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Lecture 14: Fluids II Homework #13 - Density, Pressure, Buoyancy, and Fluid Flow Equations

This lecture covers topics such as density, pressure, buoyancy, the equation of continuity, and Bernoulli's equation. Several example problems are provided to illustrate these concepts. Homework problems from Chapter 14 are assigned.

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Lecture 14: Fluids II Homework #13 - Density, Pressure, Buoyancy, and Fluid Flow Equations

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  1. Lecture 14.2 Fluids II

  2. HW #13 (Chapter 14) • Read Sections 14-1 to 14.5 • Problems: 14.4, 14.26, 14.35, 14.39, 14.59 • Due: Thursday May 8

  3. Ideas From Last Thursday • Density is a material property •  = mas/volume • Pressure is force/area (unit Pascal = 1 N/m2) • Fluids transfer pressure • Example: hydraulic lift • Pressure increases as you go down in a fluid • P = P0 +gh • Buoyancy is an upward force equal to the weight of the displaced fluid

  4. New Ideas for Today • Equation of Continuity • Bernoulli’s Equation • Maybe thought on waves • Quiz

  5. Pascal’s Law Pressure is the same at the height in a fluid F1/A1 = F2/A2

  6. Slightly harder Buoyancy problem A raft consists of a block of wood (p = 0.7 x 103 kg/m3) that is 2.0 m by 2.0 m by 0.5 m. How many 100 kg people will fit on the raft before it sinks? Steps: 1) Physical Diagram 2) Free body diagram 3) Equation that balances forces 4) Solve

  7. Q14.2 Concept Question A block of ice (density 920 kg/m3) and a block of iron (density 7800 kg/m3) are both submerged in a fluid. Both blocks have the same volume. Which block experiences the greater buoyant force? A. the block of ice B. the block of iron C. Both experience the same buoyant force. D. The answer depends on the density of the fluid.

  8. Fluid flow

  9. Fluid flow II: Equation of Continuity • The incompressibility of fluids allows calculations to be made even as pipes change. A1v1 = A2v2

  10. Bernoulli’s equation Equation allows us to calculate the effect of fluid flow on pressure Other things being equal: As velocity goes up pressure goes down!

  11. The Venturi meter

  12. Q14.5 Equation of Continuity P Q radius R radius 2R A. 4 times the fluid speed. B. 2 times the fluid speed. C. the same fluid speed. D. 1/2 the fluid speed. E. 1/4 the fluid speed. An incompressible fluid flows through a pipe of varying radius (shown in cross-section). Compared to the fluid at point P, the fluid at point Q has

  13. Q14.4 Bernoulli’s Principle P Q radius R radius 2R An incompressible fluid flows through a pipe of varying radius (shown in cross-section). Compared to the fluid at point P, the fluid at point Q has A. greater pressure and greater volume flow rate. B. greater pressure and the same volume flow rate. C. the same pressure and greater volume flow rate. D. lower pressure and the same volume flow rate. E. none of the above

  14. Bernoulli Problem (med) A large tower that is full of water consist of a cylinder that is 10 m high. It is open at the top. You drill two small holes in the tower, one half way up and a second near the bottom. Compare the speed of the water coming out each hole Steps: 1) draw system 2) locate points to apply Bernoulli’s equation 3) write equations 4) solve

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