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Chapter 8 Section 1 Fluids and Buoyant Force Defining a Fluid • A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or a liquid. • Both liquids and gases are considered fluids because they can flow and change shape. • Liquids have a definite volume; gases do not. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Density and Buoyant Force • The concentration of matter of an object is called the mass density. • Mass density is measured as the mass per unit volume of a substance. m V mass mass density volume Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Mass Density Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Density and Buoyant Force, continued • The buoyant force is the upward force exerted by a liquid on an object immersed in or floating on the liquid. • Buoyant forces can keep objects afloat. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Buoyant Force and Archimedes’ Principle Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Displaced Volume of a Fluid Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Density and Buoyant Force, continued • Archimedes’ principle describes the magnitude of a buoyant force. • Archimedes’ principle: Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object. FB = Fg (displaced fluid) = mfg magnitude of buoyant force = weight of fluid displaced Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Buoyant Force on Floating Objects Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Buoyant Force Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Density and Buoyant Force, continued • For a floating object, the buoyant force equals the object’s weight. • The apparent weight of a submerged object depends on the density of the object. • For an object with density O submerged in a fluid of density f, the buoyant force FB obeys the following ratio: Fg (object) O FB f Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Sample Problem Buoyant Force A bargain hunter purchases a “gold” crown at a flea market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is the crown made of pure gold? Explain. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Sample Problem, continued Buoyant Force 1. Define Given: Fg = 7.84 N apparent weight = 6.86 N f = pwater = 1.00 103 kg/m3 Unknown: O = ? Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Sample Problem, continued Buoyant Force Diagram: 1. Define, continued TIP: The use of a diagram can help clarify a problem and the variables involved. In this diagram, FT,1 equals the actual weight of the crown, and FT,2 is the apparent weight of the crown when immersed in water. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Sample Problem, continued Buoyant Force 2. Plan Choose an equation or situation: Because the object is completely submerged, consider the ratio of the weight to the buoyant force. Fg – FB apparent weight O FB f Fg Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Sample Problem, continued Buoyant Force 2. Plan, continued Rearrange the equation to isolate the unknown: FB Fg – apparent weight O Fg FB f Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Sample Problem, continued Buoyant Force 3. Calculate Substitute the values into the equation and solve: FB 7.84 N – 6.86 N = 0.98 N Fg 7.84 N O f 1.00 103 kg/m3 FB 0.98 N O 8.0 103 kg/m3 Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 1 Fluids and Buoyant Force Sample Problem, continued Buoyant Force 4. Evaluate From the table, the density of gold is 19.3 103 kg/m3. Because 8.0 103 kg/m3 < 19.3 103 kg/m3, the crown cannot be pure gold. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 2 Fluid Pressure Pressure • Pressure is the magnitude of the force on a surface per unit area. F P A force pressure = area • Pascal’s principle states that pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 2 Fluid Pressure Pascal’s Principle Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 2 Fluid Pressure Pressure, continued • Pressure varies with depth in a fluid. • The pressure in a fluid increases with depth. P P0 gh absolute pressure = atmospheric pressure + density free-fall acceleration depth Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 2 Fluid Pressure Fluid Pressure as a Function of Depth Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 3 Fluids in Motion Fluid Flow • Moving fluids can exhibit laminar (smooth) flow or turbulent (irregular) flow. • An ideal fluid is a fluid that has no internal friction or viscosity and is incompressible. • The ideal fluid model simplifies fluid-flow analysis. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 3 Fluids in Motion Characteristics of an Ideal Fluid Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 3 Fluids in Motion Principles of Fluid Flow • The continuity equation results from conservation of mass. • Continuity equation A1v1 = A2v2 Area speed in region 1 = area speed in region 2 Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 3 Fluids in Motion Principles of Fluid Flow, continued • The speed of fluid flow depends on crosssectional area. • Bernoulli’s principle states that the pressure in a fluid decreases as the fluid’s velocity increases. Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved. Chapter 8 Section 3 Fluids in Motion Bernoulli’s Principle Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.