preview objectives defining a fluid density and buoyant force sample problem chapter 8 section 1...

Preview

• Objectives

• Defining a Fluid

• Density and Buoyant Force

• Sample Problem

Chapter 8Section 1 Fluids and Buoyant Force

Section 1 Fluids and Buoyant ForceChapter 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.


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.


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 density mass

volume

Click below to watch the Visual Concept.

Visual Concept


Mass Density


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.



Buoyant Force and Archimedes’ Principle

Visual Concept

Chapter 8

Displaced Volume of a Fluid

Section 1 Fluids and Buoyant Force



• 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


Visual Concept


Buoyant Force on Floating Objects

Chapter 8

Buoyant Force

Section 1 Fluids and Buoyant Force



• 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


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.


Sample Problem, continued

Buoyant Force1. DefineGiven:

Fg = 7.84 Napparent weight = 6.86 N

f = pwater = 1.00 103 kg/m3

Unknown:

O = ?


Diagram:


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.



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

F

F



Buoyant Force2. Plan, continued

Rearrange the equation to isolate the unknown:

– apparent weightB g

gO f

B

F F

F

F



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 N1.00 10 kg/m

0.98 N

8.0 10 kg/m

B

gO f

B

O

F

F

F



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.

Preview

• Objectives

• Pressure

Chapter 8 Section 2 Fluid Pressure

Section 2 Fluid PressureChapter 8

Objectives

• Calculate the pressure exerted by a fluid.

• Calculate how pressure varies with depth in a fluid.


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 F

A

pressure = force

area


Visual Concept


Pascal’s Principle


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


Visual Concept


Fluid Pressure as a Function of Depth

Preview

• Objectives

• Fluid Flow

• Principles of Fluid Flow

Chapter 8 Section 3 Fluids in Motion

Section 3 Fluids in MotionChapter 8

Objectives

• Examine the motion of a fluid using the continuity equation.

• Recognize the effects of Bernoulli’s principle on fluid 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.


Visual Concept


Characteristics of an Ideal Fluid


Principles of Fluid Flow

• The continuity equation results from conserva-tion of mass.

• Continuity equation

A1v1 = A2v2

Area speed in region 1 = area speed in region 2


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.


Visual Concept


Bernoulli’s Principle

preview objectives defining a fluid density and buoyant force sample problem chapter 8 section 1...

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buoyant forcedensity

buoyant forceobjectivesdefine

buoyant force fb

continuedthe buoyant

mfgmagnitude of buoyant

upward buoyant force

upward force

submerged object