PHYS 1443 – Section 003 Lecture #20Density and Specific GravityFluid and PressureExample for PressureVariation of Pressure and DepthPascal’s Law and HydraulicsExample for Pascal’s LawSlide 8Slide 9Absolute and Relative PressureBuoyant Forces and Archimedes’ PrincipleMore Archimedes’ PrincipleSlide 13Example for Archimedes’ PrincipleExample for Buoyant ForceMonday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu1PHYS 1443 – Section 003Lecture #20Monday, Nov. 17, 2003Dr. Jaehoon Yu1. Density and Specific Gravity2. Fluid and Pressure3. Absolute and Relative Pressure4. Pascal’s Law5. Buoyant Force and Archimedes’ PrincipleWednesday’s lecture will be given by the mystery person!!Quiz #4 on Wednesday, Nov. 19, 2003!!Monday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu2Density and Specific GravityDensity, (rho) , of an object is defined as mass per unit volume VMUnit? Dimension? 3/ mkg][3MLSpecific Gravity of a substance is defined as the ratio of the density of the substance to that of water at 4.0 oC (H2O=1.00g/cm3).OHSG2substanceUnit? Dimension? None None What do you think would happen of a substance in the water dependent on SG?1SG1SGSink in the waterFloat on the surfaceMonday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu3Fluid and PressureWhat are the three states of matter? Solid, Liquid, and GasFluid cannot exert shearing or tensile stress. Thus, the only force the fluid exerts on an object immersed in it is the forces perpendicular to the surfaces of the object.AFP How do you distinguish them?By the time it takes for a particular substance to change its shape in reaction to external forces.What is a fluid?A collection of molecules that are randomly arranged and loosely bound by forces between them or by the external container.We will first learn about mechanics of fluid at rest, fluid statics. In what way do you think fluid exerts stress on the object submerged in it?This force by the fluid on an object usually is expressed in the form of the force on a unit area at the given depth, the pressure, defined asNote that pressure is a scalar quantity because it’s the magnitude of the force on a surface area A.What is the unit and dimension of pressure?Expression of pressure for an infinitesimal area dA by the force dF isdAdFP Unit:N/m2Dim.: [M][L-1][T-2]Special SI unit for pressure is Pascal2/11 mNPa Monday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu4Example for PressureThe mattress of a water bed is 2.00m long by 2.00m wide and 30.0cm deep. a) Find the weight of the water in the mattress. The volume density of water at the normal condition (0oC and 1 atm) is 1000kg/m3. So the total mass of the water in the mattress is Since the surface area of the mattress is 4.00 m2, the pressure exerted on the floor ismPTherefore the weight of the water in the mattress is Wb) Find the pressure exerted by the water on the floor when the bed rests in its normal position, assuming the entire lower surface of the mattress makes contact with the floor.MWVkg31020.1300.000.200.2100 0 mgN431018.18.91020.1 AFAmg341095.200.41018.1Monday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu5Variation of Pressure and DepthWater pressure increases as a function of depth, and the air pressure decreases as a function of altitude. Why?If the liquid in the cylinder is the same substance as the fluid, the mass of the liquid in the cylinder is MgAPPA 0It seems that the pressure has a lot to do with the total mass of the fluid above the object that puts weight on the object.Let’s consider a liquid contained in a cylinder with height h and cross sectional area A immersed in a fluid of density at rest, as shown in the figure, and the system is in its equilibrium.The pressure at the depth h below the surface of a fluid open to the atmosphere is greater than atmospheric pressure by gh.Therefore, we obtainAtmospheric pressure P0 isPaatm510013.100.1 P0APAMghMSince the system is in its equilibriumPWhat else can you learn from this?VAhAhgAPPA00ghP0Monday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu6Pascal’s Law and HydraulicsA change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container.The resultant pressure P at any given depth h increases as much as the change in P0. This is the principle behind hydraulic pressure. How?Therefore, the resultant force F2 isWhat happens if P0is changed?PSince the pressure change caused by the the force F1 applied on to the area A1 is transmitted to the F2 on an area A2.ghPP0This seems to violate some kind of conservation law, doesn’t it?d1d2F1A1A2F22FIn other words, the force gets multiplied by the ratio of the areas A2/A1 is transmitted to the F2 on the surface.No, the actual displaced volume of the fluid is the same. And the work done by the forces are still the same.2F11AF22AF121Fdd112FAAMonday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu7Example for Pascal’s LawIn a car lift used in a service station, compressed air exerts a force on a small piston that has a circular cross section and a radius of 5.00cm. This pressure is transmitted by a liquid to a piston that has a radius of 15.0cm. What force must the compressed air exert to lift a car weighing 13,300N? What air pressure produces this force?PUsing the Pascal’s law, one can deduce the relationship between the forces, the force exerted by the compressed air is1FTherefore the necessary pressure of the compressed air is212FAA N3422104 8.11033.105.015.011AF Pa5231088.11048.10 0Monday, Nov. 17, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu8Example for Pascal’s LawEstimate the force exerted on your eardrum due to the water above when you are swimming at the bottom of the pool with a depth 5.0 m.We first need to find out the pressure difference that is being exerted on the eardrum. Then estimate the area of the eardrum to find out the force exerted on the eardrum.0PP FSince the outward pressure in the middle of the eardrum is the same as normal air pressureEstimating the surface area of the eardrum at 1.0cm2=1.0x10-4 m2, we obtainghWPa4109.40.58.910 00 APP0N9.4100.1109.444Monday,
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