Physics 201, Lecture 25 Today s Topics n Fluid Mechanics (chapter 14) n Solids, Liquids, Gases, Plasmas n Pressure (14.1) n Pascal s Principle, Pressure Variation with Depth (14.2) n Pressure Measurement (14.3) States of Matter q 3+1 States: Solids, Liquids, Gases, (and Plasmas). q Solids, Liquids, and Gases are made of molecules Solids: Spacing and relative position of molecules are fixed fixed shape/volume (elasticity applies). Liquids: molecules randomly distributed but with strong bonds nearly fixed volume but no definitive shape. Gases: molecules randomly distributed, weak bonds. No definitive volume, no definitive shape Solid Liquid Gas Plasma Temperature Fluids q Fluids: Liquids or Gases Shape determined by container Close contact at boundaries. No macroscopic gaps Fluids can flow Forces exerted by fluids are always normal to the surface. (if no viscosity on smooth surface) q Fluids are matters: They are made of particles They have mass They have weight They carry energy They have velocity when flow Newton s Laws apply. Density = Mass/Volume ρ m/v Definable for solids and fluids Basic Unit: kg/m 3 Independent of shape Solids and liquids: ρ very weakly depends on temperature and pressure Gases: ρ strongly depends on temperature and pressure Solid form is not necessarily heavier than liquid form Density Substance Density ρ (10 3 kg/m 3 ) Water 1.00 Ice 0.917 Mercury 13.6 Lead 11.3 Copper 8.92 Iron 7.86 Aluminum 2.70 Wood 0.550 Blood 1.06 Oil 0.920 Room Air 0.00129 1
Pressure Force And Pressure q Fluid exerts force on the objects it contact: molecules constantly hit the surface F =Σ(Δmv/Δt) q Force exerted by fluid distributes over contact surface q Pressure: P = Force / Area P F/A Unit: N/m2 Pascal (Pa) Pressure depends on only the magnitude of F Pressure is also definable for solids when the contact surface is regular F=PA (or P=F/A) q Force: important when considering moving the whole object. (remember impulse?) q Pressure: force per area on local surface Be careful with p : momentum/power/pressure? Atmospheric Pressure q Even when there is no breeze, molecules in the air are constantly bombarding all surfaces Atmospheric pressure At sea level and at room temperature: Patmospheric = 1.01 x105 Pa = 1.01 x105 N/m2! This is a huge value! (see demos) Pascal s Principle q Pascal s Principle: Pressure is a contained fluid is transmitted to every point, in every direction, regardless of the shape of the container. Pressure is the same at same height/depth. Why? Simple, otherwise the fluid will flow until balance water q Demos: Quiz: How much weight a vacuum hook can hold. Accelerate a ping-pong ball by air pressure. oil Same level same pressure Regardless of shape, etc. (for same liquid) Magdeburg Hemispheres 1656, Magdeburg, Germany q The fluid pressure on a hard smooth surface is always perpendicular to the surface 2
Quick Quiz q Is P A = P B? Ø Answer no! fluids have different density. (P B >P A in this case) Quick Quiz q Is P A = P B? Ø Answer: Not necessary. Pascal s principle applies only for fluid within a single container. (no sealed blocker) A B A B C D fully sealed blocker q Is P C = P D? Ø Answer yes! same level same pressure regardless of shape Demo: Hydraulic Jack q Fluid transmits same pressure but not same force. P 2 = P 1 F 2 A 2 = F 1 F 2 F 1 = A 2 Variation Of Fluid Pressure With Depth q The pressure in a fluid at rest varies with depth h according to the expression: P= + ρgh h=depth The formula works for any shape q Derivation (again not required): Consider a cylinder of fluid volume of height h and top/bottom area A. (i.e. volume V=hA) The pressure at top: F 0 = A downwards The pressure at bottom: P F=PA upwards Equilibrium: F 0,F balance with weight F-F 0 -Mg =0 i.e. PA A ρhag =0 P = +ρgh 3
Example: Dam q Why the bottom of the dam is much thicker? Hydraulic Jack Again q Quick quiz: Why the equations here are not precise? P 2 = P 1 F 2 A 2 = F 1 +ρgh F 2 F 1 = A 2 Ø In practice, P 1 and P 2 are not at the same level. They could have small difference due to height difference. Demo/Exercise: Torricelli s Barometer q Shown in the figure is an exemplary barometer, express air pressure in terms of h. P B = = P atmospheric = 1x10 5 Pa P A = 0 + ρgh Vacuum P=0 Manometer q Manometer is a simple and effective device to measure pressure. q Principle diagrams: Pascal s Principle: P B = P A h= /(ρg) Mercury for H 2 O: ρ=1.0 x10 3 kg/m 3 h = 10.2 m for Hg: ρ=13.6 x10 3 kg/m 3 h =0.76m=760mm 4
Measuring Blood Pressure q Blood pressure is quite high, 120/80 mm of Hg Mercury (Hg) inside 5