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Fluids II Exam Correction: Archimedes' Principle and Fluid Flow Concepts

This lecture covers the concept of Archimedes' Principle and its application in determining the force of fluid on an immersed cube. It also discusses fluid flow concepts such as mass flow rate, volume flow rate, continuity equation, and Bernoulli's equation. Examples and calculations are provided.

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Fluids II Exam Correction: Archimedes' Principle and Fluid Flow Concepts

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  1. Exam III Physics 101: Lecture 17 Fluids IIExam correction today during lab time in 242 Loomis

  2. Archimedes’ Principle • Determine force of fluid on immersed cube • Draw FBD • Buoyant force is weight of displaced fluid! 43

  3. Fb mg Mg Archimedes Example A cube of plastic 4.0 cm on a side with density = 0.8 g/cm3 is floating in the water. When a 9 gram coin is placed on the block, how much sinks below water surface? h 12

  4. Question 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. 2. Go down. 3. Stay the same. Must be same! 14

  5. Archimedes’ Principle • If object is floating… 8

  6. Archimedes’ Principle • Which picture looks like an ice cube floating?… B C A 8

  7. How much of the Iceberg can you see?

  8. Where are you going to hit the Iceberg?

  9. Tub of water + ship Tub of water Overflowed water Question 2 Which weighs more: 1. A large bathtub filled to the brim with water. 2. A large bathtub filled to the brim with water with a battle-ship floating in it. 3. They will weigh the same. Weight of ship = Buoyant force = Weight of displaced water 16

  10. r A1P1 v1 A2 P2 v2 Fluid Flow Concepts • Mass flow rate: Av (kg/s) • Volume flow rate: Av (m3/s) • Continuity: A1 v1 = A2 v2 • i.e., mass flow rate the same everywhere • e.g., flow of river 21

  11. r A1P1 v1 A2 P2 v2 Bernoulli’s Eq. And Work • W = DK + DU • W=F d = PA d = P V (P1-P2) V = ½ m (v22 – v12) + mg(y2-y1) (P1-P2) V = ½ rV (v22 – v12) + rVg(y2-y1) P1+rgy1 + ½ rv12 = P2+rgy2 + ½rv22 Compare P1, P2 33

  12. Example: hose A garden hose w/ inner diameter 2 cm, carries water at 2.0 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 Bernoulli Equation

  13. Example: Lift a House Calculate the net lift on a 15 m x 15 m house when a 30 m/s wind (1.29 kg/m3) blows over the top. 48

  14. Is Bernoulli’s Eq. involved in airfoil lift?

  15. r A1P1 v1 A2 P2 v2 Fluid Flow Summary • Mass flow rate: Av (kg/s) • Volume flow rate: Av (m3/s) • Continuity: A1 v1 = A2 v2 • Bernoulli: P1 + 1/2v12 + gh1 = P2 + 1/2v22 + gh2 50

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