1. About Midterm Exam 3 l When and where çThurs April 21 th, 5:45-7:00 pm  TODAY! çRooms: Same as Exam I and II, See course webpage. çYour TA will give a brief review during the discussion session. l Coverage: Chapts 9 – 12 (4 chapters) l Format çClosed book, 20 multiple-choices questions (format as in practice exams) ç1 page 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc. çBring a calculator (but no lap-top computer). Only basic calculation functionality can be used. Bring a 2B pencil for Scantron. çFill in your ID and section # ! l Special requests: çIf different from Exam II, email me at than@hep.wisc.edu çOne alternative exam: 3:30pm – 4:45pm, Thurs April 21, Cham 5280 (as before). 15/14/2015Phys 201, Spring 2011

2. 5/14/2015Phys 201, Spring 20112 Physics 201: Lecture 25 Fluids (cont’d) l Today’s lecture will cover çPascal’s Principle, Archimedes’ Principle revisit çFluids in motion: Continuity & Bernoulli’s equation

3. 5/14/2015Phys 201, Spring 20113 Archimede’s and Pascal’s Principles Archimede’s Principle: Buoyant Force çweight of fluid displaced »B = ρ fluid g V displaced, W = ρ object g V object »object sinks if ρ object > ρ fluid »object floats if ρ object < ρ fluid If object stays floating: B=W »Therefore ρ fluid g V displaced = ρ object g V object »Therefore V displaced /V object = ρ object / ρ fluid A1A1 F1F1 F2F2 A1A1 A2A2

4. 5/14/2015Phys 201, Spring 20114 Two identical glasses are filled to the same level with water. One of the two glasses has plastic balls floating in it. If the density of the plastic balls is less than that of ice, which of the two glasses weighs more? 1. The glass without plastic balls 2. The glass with plastic balls 3. Both glasses weigh the same CORRECT The plastic balls displace exactly their own weight in water, so the two glasses weigh the same amount. Floating Balls

5. 5/14/2015Phys 201, Spring 20115 Two identical glasses are filled to the same level with water. Solid steel balls are at the bottom in one of the glasses. Which of the two glasses weighs more? 1. The glass without steel balls 2. The glass with steel balls 3. Both glasses weigh the same The steel balls sink. The buoyant force equal to the weight of the displaced water is not sufficient to counter the weight of the steel balls. Therefore, the glass with steel balls weighs more. CORRECT Sunken Balls

6. 5/14/2015Phys 201, Spring 20116 Fluid Flow Volume flow rate: ΔV/Δt = A Δd/Δt = Av (m 3 /s) No source, no sink Continuity: A 1 v 1 = A 2 v 2 = 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 Fluid flow without friction

7. 5/14/2015Phys 201, Spring 20117 Faucet 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 A1A1 A2A2 V1V1 V2V2 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.

8. 5/14/2015Phys 201, Spring 20118 An artery with cross sectional area of 1 cm 2 branches into 20 smaller arteries each with 0.5 cm 2 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

9. 5/14/2015Phys 201, Spring 20119 Bernoulli’s Equation

10. 5/14/2015Phys 201, Spring 201110 Bernoulli’s Equation l Pressure drops in a rapidly moving fluid çwhether or not the fluid is confined to a tube l For incompressible, frictionless fluid:

11. 5/14/2015Phys 201, Spring 201111 (a) 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/m 3. (b) Discuss whether this force is great enough to be effective for propelling a sail boat. 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

12. 5/14/2015Phys 201, Spring 201112 (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. Pressure drop

13. 5/14/2015Phys 201, Spring 201113 Velocity Measurement: Pitot tube Two openings at 1 and 2:

14. 5/14/2015Phys 201, Spring 201114 Torricelli’s Theorem h P 2 =P 1, v 2, h 2 P 1, v 1, h 1