids. Description. So far we have only considered motion of point particles. So point Fluid = too many particles (e.g. ~1019 molecules in 1cm3 of air) Fluid too Need new collective description, new physical quantities Need new But! We shall use the same physical laws: But! same Newton’s Laws, Conservation Laws etc. 3 Fluids. Parameters. Fluids. Parameters. Density (for homogeneous fluid) Air Ice Densities (kg/m3) Space Lab vacuum 10-20 10-17 1.21 900 1000 13600 19600 21400 1017 1018 1019 Sample problem: What is the mass of the air in this room? Compare with the mass of people in this room. Water Mercury Gold Platinum Uranium nucleus Neutron star Black hole (solar mass) 4 Fluids. Parameters. Fluids. Parameters. Pressure - similar to stress, BUT! Different physical mechanism (collisions of molecules – will learn in 2 weeks) Stress: something pooling/stretching Pressure: something pushing out (in other words: stress = -pressure) Pressure is a scalar (F is the force magnitude) Vector force perpendicular to given plane, NO shear stress in (non-viscous) fluids! 5 Fluids. Parameters. Fluids. Parameters. Density (for homogeneous fluid) Air Ice Densities (kg/m3) Space Lab vacuum 10-20 10-17 1.21 900 1000 13600 19600 21400 1017 1018 1019 Sample problem: What is the mass of the air in this room? Compare it with the mass of people in this room. Water Mercury Gold Platinum Uranium nucleus Neutron star Black hole (solar mass) 6 Pressure. Units. Pressure. Units. SI: Pascal, 1 Pa = 1 N/m2 Torr: named after Evangelista Torricelli (Galileo’s apprentice, first to measure the atmospheric pressure) Equal to the millimeter of mercury, or mmHg American: pounds/in2 or psi Conversions: 1 atm = 1.01 x 105 Pa = 760 Torr = 14.7psi (where 1 atm is the average pressure at sea level due to the large fluid mass of the atmosphere above and around us) Sample problem: You inflate the front tires on your car to 28 psi. Later you measure your blood pressure, obtaining a reading of 120/80, the reading s being in mm Hg. In kilopascals, what are (a) your tire pressure and (b) Your blood pressure? 7 Pressure. Observed phenomena. Pressure. Observed Fluids exert pressure on their surroundings. Need to explain: 1) Pressure increases under water - your years feel this effect 2) Pressure decreases at high altitudes - harder to breathe on mountaintops - ears “popping” in airplanes 3) 4) Pascal vases (demo) 8 Pressure. Pascal’s Law. Pascal’s 1) Isolated fluid (no external forces) Free body diagram 2) Fluid in gravitational field A h p=const 9 Pascal’s Law. Sample problem. Q: In which container is pressure highest at depth h? A: None. They are all the same. 10 Pascal’s Law. Applications. Hydraulic press Gain in force! 11 Archimedes principle. Bouyancy. "any body partially or completely submerged in a fluid is buoyed up by a force equal to the weight of the fluid is displaced by the body." displaced Indeed, the bouyant force (see previous slide): Block ( ) in water ( A h ) Free body diagram floats sinks Bouyant force = weight of liquid within volume displaced by body 12 Archimedes principle. Sample problems. 1. Block of ice is floating in water. Block What fraction of the block is submerged? What 2. Block of ice is floating in water covered 2. with a thick layer of oil (density 700 kg/m3). with ). What fraction of the block is submerged into water? (Water and oil do not mix.) water? 13 Conservation laws. Mass. Cross section changing in the middle: Incoming volume Outgoing volume All that flows in flows out (fluid incompressible – density const) luid Continuity equation =R rate 14 “ the narrower – the faster” the Continuity equation. Sample problem. What is the volume flow rate from the faucet? 15 Conservation laws. Energy. Bernoulli equation or work work per unit volume volume kinetic energy kinetic per unit volume per potential energy potential per unit volume per For constant “y”, faster flowing fluids have lower pressure than slower flowing fluids 16 Bernoulli equation. Example. Bernoulli Example. Top view Not spinning: Not a Curve Ball Spinning: Curve Ball Figure taken from Georgia State University 17 Physics Department website Bernoulli equation. Applications. Bernoulli Applications. Lift force on airplane wing Curves represent velocity field lines: (analogously to electric field lines) denser lines imply greater speed, hence regions of lower pressure Velocity of air above wing greater than that under wing Pressure difference exerts Lift Force on wing 18 What we learned: Pressure & Pascal’s Law fluid pressure at all points in a connected body of an incompressible fluid at rest, which are at the same absolute height, are the same Archimedes’ principle & buoyancy Bouyant force = weight of liquid within volume displaced by body Equation of continuity (tthe narrower – the faster) he A1v1=A2v2 Bernoulli’s equation (faster flowing fluids have lower pressure) 19 Next Time Sound Sound Beats, Beats, , and shock waves 20 Creative problems (next Monday’s recitation). 1) Find the density of a cork, using a hard (massless) wire and a graduated jar. 2) Explain how the sprinkler works (Fig 1). 3) A tank is filled with water to a height H. A hole is punched in one of the walls at a depth h below the water surface (see figure below). What value of h would maximize the distance x? Check your prediction using a plastic bottle and water. Fig 1 Fig 2 21 ...
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