Chapter 1 Introduction and Basic Concepts
1-5C
Solutions Manual – Fox and McDonald’s
Introduction to Fluid Mechanics 10th Edition |
PDF
Introduction, Classification, And System
1-1C
SOLUT ION We Are To Define A Fluid And How It Differs Between A Solid And A Gas.
ANALYSIS: A Substance In The Liquid Or Gas Phase Is Referred To As A Fluid. A Fluid Differs
From A Solid In That A Solid Can Resist An Applied Shear Stress By Deforming, Whereas A Fluid Deform s
Continuously Under The Influence Of Shear Stress, No Matter How Small. A Liquid Takes The Shape Of
The Container It Is In, And A Liquid Forms A Free Surface In A Larger Container In A Gravitational
Field. A Gas, On The Other Hand, Ex pands Until It Encounters The Walls Of The Container And Fills The
1-1
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-5C
Entire Av ailable Space.
Discussion The Subject Of Fluid Mechanics Deals With Ball Fluids, Both Gases And Liquids.
1-2C
SOLUT ION We Are To Determine Whether The Flow Of Air Ov er The Wings Of An Aircraft And The Flow Of
Gases Through A Jet Engine Is Internal Or Ex ternal.
ANALYSIS: The Flow Of Air Ov er The Wings Of An Aircraft Is Ex ternal Since This Is An Unbounded
Fluid Flow Ov er A Surface. The Flow Of Gases Through A Jet Engine Is Internal Flow Since The Fluid Is
Completely Bounded By The Solid Surfaces Of The Engine.
Discussion If We Consider The Entire Airplane, The Flow Is Both Internal (Through The Jet Engines) And
Ex ternal (Ov er The Body And Wings).
1-3C
SOLUT ION We Are To Define Incompressible And Compressible Flow, And Discuss Fluid Compressibility.
ANALYSIS: A Fluid Flow During Which The Density Of The Fluid Rem ains Nearly Constant Is Called
Incompressible Flow. A Flow In Which Density Varies Significantly Is Called Compressible Flow. A Fluid
Whose Density Is Practically Independent Of Pressure (Such As A Liquid) Is Commonly Referred To As An
“Incompressible Fluid,” Although It Is More Proper To Refer To Incompressible Flow. The Flow Of
Compressible Fluid (Such As Air) Does Not Necessarily Need To Be Treated As Compressible Since The Density
Of A Compressible Fluid May Still Remain Nearly Constant During Flow – Especially Flow At Low Speeds.
Discussion It Turns Out That The Mach Number Is The Critical Parameter To Determine Whether The Flow
Of A Gas Can Be Approx imated As An Incompressible Flow. If Ma Is Less Than About 0.3, The Incompressible
Approximation Yields Results That Are In Error By Less Than A Couple Percent.
1-4C
SOLUT ION We Are To Define Internal, Ex ternal, And Open-Channel Flows.
ANALYSIS: Ex ternal Flow Is The Flow Of An Unbounded Fluid Over A Surface Such As A Plate, A Wire,
Or A Pipe. The Flow In A Pipe Or Duct Is Internal Flow If The Fluid Is Completely Bounded By Solid
Surfaces. The Flow Of Liquids In A Pipe Is Called Open-Channel Flow If The Pipe Is Partially Filled With
T he Liquid And There Is A Free Surface , Such As The Flow Of Water In Riv ers And Irrigation Ditches.
Discussion As We Shall See In Later Chapters, Different Approx imations Are Used In The ANALY SIS: Of
Fluid Flows Based On Their Classification.
SOLUT ION We Are To Define The Mach Number Of A Flow And The Meaning For A Mach Number Of 2.
ANALYSIS: The Mach Number Of A Flow Is Defined As T he Ratio Of T he Speed Of Flow T o The
Speed Of Sound In The Flowing Fluid. A Mach Num ber Of 2 Indicate A Flow Speed T hat Is Twice
T he Speed Of Sound In T hat Fluid.
Discussion Mach Number Is An Ex ample Of A Dimensionless (Or Nondimensional) Parameter.
1-6C
SOLUT ION We Are To Discuss If The Mach Number Of A Constant-Speed Airplane Is Constant.
1-2
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-5C
ANALYSIS: No. The Speed Of Sound, And Thus The Mach Number, Changes With Temperature
Which May Change Considerably From Point To Point In The Atmosphere.
1-7 C
SOLUT ION We Are To Determine If The Flow Of Air With A Mach Number Of 0.1 2 Should Be
Approximated As Incompressible.
ANALYSIS: Gas Flows Can Often Be Approx imated As Incompressible If The Density Changes Are Under
About 5 Percent, Which Is Usually The Case When Ma < 0.3. Therefore, Air Flow With A Mach Number Of 0.12
May Be Approx imated As Being Incompressible.
Discussion Air Is Of Course A Compressible Fluid, But At Low Mach Numbers, Compressibility Effects Are
Insignificant.
1-8C
SOLUT ION We Are To Define The No-Slip Condition And Its Cause.
ANALYSIS: A Fluid In Direct Contact With A Solid Surface Sticks T o The Surface And There Is
No Slip. This Is Known As The No -Slip Condition, And It Is Due To The V iscosity Of The Fluid.
Discussion There Is No Such Thing As An Inviscid Fluid, Since All Fluids Hav e V iscosity.
1-9C
SOLUT ION We Are To Define Forced Flow And Discuss The Difference Between Forced And Natural Flow.
We Are Also To Discuss Whether Wind-Driv en Flows Are Forced Or Natural.
ANALYSIS: In Forced Flow, The Fluid Is Forced To Flow Ov er A Surface Or In A Tube By External Means
Such As A Pump Or A Fan. In Natural Flow, Any Fluid Motion Is Caused By Natural Means Such As The
Buoy ancy Effect That Manifests Itself As The Rise Of The Warmer Fluid And The Fall Of The Cooler Fluid. The
Flow Caused By Winds Is Natural Flow For The Earth, But It Is Forced Flow For Bodies
Subjected To The Winds Since For The Body It Makes No Difference Whether The Air Motion Is Caused By A
Fan Or By The Winds.
Discussion As Seen Here, The Classification Of Forced V s. Natural Flow May Depend On Y our Frame Of Reference.
1-3
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-10C
SOLUT ION We Are To Define A Boundary Layer, And Discuss Its Cause.
ANALYSIS: The Region Of Flow (Usually Near A Wall) In Which The Velocity Gradients Are
Significant And Frictional Effects Are Important Is Called The Boundary Layer. When A Fluid Stream
Encounters A Solid Surface That Is At Rest, The Fluid V elocity Assumes A V alue Of Zero At That Surface. The
Velocity Then V aries From Zero At The Surface To Some Larger V alue Sufficiently Far From The Surface. The
Dev elopment Of A Boundary Layer Is Caused By The No -Slip Condition.
Discussion As We Shall See Later, Flow Within A Boundary Layer Is Rotational (Individual Fluid Particles
Rotate), While That Outside The Boundary Layer Is Typically Irrotational (Indiv idual Fluid Particles Move, But
Do Not Rotate).
1-11C
SOLUT ION We Are To Discuss The Differences Between Classical And Statistical Approaches.
ANALYSIS: The Classical Approach Is A Macroscopic Approach , Based On Ex periments Or ANALYSIS: Of
The Gross Behavior Of A Fluid, Without Knowledge Of Indiv idual Molecules, Whereas The Statistical Approach
Is A Microscopic Approach Based On The Av erage Behavior Of Large Groups Of Ind iv idual Molecules.
Discussion The Classical Approach Is Easier And Much More Common In Fluid Flow ANALYSIS:.
1-12C
SOLUT ION We Are To Define A Steady -Flow Process.
ANALYSIS: A Process Is Said To Be Steady If It Inv olves No Changes With T ime Anywhere Within The
Sy stem Or At The Sy stem Boundaries.
Discussion The Opposite Of Steady Flow Is Unsteady Flow, Which Involves Changes With Time.
1-13C
SOLUT ION We Are To Define Stress, Normal Stress, Shear Stress, And Pressure.
ANALYSIS: Stress Is Defined As Force Per Unit Area, And Is Determined By Div iding The Force By The
Area Upon Which It Acts. The Norm al Com ponent Of A Force Acting On A Surface Per Unit Area Is
Called The Normal Stress, And The Tangential Com ponent Of A Force Acting On A Surface Per Unit
Area Is Called Shear Stress. In A Fluid At Rest, The Normal Stress Is Called Pressure.
Discussion Fluids In Motion May Have Both Shear Stresses And Additional Normal Stresses Besides
Pressure, But When A Fluid Is At Rest, The Only Normal Stress Is The Pressure, And There Are No Shear
Stresses.
1-14C
SOLUT ION We Are To Discuss How To Select Sy stem When Analy zing The Acceleration Of Gases As They
Flow Through A Nozzle.
ANALYSIS: When Analy zing The Acceleration Of Gases As They Flow Through A Nozzle, A Wise Choice For
The Sy stem Is T he Volume Within The Nozzle, Bounded By The Entire Inner Surface Of The Nozzle And The
Inlet And Outlet Cross-Sections. This Is A Control Volume (Or Open Sy stem) Since Mass Crosses The
Boundary .
1-4
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
1-5C
Solutions Manual – Fox and McDonald’s
Introduction to Fluid Mechanics 10th Edition |
Introduction, Classification, And System
1-1C
SOLUT ION We Are To Define A Fluid And How It Differs Between A Solid And A Gas.
ANALYSIS: A Substance In The Liquid Or Gas Phase Is Referred To As A Fluid. A Fluid Differs
From A Solid In That A Solid Can Resist An Applied Shear Stress By Deforming, Whereas A Fluid Deform s
Continuously Under The Influence Of Shear Stress, No Matter How Small. A Liquid Takes The Shape Of
The Container It Is In, And A Liquid Forms A Free Surface In A Larger Container In A Gravitational
Field. A Gas, On The Other Hand, Ex pands Until It Encounters The Walls Of The Container And Fills The
1-1
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-5C
Entire Av ailable Space.
Discussion The Subject Of Fluid Mechanics Deals With Ball Fluids, Both Gases And Liquids.
1-2C
SOLUT ION We Are To Determine Whether The Flow Of Air Ov er The Wings Of An Aircraft And The Flow Of
Gases Through A Jet Engine Is Internal Or Ex ternal.
ANALYSIS: The Flow Of Air Ov er The Wings Of An Aircraft Is Ex ternal Since This Is An Unbounded
Fluid Flow Ov er A Surface. The Flow Of Gases Through A Jet Engine Is Internal Flow Since The Fluid Is
Completely Bounded By The Solid Surfaces Of The Engine.
Discussion If We Consider The Entire Airplane, The Flow Is Both Internal (Through The Jet Engines) And
Ex ternal (Ov er The Body And Wings).
1-3C
SOLUT ION We Are To Define Incompressible And Compressible Flow, And Discuss Fluid Compressibility.
ANALYSIS: A Fluid Flow During Which The Density Of The Fluid Rem ains Nearly Constant Is Called
Incompressible Flow. A Flow In Which Density Varies Significantly Is Called Compressible Flow. A Fluid
Whose Density Is Practically Independent Of Pressure (Such As A Liquid) Is Commonly Referred To As An
“Incompressible Fluid,” Although It Is More Proper To Refer To Incompressible Flow. The Flow Of
Compressible Fluid (Such As Air) Does Not Necessarily Need To Be Treated As Compressible Since The Density
Of A Compressible Fluid May Still Remain Nearly Constant During Flow – Especially Flow At Low Speeds.
Discussion It Turns Out That The Mach Number Is The Critical Parameter To Determine Whether The Flow
Of A Gas Can Be Approx imated As An Incompressible Flow. If Ma Is Less Than About 0.3, The Incompressible
Approximation Yields Results That Are In Error By Less Than A Couple Percent.
1-4C
SOLUT ION We Are To Define Internal, Ex ternal, And Open-Channel Flows.
ANALYSIS: Ex ternal Flow Is The Flow Of An Unbounded Fluid Over A Surface Such As A Plate, A Wire,
Or A Pipe. The Flow In A Pipe Or Duct Is Internal Flow If The Fluid Is Completely Bounded By Solid
Surfaces. The Flow Of Liquids In A Pipe Is Called Open-Channel Flow If The Pipe Is Partially Filled With
T he Liquid And There Is A Free Surface , Such As The Flow Of Water In Riv ers And Irrigation Ditches.
Discussion As We Shall See In Later Chapters, Different Approx imations Are Used In The ANALY SIS: Of
Fluid Flows Based On Their Classification.
SOLUT ION We Are To Define The Mach Number Of A Flow And The Meaning For A Mach Number Of 2.
ANALYSIS: The Mach Number Of A Flow Is Defined As T he Ratio Of T he Speed Of Flow T o The
Speed Of Sound In The Flowing Fluid. A Mach Num ber Of 2 Indicate A Flow Speed T hat Is Twice
T he Speed Of Sound In T hat Fluid.
Discussion Mach Number Is An Ex ample Of A Dimensionless (Or Nondimensional) Parameter.
1-6C
SOLUT ION We Are To Discuss If The Mach Number Of A Constant-Speed Airplane Is Constant.
1-2
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-5C
ANALYSIS: No. The Speed Of Sound, And Thus The Mach Number, Changes With Temperature
Which May Change Considerably From Point To Point In The Atmosphere.
1-7 C
SOLUT ION We Are To Determine If The Flow Of Air With A Mach Number Of 0.1 2 Should Be
Approximated As Incompressible.
ANALYSIS: Gas Flows Can Often Be Approx imated As Incompressible If The Density Changes Are Under
About 5 Percent, Which Is Usually The Case When Ma < 0.3. Therefore, Air Flow With A Mach Number Of 0.12
May Be Approx imated As Being Incompressible.
Discussion Air Is Of Course A Compressible Fluid, But At Low Mach Numbers, Compressibility Effects Are
Insignificant.
1-8C
SOLUT ION We Are To Define The No-Slip Condition And Its Cause.
ANALYSIS: A Fluid In Direct Contact With A Solid Surface Sticks T o The Surface And There Is
No Slip. This Is Known As The No -Slip Condition, And It Is Due To The V iscosity Of The Fluid.
Discussion There Is No Such Thing As An Inviscid Fluid, Since All Fluids Hav e V iscosity.
1-9C
SOLUT ION We Are To Define Forced Flow And Discuss The Difference Between Forced And Natural Flow.
We Are Also To Discuss Whether Wind-Driv en Flows Are Forced Or Natural.
ANALYSIS: In Forced Flow, The Fluid Is Forced To Flow Ov er A Surface Or In A Tube By External Means
Such As A Pump Or A Fan. In Natural Flow, Any Fluid Motion Is Caused By Natural Means Such As The
Buoy ancy Effect That Manifests Itself As The Rise Of The Warmer Fluid And The Fall Of The Cooler Fluid. The
Flow Caused By Winds Is Natural Flow For The Earth, But It Is Forced Flow For Bodies
Subjected To The Winds Since For The Body It Makes No Difference Whether The Air Motion Is Caused By A
Fan Or By The Winds.
Discussion As Seen Here, The Classification Of Forced V s. Natural Flow May Depend On Y our Frame Of Reference.
1-3
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-10C
SOLUT ION We Are To Define A Boundary Layer, And Discuss Its Cause.
ANALYSIS: The Region Of Flow (Usually Near A Wall) In Which The Velocity Gradients Are
Significant And Frictional Effects Are Important Is Called The Boundary Layer. When A Fluid Stream
Encounters A Solid Surface That Is At Rest, The Fluid V elocity Assumes A V alue Of Zero At That Surface. The
Velocity Then V aries From Zero At The Surface To Some Larger V alue Sufficiently Far From The Surface. The
Dev elopment Of A Boundary Layer Is Caused By The No -Slip Condition.
Discussion As We Shall See Later, Flow Within A Boundary Layer Is Rotational (Individual Fluid Particles
Rotate), While That Outside The Boundary Layer Is Typically Irrotational (Indiv idual Fluid Particles Move, But
Do Not Rotate).
1-11C
SOLUT ION We Are To Discuss The Differences Between Classical And Statistical Approaches.
ANALYSIS: The Classical Approach Is A Macroscopic Approach , Based On Ex periments Or ANALYSIS: Of
The Gross Behavior Of A Fluid, Without Knowledge Of Indiv idual Molecules, Whereas The Statistical Approach
Is A Microscopic Approach Based On The Av erage Behavior Of Large Groups Of Ind iv idual Molecules.
Discussion The Classical Approach Is Easier And Much More Common In Fluid Flow ANALYSIS:.
1-12C
SOLUT ION We Are To Define A Steady -Flow Process.
ANALYSIS: A Process Is Said To Be Steady If It Inv olves No Changes With T ime Anywhere Within The
Sy stem Or At The Sy stem Boundaries.
Discussion The Opposite Of Steady Flow Is Unsteady Flow, Which Involves Changes With Time.
1-13C
SOLUT ION We Are To Define Stress, Normal Stress, Shear Stress, And Pressure.
ANALYSIS: Stress Is Defined As Force Per Unit Area, And Is Determined By Div iding The Force By The
Area Upon Which It Acts. The Norm al Com ponent Of A Force Acting On A Surface Per Unit Area Is
Called The Normal Stress, And The Tangential Com ponent Of A Force Acting On A Surface Per Unit
Area Is Called Shear Stress. In A Fluid At Rest, The Normal Stress Is Called Pressure.
Discussion Fluids In Motion May Have Both Shear Stresses And Additional Normal Stresses Besides
Pressure, But When A Fluid Is At Rest, The Only Normal Stress Is The Pressure, And There Are No Shear
Stresses.
1-14C
SOLUT ION We Are To Discuss How To Select Sy stem When Analy zing The Acceleration Of Gases As They
Flow Through A Nozzle.
ANALYSIS: When Analy zing The Acceleration Of Gases As They Flow Through A Nozzle, A Wise Choice For
The Sy stem Is T he Volume Within The Nozzle, Bounded By The Entire Inner Surface Of The Nozzle And The
Inlet And Outlet Cross-Sections. This Is A Control Volume (Or Open Sy stem) Since Mass Crosses The
Boundary .
1-4
PROPRIETARY MATERIAL. © 2013 The M cGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
educators for course preparation. If you are a student using this M anual, you are using it without permission.
