© fox, mcdonald & pritchard introduction to fluid mechanics chapter 5 introduction to...
TRANSCRIPT
![Page 1: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/1.jpg)
© Fox, McDonald & Pritchard
Introduction to Fluid Mechanics
Chapter 5
Introduction to Differential Analysis of
Fluid Motion
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© Fox, McDonald & Pritchard
Main Topics
Conservation of MassStream Function for Two-Dimensional
Incompressible FlowMotion of a Fluid Particle (Kinematics)Momentum Equation
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Conservation of Mass
Basic Law for a System
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Conservation of Mass
Rectangular Coordinate System
![Page 5: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/5.jpg)
© Fox, McDonald & Pritchard
Conservation of Mass
Rectangular Coordinate System
![Page 6: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/6.jpg)
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Conservation of Mass
Rectangular Coordinate System
“Continuity Equation”
![Page 7: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/7.jpg)
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Conservation of Mass
Rectangular Coordinate System
“Del” Operator
![Page 8: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/8.jpg)
© Fox, McDonald & Pritchard
Conservation of Mass
Rectangular Coordinate System
![Page 9: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/9.jpg)
© Fox, McDonald & Pritchard
Conservation of Mass
Rectangular Coordinate System
Incompressible Fluid:
Steady Flow:
![Page 10: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/10.jpg)
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Conservation of Mass
Cylindrical Coordinate System
![Page 11: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/11.jpg)
© Fox, McDonald & Pritchard
Conservation of Mass
Cylindrical Coordinate System
![Page 12: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/12.jpg)
© Fox, McDonald & Pritchard
Conservation of Mass
Cylindrical Coordinate System
“Del” Operator
![Page 13: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/13.jpg)
© Fox, McDonald & Pritchard
Conservation of Mass
Cylindrical Coordinate System
![Page 14: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/14.jpg)
© Fox, McDonald & Pritchard
Conservation of Mass
Cylindrical Coordinate System
Incompressible Fluid:
Steady Flow:
![Page 15: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/15.jpg)
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Stream Function forTwo-Dimensional
Incompressible Flow
Two-Dimensional Flow
Stream Function
![Page 16: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/16.jpg)
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Stream Function forTwo-Dimensional
Incompressible Flow
Cylindrical Coordinates
Stream Function (r,)
![Page 17: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/17.jpg)
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Motion of a Fluid Particle (Kinematics)
Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
Fluid RotationFluid Deformation
• Angular Deformation• Linear Deformation
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© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
![Page 19: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/19.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
![Page 20: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/20.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
![Page 21: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/21.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
![Page 22: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/22.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Translation: Acceleration of aFluid Particle in a Velocity Field (Cylindrical)
![Page 23: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/23.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Rotation
![Page 24: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/24.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Rotation
![Page 25: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/25.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Rotation
![Page 26: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/26.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Deformation:• Angular Deformation
![Page 27: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/27.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Deformation:• Angular Deformation
![Page 28: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/28.jpg)
© Fox, McDonald & Pritchard
Motion of a Fluid Particle (Kinematics)
Fluid Deformation:• Linear Deformation
![Page 29: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/29.jpg)
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Momentum Equation
Newton’s Second Law
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Momentum Equation
Forces Acting on a Fluid Particle
![Page 31: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/31.jpg)
© Fox, McDonald & Pritchard
Momentum Equation
Forces Acting on a Fluid Particle
![Page 32: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/32.jpg)
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Momentum Equation
Differential Momentum Equation
![Page 33: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/33.jpg)
© Fox, McDonald & Pritchard
Momentum Equation
Newtonian Fluid: Navier-Stokes Equations
![Page 34: © Fox, McDonald & Pritchard Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion](https://reader033.vdocuments.us/reader033/viewer/2022061511/56649e795503460f94b798a5/html5/thumbnails/34.jpg)
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Momentum Equation
Special Case: Euler’s Equation