Fluid Mechanics with teacher's notes

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$Holt Math Minnesota Test Prep Workbook for Grade 9$

$Math Skills: More Practice$

Section Review Bernoulli’s equation Copyright © by Holt, Rinehart and Winston. All rights reserved. 1. A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 16 m below the water level. If the rate of flow of water from the leak is 2.5 × 10 −3 m 3 /min, determine the following: a. the speed at which the water leaves the hole b. the diameter of the hole 2. A liquid with a density of 1.65 × 10 3 kg/m 3 flows through two horizontal sections of tubing joined end to end. In the first section, the crosssectional area is 10.0 cm 2 , the flow speed is 275 cm/s, and the pressure is 1.20 × 10 5 Pa. In the second section, the cross-sectional area is 2.50 cm 2 . Calculate the following: a. the flow speed in the smaller section b. the pressure in the smaller section 3. When a person inhales, air moves down the windpipe at 15 cm/s. The average flow speed of the air doubles when passing through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction. 1. The time required to fill a bucket with water from a certain garden hose is 30.0 s. If you cover part of the hose’s nozzle with your thumb so that the speed of the water leaving the nozzle doubles, how long does it take to fill the bucket? 2. Water at a pressure of 3.00 × 10 5 Pa flows through a horizontal pipe at a speed of 1.00 m/s. The pipe narrows to one-fourth its original diameter. Find the following: a. the flow speed in the narrow section b. the pressure in the narrow section 3. The water supply of a building is fed through a main entrance pipe that is 6.0 cm in diameter. A 2.0 cm diameter faucet tap positioned 2.00 m above the main pipe fills a 2.5 × 10 −2 m 3 container in 30.0 s. a. What is the speed at which the water leaves the faucet? b. What is the gauge pressure in the main pipe? PRACTICE 9D Fluid Mechanics 337 SECTION 9-3 PRACTICE GUIDE 9D Solving for: v PE Sample, 1, 2a; Ch. Rvw. 23–24 PW 5–7 PB 5–7 P PE 2b, 3; Ch. Rvw. 38, 39*, 58 PW Sample, 1–2 PB 8–10 h PE Ch. Rvw. 48*, 49*, 56* PW 3–4 PB Sample, 1–4 ANSWERS TO Practice 9D Bernoulli’s equation 1. a. 18 m/s b. 1.7 × 10 −3 m 2. a. 11.0 m/s b. 2.7 × 10 4 Pa 3. −4.4 × 10 −2 Pa Section Review ANSWERS 1. 30.0 s because the volume rate of flow is constant 2. a. 16.0 m/s b. 1.72 × 10 5 Pa 3. a. 2.7 m/s b. 2.32 × 10 4 Pa 337
Section 9-4 Demonstration 10 Temperature, pressure, and volume Purpose Demonstrate that the same amount of gas occupies a larger volume at a higher temperature. Materials Pyrex flask, balloon, water, Bunsen burner, goggles CAUTION Be sure to wear safety goggles at all times when operating the Bunsen burner, and use tongs when handling the heated glassware. Procedure Place a small amount of water in the flask, and cap it with the balloon. Emphasize that no gas can flow in or out of the flask or the balloon. Ask students what the air volume is in this closed system (about equal to that of the flask). Heat the flask until the balloon expands (no need to let water boil). Have students estimate and record the balloon’s approximate size. Ask them how much air is in the flask now (same volume, but fewer molecules) and in the balloon and flask together (same amount as before, but in a larger volume). Place the balloon under cold water (not the flask, to avoid breakage) to return it to its original size. 338 9-4 SECTION OBJECTIVES • Define the general properties of an ideal gas. • Use the ideal gas law to predict the properties of an ideal gas under different conditions. Figure 9-16 The balloon is inflated because the volume and pressure of the air inside are both increasing. 338 Chapter 9 9-4 Properties of gases GAS LAWS When the density of a gas is sufficiently low, the pressure, volume, and temperature of the gas tend to be related to one another in a fairly simple way. In addition, the relationship is a good approximation for the behavior of many real gases over a wide range of temperatures and pressures. These observations have led scientists to develop the concept of an ideal gas. Volume, pressure, and temperature are the three variables that completely describe the macroscopic state of an ideal gas. One of the most important equations in fluid mechanics relates these three quantities to each other. The ideal gas law relates gas volume, pressure, and temperature The ideal gas law is an expression that relates the volume, pressure, and temperature of a gas. This relationship can be written as follows: IDEAL GAS LAW PV = Nk BT pressure × volume = number of gas particles × Boltzmann’s constant × temperature The symbol k B represents a constant called Boltzmann’s constant. Its value has been experimentally determined to be 1.38 × 10 −23 J/K. Note that when applying the ideal gas law, you must express the temperature in the Kelvin scale (see Section 9-2). Also, the ideal gas law makes no mention of the composition of the gas. The gas particles could be oxygen, carbon dioxide, or any other gas. In this sense, the ideal gas law is universally applicable to all gases. If a gas undergoes a change in volume, pressure, or temperature (or any combination of these), the ideal gas law can be expressed in a particularly useful form. If the number of particles in the gas is constant, the initial and final states of the gas are related as follows: N1 = N2 P ⎯ 1V1 ⎯ = ⎯ T1 P2V2 ⎯ T2 This relation is illustrated in the experiment shown in Figure 9-16. In this experiment, a flask filled with air (V 1 equals the volume of the flask) at room temperature (T 1) and atmospheric pressure (P 1 = P 0) is placed over a heat Copyright © by Holt, Rinehart and Winston. All rights reserved.
Page 1 and 2: Chapter 9 Overview Section 9-1 defi
Page 3 and 4: Section 9-1 Demonstration 1 Volume
Page 5 and 6: SECTION 9-1 The Language of Physics
Page 7 and 8: SECTION 9-1 Demonstration 4 Lifting
Page 9 and 10: SECTION 9-1 PRACTICE GUIDE 9A Solvi
Page 11 and 12: SECTION 9-2 STOP 326 Misconception
Page 13 and 14: SECTION 9-2 Visual Strategy Figure
Page 15 and 16: SECTION 9-2 Classroom Practice The
Page 17 and 18: Section 9-3 Demonstration 7 Fluid f
Page 19 and 20: SECTION 9-3 Misconception STOP Aler
Page 21: SECTION 9-3 Classroom Practice The
Page 25 and 26: SECTION 9-4 Classroom Practice The
Page 27 and 28: Chapter 9 Summary Teaching Tip Ask
Page 29 and 30: 9 REVIEW & ASSESS 12. because the p
Page 31 and 32: 9 REVIEW & ASSESS 42. 7.1 m 43. 17
Page 33 and 34: 9 REVIEW & ASSESS 63. 60.9 m/s 2 64
Page 35 and 36: Chapter 9 Laboratory Exercise NOTE
Page 37 and 38: CHAPTER 9 LAB Boyle’s Law Apparat

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