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Understanding Fluids: Density, Pressure, and Applications in Physics

In this chapter, we explore the essential principles of fluid mechanics, focusing on density and pressure. Density is defined as mass per unit volume (ρ = M/V) and varies among materials, with examples including gold and fresh water. We detail the concept of pressure (P = F/A) as the force applied per area and its dependence on force and area. Atmospheric pressure is discussed, along with its measurement using barometers. We also examine the relationship between pressure and depth in fluids, illustrating how water seeks its own level.

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Understanding Fluids: Density, Pressure, and Applications in Physics

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  1. Chapter 15 Fluids Dr. Jie Zou PHY 1151G Department of Physics

  2. Outline • Density • Pressure • Atmospheric pressure • Pressure and depth • Applications: barometer • Water seeks its own level Dr. Jie Zou PHY 1151G Department of Physics

  3. Density • Definition of density, : The density of a material is defined as the mass per volume. •  = M/V. SI unit: kg/m3. • The denser a material, the more mass it has in any given volume. • Examples of density of different materials: gold, 19,300 kg/m3; fresh water, 1000 kg/m3; helium, 0.179 kg/m3 (See Table 15-1) • Example: Find the mass of a gallon of water.(1 gallon = 3.79 L = 3.79  10-3 m3) Dr. Jie Zou PHY 1151G Department of Physics

  4. Pressure • Definition of pressure: Pressure is a measure of the amount of force per area. • P = F/A. SI unit: N/m2. • Pressure is increased if the force applied to a given area is increased, or if a given force is applied to a smaller area. This bird exerts only a small pressure on the lily pad because its weight spreads out over a large area by its long toes. The same force applied to the small area of a needle tip causes a large enough pressure to rupture the balloon. Dr. Jie Zou PHY 1151G Department of Physics

  5. Example • Find the pressure exerted on the skin of a balloon if you press with a force of 2.1 N using • (a) your finger or (b) a needle (Assume the area of your fingertip is 1.0  10-4 m2, and the area of the needle tip is 2.5  10-7 m2.) • (c) Find the minimum force necessary to pop the balloon with the needle, given that the balloon pops with a pressure of 3.0  105 N/m2. Dr. Jie Zou PHY 1151G Department of Physics

  6. Atmospheric pressure • Atmospheric pressure, Pat, is a direct result of the weight of the air above us. Pat = 1.01  105 N/m2 (about 14.7 pounds per square inch). • A Shorthand unit for N/m2 is the pascal (Pa): 1 Pa = 1 N/m2. • A common unit for atmospheric pressure in weather forecasting is the bar, defined as follows: 1 bar = 105 Pa ≈ 1 Pat. • Gauge pressure: Pg = P - Pat Dr. Jie Zou PHY 1151G Department of Physics

  7. Pressure and depth in fluids • At a depth h, the pressure P is given by: • P = Pat + gh. • : density of the fluid • If the pressure at one point is P1, the pressure P2 at a depth h below that point is the following: • P2 = P1 + gh. Pat P Dr. Jie Zou PHY 1151G Department of Physics

  8. Example • The titanic was found in 1985 lying on the bottom of the North Atlantic at a depth of 2.5 miles. What is the pressure at this depth? (The density of sea water is 1025 kg/m3 and 1 mile = 1609 m.) Dr. Jie Zou PHY 1151G Department of Physics

  9. Application: barometer • A simple barometer: A device used to measure atmospheric pressure • Atmospheric pressure Pat is related to the height of fluid in the tube by the relation: Pat = gh. Dr. Jie Zou PHY 1151G Department of Physics

  10. Water seeks its own level • Water seeks its own level. • Example 15-4: A U-shaped tube is filled mostly with water, but a small amount of vegetable oil has been added to one side. wateris 1.00 x 103 kg/m3, and oil is 9.20 x 102 kg/m3. If the depth of the oil is 5.00 cm, what is the difference in level h between the top of the oil on one side of the U and the top of the water on the other side? Dr. Jie Zou PHY 1151G Department of Physics

  11. Homework • See online assignment on www.masteringphysics.com Dr. Jie Zou PHY 1151G Department of Physics

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