Lesson Plans

Physics 1st Edition ©2002

by James S. Walker

Week 15

Chapter 15: Fluids

College Board Performance Objectives:

• Define the properties of fluids.
• In terms of structure, distinguish the differences between solids, liquids, gases, and plasma.
• Distinguish between mass density, weight density, and specific gravity.
• Define the concept of pressure and that of absolute pressure.
• State and apply Pascal's principle to physical situations.
• State Archimedes' principle and its relationship to buoyancy.
• Apply Archimedes' principle to floating and submersed bodies in a fluid.
• Understand the use of the equation of continuity and its application to ideal fluids.
• Understand the effect of friction on fluid flow through a horizontal pipe of circular cross section.
• Understand Bernoulli's equation and its application to ideal fluids.
• Demonstrate an understanding of the workings of an airfoil.
• Discuss surface tension and viscosity.
• Write Poiseuille's equation and give several examples.

College Board Lab Objectives:

• Determine the density of several solid objects with a density greater than water.
• Determine the density of a solid material with a density less than water.
• Determine the density of several liquids.
• Design an experiment to measure buoyant effects in fluids.
• Design and conduct an experiment to study and measure liquid viscosity.

Suggested Labs:

• Density and Specific Gravity
• Archimedes' Principle
• Viscosity

Resources:

• Student Edition — pp. 460–491
• Student Study Guide — pp. 254–271
• Instructor's Solution Manual Volume 1 — pp. 218–241
• Instructor's Solution Manual CD — Chapter 15.doc
• Instructor's Resource Guide — pp. 63–66
• Test Items File — pp. 184–202
• Media Portfolio CD — Lecture Resources Chapter 15

Pacing Guide:

• Density—day 1
• Pressure—day 1
• Static Equilibrium in Fluids; Pressure and Depth—days 1 and 2
• Archimedes' Principle and Buoyancy—days 1 and 2
• Applications of Archimedes' Principle—day 2
• Fluid Flow and Continuity—days 2 and 3
• Bernoulli's Equation—days 3 and 4
• Applications of Bernoulli's Equation—days 3 and 4
• Viscosity and Surface Tension—day 4
• Lab—day 5
• Block Scheduling
  Density, Pressure, Static Equilibrium in Fluids, and Archimedes' Principle and Buoyancy require one block. Applications of Archimedes' Principle, Fluid Flow and Continuity and Bernoulli's Equation require a second block. Applications of Bernoulli's Equation, Viscosity and Surface Tension require one block. Stress problem solving with Bernoulli's equation and the equation of continuity.

Key Words:

Critical Thinking Questions:

1. A metal object has a weight of 95.0 N in air and 80.5 N when immersed in water. (a) Determine the volume of the object. (b) Calculate the mass density of the object. (c) The same object is submerged in a liquid where its apparent weight is 84.5 N. What is the mass density of the liquid?
2. Water flows smoothly at a speed v through a cylindrical tube of radius R. What is the speed of the water at the point where the tube is reduced to a radius of R/8?
3. Water enters a building through an 8.0 cm diameter pipe with a speed of 1.5 m/s. The water exits 18.0 m above a 3.0 cm diameter pipe with a velocity of 10.7 m/s. What is the pressure differential between these two points?
4. Old Faithful periodically ejects a stream of water that reaches a height of 36.6 m. (a) What excess pressure within Old Faithful is required to cause the stream to reach this height? (b) What is the velocity of the water stream as it emerges?
5. A deep sea submersible vehicle dives to a depth of 2500 m in the ocean. What pressure is exerted on it (a) Pa and (b) atmospheres?
6. Solve problem 40 on p. 495 in the textbook.
7. Solve problem 82 on p. 497 in the textbook.

Answers: 1. (a) 1.48x10^–3 m³, (b) 6543 kg/m³, (c) 723 kg/m³; 2. v₂ = 64v₁; 3. 2.3x10⁵ Pa; 4. (a) 359 kPa and (b) 26.7 m/s; 5. (a) 2.55x10⁷ Pa and (b) 251 atm; 6. (a) 1.0 N, (b) The tension stays the same because the only quantity that changes with depth is pressure. The buoyant force and, thus, the tension don't depend on pressure. (c) 4.0 m/s² upward; 7. 4.4 m

Troubleshooting Tips/Error Traps:

• Stress the differences between mass density, weight density, and specific gravity with examples.
• Stress that objects that sink in a fluid will have a buoyant force acting on them.
• Expressing pressure is complicated. Students are often confused when subjected to pressure units: pascal, atmosphere, in. of Hg, mm of Hg, torr, bar, psi, and other ways of expressing pressure. Explain proper use. Usually, a historical background can be given to show why all these different units exist. Applying dimensional analysis will help show the relationships.
• Students will usually be confused when calculating the pressure due to a static column of fluid. The stumbling block is whether or not to include atmospheric pressure. Provide examples that show that atmospheric pressure must be added to the calculations.
• When making calculations with buoyancy, students often tend to use the weight of the body instead of the weight of an equivalent volume of the fluid being displaced.
• Use of Bernoulli's equation requires consistency in using units and proper identification of terms.
• Students may be confused in solving problems involving the SI pressure unit the pascal, (Pa). Express the pascal in newtons per square meter (1 PA = 1 N/m²).

End of Chapter Activity:

1. A pressure of 1 pascal is equal to
   1. 1 atmosphere.
   2. 1 kg/m³.
   3. 1 bar.
   4. 1 N/m².
   5. 1 mm of Hg.
2. The density of a material is the
   1. product of mass and volume.
   2. volume divided by the mass.
   3. mass divided by the volume.
   4. force divided by the cross sectional area.
   5. force multiplied by the cross sectional area.
3. The buoyant force of a fluid is
   1. the product of the volume of the displaced fluid and the mass density of the object.
   2. a function of the mass of the submerged object.
   3. always greater than the weight of the submerged object.
   4. less than the weight of the displaced fluid if the object sinks.
   5. equal to the weight of the displaced fluid.
4. A cylindrical storage tank with a radius of 7.50 m and height of 10.0 m is filled with water. What is the pressure at the bottom of this tank?
   1. 9800 N/m²
   2. 9.8x10⁴ N/m²
   3. 9.8x10⁵ N/m²
   4. 9.8 kPa
   5. 980 kPa
5. When a block of plastic floats in water, the buoyant force acting on it is equal to the
   1. weight of the plastic block.
   2. mass of the plastic block.
   3. difference of the plastic block and the weight of the displaced water.
   4. product of the surface area of the block and mass of water displaced.
   5. product of the surface area of the block and weight of water displaced.
6. The two pistons in a hydraulic lift have radii of 2.67 cm and 20.00 cm respectively. What force must be applied to the 2.67 cm piston so that a 2.0x10³ kg mass resting on the 20.0 cm piston is lifted?
   1. 35 N
   2. 0.27 kN
   3. 0.35 kN
   4. 1.5 kN
   5. 3.0 kN
7. A cubic block of metal measurinh 0.10 m on a side and having a weight of 87.8 N in air is suspended in water. What is the weight of the block in water?
   1. 62 N
   2. 68 N
   3. 72 N
   4. 78 N
   5. 82 N
8. An incompressible, ideal fluid flows through a horizontal pipe and encounters a region where the diameter is doubled. The ratio of the fluid velocity in the larger diameter pipe to that of the smaller diameter is
   1. one to two.
   2. one to 1.414.
   3. one to four.
   4. two to one.
   5. four to one.
9. A wood block floats with 65% of its entire volume submersed in water. What is the mass density of the wood?
   1. 3.5 kg/m³
   2. 6.5 kg/m³
   3. 350 kg/m³
   4. 650 kg/m³
   5. 980 kg/m³
10. If the flow rate of water moving through a 4.0 cm diameter pipe is 8x10^–3 m³/s, the average fluid speed in the pipe is
    1. 0.064 m/s
    2. 0.640 m/s
    3. 1.00 m/s
    4. 2.42 m/s
    5. 3.20 m/s

Answers: 1 (d), 2 (c), 3 (e), 4 (b), 5 (a), 6 (c), 7 (d), 8 (c), 9 (d), 10 (b)

Suggested Conceptual Questions:

Suggested Problem Assignments: