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Midterm Exam 3 Today - April 21st, 5:45-7:00pm

This is a reminder about the Midterm Exam 3 for Physics 201. It will cover chapters 9-12 and follow a multiple-choice format. Make sure to bring a calculator, a 2B pencil, and a self-prepared formula sheet. Special requests should be emailed to the instructor.

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Midterm Exam 3 Today - April 21st, 5:45-7:00pm

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  1. About Midterm Exam 3 • When and where • Thurs April 21th , 5:45-7:00 pm  TODAY! • Rooms: Same as Exam I and II, See course webpage. • Your TA will give a brief review during the discussion session. • Coverage: Chapts 9 – 12 (4 chapters) • Format • Closed book, 20 multiple-choices questions (format as in practice exams) • 1 page 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc. • Bring a calculator (but no lap-top computer). Only basic calculation functionality can be used. Bring a 2B pencil for Scantron. • Fill in your ID and section # ! • Special requests: • If different from Exam II, email me at than@hep.wisc.edu • One alternative exam: 3:30pm – 4:45pm, Thurs April 21, Cham 5280 (as before). Phys 201, Spring 2011

  2. Physics 201: Lecture 25Fluids (cont’d) • Today’s lecture will cover • Pascal’s Principle, Archimedes’ Principle revisit • Fluids in motion: Continuity & Bernoulli’s equation Phys 201, Spring 2011

  3. Archimede’s and Pascal’s Principles F1 A1 A1 F2 A2 • Pascal’s Principle: A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. • This principle is used in hydraulic system • P1 = P2 • (F1 / A1) = (F2 / A2) Archimede’s Principle: Buoyant Force • weight of fluid displaced • B = ρfluid gVdisplaced, W = ρobject gVobject • object sinks if ρobject > ρfluid • object floats if ρobject < ρfluid If object stays floating: B=W • Therefore ρfluid gVdisplaced = ρobject gVobject • Therefore Vdisplaced/Vobject = ρobject / ρfluid Phys 201, Spring 2011

  4. Fluid Flow Fluid flow without friction • Volume flow rate: ΔV/Δt = A Δd/Δt = Av (m3/s) • No source, no sink • Continuity: A1 v1 = A2 v2 = Flow rate • i.e., flow rate the same everywhere • e.g., flow of river: more slowly in wider area • Water through a narrow hose moves faster Phys 201, Spring 2011

  5. Faucet A1 V1 A2 V2 A stream of water gets narrower as it falls from a faucet (try it & see). Explanation: the equation of continuity The velocity of the liquid increases as the water falls due to gravity. If the volume flow rate is conserved, them the cross-sectional area must decrease in order to compensate The density of the water is the same no matter where it is in space and time, so as it falls down and accelerates because of gravity,the water is in a sense stretched, so it thins out at the end. Phys 201, Spring 2011

  6. An artery with cross sectional area of 1 cm2 branches into 20 smaller arteries each with 0.5 cm2 cross sectional area. If the velocity of blood in thicker artery is v, what is the velocity of the blood in the thinner arteries? 1. 0.1 v 2. 0.2 v 3. 0.5 v 4. v 5. 2 v Phys 201, Spring 2011

  7. Bernoulli’s Equation Bernoulli’s Equation Phys 201, Spring 2011

  8. Bernoulli’s Equation • Pressure drops in a rapidly moving fluid • whether or not the fluid is confined to a tube • For incompressible, frictionless fluid: Phys 201, Spring 2011

  9. Applications of Bernoulli’s Principle • Wings and sails • Higher velocity on one side of sail or wing versus the other results in a pressure difference that can even allow the boat to sail into the wind Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 6 m/s parallel to its front surface and 3.5 m/s along its back surface. Take the density of air to be 1.29 kg/m3. (b) Discuss whether this force is great enough to be effective for propelling a sail boat. Phys 201, Spring 2011

  10. Pressure drop (a) What is the pressure drop due to Bernoulli effect as water goes into a 3 cm diameter nozzle from a 9 cm diameter fire hose while carrying a flow of 40 L/s? (b) To what maximum height above the nozzle can this water rise neglecting air resistance. Phys 201, Spring 2011

  11. Velocity Measurement: Pitot tube Two openings at 1 and 2: Phys 201, Spring 2011

  12. Torricelli’s Theorem P1, v1, h1 h P2=P1 , v2 , h2 Phys 201, Spring 2011

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