Page Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 1Lecture 21Goals:Goals:••Chapter 15, fluids Chapter 15, fluids ••AssignmentAssignment HW-8 due Tuesday, Nov 15 Wednesday: Read through Chapter 16Physics 207: Lecture 21, Pg 2FluidslAnother parameter Pressure (force per unit area) P=F/ASI unit for pressure is 1 Pascal = 1 N/m21 atm = 1.013 x105Pa= 1013 mbar= 760 Torr= 14.7 lb/ in2(=PSI)lThe atmospheric pressure at sea-level isPage Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 3Incompressible fluids (liquids) Area=AylWhat is the pressure at the bottom of the container?F=Mg=ρVgF=ρAygPressure=F/A=ρygP=ρgyPhysics 207: Lecture 21, Pg 4What if there is outside gas?Area=AyPressure=P0F=P0A+MgP=P0+ρgyP0APage Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 5Area=Ay1Pressure=P0P1=P0+ρgy1P2=P0+ρgy2y2P2-P1=ρg(y2-y1)Physics 207: Lecture 21, Pg 6What is the pressure 10m down?P=P0+ρgy=P0+(1000 kg/m3)(10 m/s2) (10 m)=P0+105N/m2= approximately 2 atmlHome exercise: what is the pressure 6 miles down?Page Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 7y1y2lConsider the open, connected container shown below. How would the two heights compare?A)y1<y2B)y1=y2C)y1>y2Physics 207: Lecture 21, Pg 8Pressure vs. DepthlIn a connected liquid, the pressure is the same at all points through a horizontal line.pPage Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 9Pressure Measurements: BarometerlInvented by TorricellilA long closed tube is filled with mercury and inverted in a dish of mercury The closed end is nearly a vacuumlMeasures atmospheric pressure as 1 atm = 0.760 m (of Hg)P0=ρghPhysics 207: Lecture 21, Pg 10Archimedes’ PrinciplelSuppose we weigh an object in air (1) and in water (2).How do these weights compare? W2?W1a) W1< W2b) W1= W2c) W1> W2Page Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 11Buoyancyy1y2F2F1F2=P2AreaF1=P1AreaF2-F1=(P2-P1) Area=ρg(y2-y1) Area=ρ g Vobject=weight of the fluiddisplaced by the objectPhysics 207: Lecture 21, Pg 12Float or sink?lIf we immerse the object completely in the liquid:weight of the object < bouyant forcefloatρobject< ρfluidfloatlHow does a steel ship float?A)ρsteel< ρwaterB)overall density of the ship < ρwaterC) none of the aboveρobjectVobject< ρfluidVobjectfloatPage Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 13FloatlIf the object floats, then we can find the portion of the object that will be immersed in the fluidFBFB=mgVimmersedρfluidg =Vobjectρobjectg Vimmersedρfluid=VobjectρobjectPhysics 207: Lecture 21, Pg 14Pascal’s PrincipleAny change in the pressure applied to an enclosed fluid is transmitted to every portion of the fluid and to the walls of the containing vessel.yPressure=P0P=P0+ρgyPage Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 15Pascal’s Principle in action: Hydraulics, a force amplifierlConsider the system shown: A downward force F1is applied to the piston of area A1. This force is transmitted through the liquid to create an upward force F2. Pascal’s Principle says that increased pressure from F1(F1/A1) is transmitted throughout the liquid.FF12d2d1AA21P1= P2 F1/ A1 = F2/ A2A2/ A1 = F2/ F1Physics 207: Lecture 21, Pg 16Fluid dynamicslTo describe fluid motion, we need something that describes flow: Velocity vlIdeal fluid model: Incompressible fluid. No viscosity (no friction). Steady flowPage Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 17Types of Fluid FlowPhysics 207: Lecture 21, Pg 18StreamlineslKeep track of a small portion of the fluid:Page Physics 207 – Lecture 21Physics 207: Lecture 21, Pg 19Continuity equationA1A2v1v2A1v1: units of m2m/s = volume/sA2v2: units of m2m/s =
View Full Document