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Chapter 8. Fluid Mechanics. Table of Contents. Section 1 Fluids and Buoyant Force Section 2 Fluid Pressure Section 3 Fluids in Motion. Section 1 Fluids and Buoyant Force. Chapter 8. Objectives. Define a fluid. Distinguish a gas from a liquid. - PowerPoint PPT PresentationTRANSCRIPT
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Fluid MechanicsChapter 8
Table of Contents
Section 1 Fluids and Buoyant Force
Section 2 Fluid Pressure
Section 3 Fluids in Motion
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Section 1 Fluids and Buoyant Force
Chapter 8
Objectives• Define a fluid.
• Distinguish a gas from a liquid.
• Determine the magnitude of the buoyant force exerted on a floating object or a submerged object.
• Explain why some objects float and some objects sink.
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Section 1 Fluids and Buoyant Force
Chapter 8
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.
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Section 1 Fluids and Buoyant Force
Chapter 8
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.
mV
mass density mass
volume
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Chapter 8
Mass Density
Section 1 Fluids and Buoyant Force
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Section 1 Fluids and Buoyant Force
Chapter 8
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.
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Chapter 8
Buoyant Force and Archimedes’ Principle
Section 1 Fluids and Buoyant Force
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Chapter 8
Displaced Volume of a Fluid
Section 1 Fluids and Buoyant Force
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Section 1 Fluids and Buoyant Force
Chapter 8
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) = mfgmagnitude of buoyant force = weight of fluid displaced
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Chapter 8
Buoyant Force on Floating Objects
Section 1 Fluids and Buoyant Force
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Chapter 8
Buoyant Force
Section 1 Fluids and Buoyant Force
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Section 1 Fluids and Buoyant Force
Chapter 8
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)FB
O
f
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Section 1 Fluids and Buoyant Force
Chapter 8
Sample ProblemBuoyant 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.
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Section 1 Fluids and Buoyant Force
Chapter 8
Sample Problem, continued
Buoyant Force1. DefineGiven:
Fg = 7.84 Napparent weight = 6.86 Nf = pwater = 1.00 103 kg/m3
Unknown:O = ?
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Section 1 Fluids and Buoyant Force
Chapter 8
Diagram:
Sample Problem, continued
Buoyant Force1. 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.
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Section 1 Fluids and Buoyant Force
Chapter 8
Sample Problem, continued
Buoyant Force2. Plan
Choose an equation or situation: Because the object is completely submerged, consider the ratio of the weight to the buoyant force.
– apparent weightg B
g O
B f
F F
FF
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Section 1 Fluids and Buoyant Force
Chapter 8
Sample Problem, continued
Buoyant Force2. Plan, continued
Rearrange the equation to isolate the unknown:
– apparent weightB g
gO f
B
F F
FF
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Section 1 Fluids and Buoyant Force
Chapter 8
Sample Problem, continued
Buoyant Force3. Calculate
Substitute the values into the equation and solve:
3 3
3 3
7.84 N – 6.86 N = 0.98 N
7.84 N 1.00 10 kg/m0.98 N
8.0 10 kg/m
B
gO f
B
O
FFF
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Section 1 Fluids and Buoyant Force
Chapter 8
Sample Problem, continued
Buoyant Force4. 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.
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Section 2 Fluid Pressure
Chapter 8
Objectives• Calculate the pressure exerted by a fluid.
• Calculate how pressure varies with depth in a fluid.
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Section 2 Fluid Pressure
Chapter 8
Pressure• Pressure is the magnitude of the force on a surface
per unit 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.
P FA
pressure = forcearea
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Chapter 8
Pascal’s Principle
Section 2 Fluid Pressure
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Section 2 Fluid Pressure
Chapter 8
Pressure, continued
• Pressure varies with depth in a fluid.
• The pressure in a fluid increases with depth.
0
absolute pressure = atmospheric pressure +
density free-fall acceleration depth
P P gh
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Chapter 8
Fluid Pressure as aFunction of Depth
Section 2 Fluid Pressure
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Section 3 Fluids in Motion
Chapter 8
Objectives• Examine the motion of a fluid using the continuity
equation.
• Recognize the effects of Bernoulli’s principle on fluid motion.
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Section 3 Fluids in Motion
Chapter 8
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.
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Chapter 8
Characteristics of an Ideal Fluid
Section 3 Fluids in Motion
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Section 3 Fluids in Motion
Chapter 8
Principles of Fluid Flow• The continuity equation
results from conserva-tion of mass.
• Continuity equationA1v1 = A2v2
Area speed in region 1 = area speed in region 2
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Section 3 Fluids in Motion
Chapter 8
Principles of Fluid Flow, continued
• The speed of fluid flow depends on cross-sectional area.
• Bernoulli’s principle states that the pressure in a fluid decreases as the fluid’s velocity increases.
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Chapter 8
Bernoulli’s Principle
Section 3 Fluids in Motion
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Section 3 Fluids in Motion
Chapter 8
Principles of Fluid Flow
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Section 3 Fluids in Motion
Chapter 8
Principles of Fluid Flow