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UW-Madison PHYSICS 207 - Fluids

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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 =


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UW-Madison PHYSICS 207 - Fluids

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