Physics 101: Lecture 18 Fluids II

Transcription

1 Exam III Physics 101: Lecture 18 Fluids II Textbook Sections Physics 101: Lecture 18, Pg 1

2 Review Static Fluids Pressure is force exerted by molecules bouncing off container P = F/A Gravity/weight effects pressure P = P 0 + rgd Buoyant force is weight of displaced fluid. F = r g V Today include moving fluids! A 1 v 1 = A v P 1 +rgy 1 + ½ rv 1 = P +rgy + ½rv Physics 101: Lecture 18, Pg

3 Archimedes Principle Determine force of fluid on immersed cube Draw FBD» F B = F F 1» = P A P 1 A» = (P P 1 )A» = r g d A» = r g V Buoyant force is weight of displaced fluid! Physics 101: Lecture 18, Pg 3

4 Archimedes Example F b A cube of plastic 4.0 cm on a side with density = 0.8 g/cm 3 is floating in the water. When a 9 gram coin is placed on the block, how much does it sink below the water surface? S F = m a F b Mg mg = 0 r g V disp = (M+m) g V disp = (M+m) / r h A = (M+m) / r h = (M + m)/ (r A) = (51.+9)/(1 x 4 x 4) = 3.76 cm h Mg mg M = r plastic V cube = 4x4x4x0.8 = 51. g Physics 101: Lecture 18, Pg 4

5 Archimedes Principle Buoyant Force (F B ) weight of fluid displaced F B = r fluid Vol displaced g F g = mg = r object Vol object g object sinks if r object > r fluid object floats if r object < r fluid If object floats F B = F g Therefore: r fluid g Vol displ. = r object g Vol object Therefore: Vol displ. /Vol object = r object / r fluid Physics 101: Lecture 18, Pg 5

6 Suppose you float a large ice-cube in a glass of water, and that after you place the ice in the glass the level of the water is at the very brim. When the ice melts, the level of the water in the glass will: 1. Go up, causing the water to spill out of the glass.. Go down. Checkpoint Q1 3. Stay the same. CORRECT F B = r W g Vol displaced W = r ice g Vol ice r W g Vol melted_ice Physics 101: Lecture 18, Pg 6

7 Checkpoint Q Which weighs more: 1. A large bathtub filled to the brim with water.. A large bathtub filled to the brim with water with a battle-ship floating in it. 3. They will weigh the same. Tub of water + ship CORRECT Tub of water Weight of ship = Buoyant force = Weight of displaced water Overflowed water Physics 101: Lecture 18, Pg 7

8 Continuity of Fluid Flow Watch plug of fluid moving through the narrow part of the tube (A 1 ) Time for plug to pass point Dt = x 1 / v 1 Mass of fluid in plug m 1 = r Vol 1 =r A 1 x 1 or m 1 = ra 1 v 1 Dt Watch plug of fluid moving through the wide part of the tube (A ) Time for plug to pass point Dt = x / v Mass of fluid in plug m = r Vol =r A x or m = ra v Dt Continuity Equation says m 1 = m fluid isn t building up or disappearing A 1 v 1 = A v Physics 101: Lecture 18, Pg 8

9 Faucet Prelecture A stream of water gets narrower as it falls from a faucet (try it & see). Explain this phenomenon using the equation of V continuity 1 A 1 A As the water flows down, gravity makes the velocity of the water go faster so the area of the water decreases. V Because it scared of the dirty dishes in the sink. wow it does! My faucet does not act this way Physics 101: Lecture 18, Pg 9

10 Fluid Flow Concepts r A 1 P 1 v 1 A P v Mass flow rate: rav (kg/s) Volume flow rate: Av (m 3 /s) Continuity: ra 1 v 1 = ra v i.e., mass flow rate the same everywhere e.g., flow of river Physics 101: Lecture 18, Pg 10

11 Pressure, Flow and Work Continuity Equation says fluid speeds up going to smaller opening, slows down going to larger opening A 1 v 1 = A v A 1 Dx 1 = A Dx = V Acceleration due to change in pressure. P 1 > P Smaller tube has faster water and LOWER pressure Demo Change in pressure does work! Recall: W=F d = PA d = P Vol W = F 1 Dx 1 - F Dx =P 1 A 1 Dx 1 - P A Dx = (P 1 P )V olume Physics 101: Lecture 18, Pg 11

12 Pressure ACT What will happen when I blow air between the two plates? A) Move Apart B) Come Together C) Nothing There is air pushing on both sides of plates. If we get rid of the air in the middle, then just have air on the outside pushing them together. Physics 101: Lecture 18, Pg 1

13 Bernoulli s Eqs. And Work Consider tube where both Area, height change. W = DK + DU (P 1 -P ) V = ½ m (v v 1 ) + mg(y -y 1 ) (P 1 -P ) V = ½ rv (v v 1 ) + rvg(y -y 1 ) P 1 +rgy 1 + ½ rv 1 = P +rgy + ½rv Note: W=F d = PA d = P V Physics 101: Lecture 18, Pg 13

14 Bernoulli ACT Through which hole will the water come out fastest? P 1 +rgy 1 + ½ rv 1 = P +rgy + ½rv Note: All three holes have same pressure P=1 Atmosphere rgy 1 + ½ rv 1 = rgy + ½rv gy 1 + ½ v 1 = gy + ½v A B C Smaller y gives larger v. Hole C is fastest Physics 101: Lecture 18, Pg 14

15 Act A large bucket full of water has two drains. One is a hole in the side of the bucket at the bottom, and the other is a pipe coming out of the bucket near the top, which bent is downward such that the bottom of this pipe even with the other hole, like in the picture below: Though which drain is the water spraying out with the highest speed? 1. The hole. The pipe 3. Same CORRECT Both are exiting at the same height! Physics 101: Lecture 18, Pg 15

16 Lift a House Calculate the net lift on a 15 m x 15 m house when a 30 m/s wind (1.9 kg/m 3 ) blows over the top. P 1 +rgy 1 + ½ rv 1 = P +rgy + ½rv P 1 P = ½ r (v v 1 ) F = P A = ½ r (v v 1 ) = ½ (1.9) (30 ) N / m = 581 N/ m = 581 N/ m (15 m)(15 m) = 131,000 N = 9,000 pounds! (note roof weighs 15,000 lbs) Physics 101: Lecture 18, Pg 16 48

17 Example (like HW) A garden hose w/ inner diameter cm, carries water at.0 m/s. To spray your friend, you place your thumb over the nozzle giving an effective opening diameter of 0.5 cm. What is the speed of the water exiting the hose? What is the pressure difference between inside the hose and outside? Continuity Equation A 1 v 1 = A v v = v 1 ( A 1 /A ) = v 1 ( π r 1 / π r ) = m/s x 16 = 3 m/s Bernoulli Equation P 1 +rgy 1 + ½ rv 1 = P +rgy + ½rv P 1 P = ½ r (v v 1 ) = ½ x (1000 kg/m 3 ) (100 m /s ) = 5.1x10 5 PA Physics 101: Lecture 18, Pg 17

18 Fluid Flow Summary r A 1 P 1 v 1 A P v Mass flow rate: rav (kg/s) Volume flow rate: Av (m 3 /s) Continuity: ra 1 v 1 = ra v Bernoulli: P / rv 1 + rgh 1 = P + 1 / rv + rgh Physics 101: Lecture 18, Pg 18 50

19 Good luck on the exam! Physics 101: Lecture 18, Pg 19