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Lecture 21 Goals: • Chapter 15, fluids • Assignment HW-8 due Tuesday, Nov 15 Wednesday: Read through Chapter 16 Physics 207: Lecture 21, Pg 1 Fluids Another parameter Pressure (force per unit area) P=F/A SI unit for pressure is 1 Pascal = 1 N/m2 The atmospheric pressure at sea-level is 1 atm = 1.013 x105 Pa = 1013 mbar = 760 Torr = 14.7 lb/ in2 (=PSI) Physics 207: Lecture 21, Pg 2 Incompressible fluids (liquids) What is the pressure at the bottom of the container? F=Mg=ρVg F=ρAyg Pressure=F/A=ρyg y P=ρgy Area=A Physics 207: Lecture 21, Pg 3 What if there is outside gas? Pressure=P0 F=P0A+Mg P0A P=P0+ρgy y Area=A Physics 207: Lecture 21, Pg 4 P1=P0+ρgy1 Pressure=P0 y1 P2=P0+ρgy2 y2 P2-P1=ρg(y2-y1) Area=A Physics 207: Lecture 21, Pg 5 What is the pressure 10m down? P=P0+ρgy =P0+(1000 kg/m3)(10 m/s2) (10 m) =P0+105 N/m2 = approximately 2 atm Home exercise: what is the pressure 6 miles down? Physics 207: Lecture 21, Pg 6 Consider the open, connected container shown below. How would the two heights compare? A)y1<y2 B)y1=y2 C)y1>y2 y1 y2 Physics 207: Lecture 21, Pg 7 Pressure vs. Depth In a connected liquid, the pressure is the same at all points through a horizontal line. p Physics 207: Lecture 21, Pg 8 Pressure Measurements: Barometer Invented by Torricelli A long closed tube is filled with mercury and inverted in a dish of mercury The closed end is nearly a vacuum P0=ρgh Measures atmospheric pressure as 1 atm = 0.760 m (of Hg) Physics 207: Lecture 21, Pg 9 Archimedes’ Principle Suppose we weigh an object in air (1) and in water (2). W1 W2? How do these weights compare? a) W1 < W2 b) W1 = W2 c) W1 > W2 Physics 207: Lecture 21, Pg 10 Buoyancy y1 F1 y2 F2 F2=P2 Area F1=P1 Area F2-F1=(P2-P1) Area =ρg(y2-y1) Area =ρ g Vobject =weight of the fluid displaced by the object Physics 207: Lecture 21, Pg 11 Float or sink? If we immerse the object completely in the liquid: weight of the object < bouyant force float ρobject Vobject< ρfluid Vobject float ρobject < ρfluid float How does a steel ship float? A)ρsteel < ρwater B)overall density of the ship < ρwater C) none of the above Physics 207: Lecture 21, Pg 12 Float If the object floats, then we can find the portion of the object that will be immersed in the fluid FB=mg Vimmersed ρfluid g =Vobject ρobject g FB Vimmersed ρfluid =Vobject ρobject Physics 207: Lecture 21, Pg 13 Pascal’s Principle Any 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. Pressure=P0 y P=P0+ρgy Physics 207: Lecture 21, Pg 14 Pascal’s Principle in action: Hydraulics, a force amplifier F1 Consider the system shown: F2 A downward force F1 is 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. d2 d1 A1 A2 P1 = P2 F1 / A1 = F2 / A2 A2 / A1 = F2 / F1 Physics 207: Lecture 21, Pg 15 Fluid dynamics To describe fluid motion, we need something that describes flow: Velocity v Ideal fluid model: Incompressible fluid. No viscosity (no friction). Steady flow Physics 207: Lecture 21, Pg 16 Types of Fluid Flow Physics 207: Lecture 21, Pg 17 Streamlines Keep track of a small portion of the fluid: Physics 207: Lecture 21, Pg 18 Continuity equation A 2 A 1 v 1 v 2 A1v1 : units of m2 m/s = volume/s A2v2 : units of m2 m/s = volume/s A1v1=A2v2 Physics 207: Lecture 21, Pg 19