Introduction to Fluid Mechanics

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© Fox, Pritchard, & McDonald

Introduction to Fluid Mechanics

Chapter 5

Introduction to
Differential Analysis of
Fluid Motion

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Main Topics


Conservation of Mass


Stream Function for Two
-
Dimensional
Incompressible Flow


Motion 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

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Conservation of Mass


Rectangular Coordinate System

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Conservation of Mass


Rectangular Coordinate System

“Continuity Equation”

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Conservation of Mass


Rectangular Coordinate System

“Del” Operator

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Conservation of Mass


Rectangular Coordinate System

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Conservation of Mass


Rectangular Coordinate System

Incompressible Fluid:

Steady Flow:

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Conservation of Mass


Cylindrical Coordinate System

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Conservation of Mass


Cylindrical Coordinate System

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Conservation of Mass


Cylindrical Coordinate System

“Del” Operator

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Conservation of Mass


Cylindrical Coordinate System

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Conservation of Mass


Cylindrical Coordinate System

Incompressible Fluid:

Steady Flow:

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Stream Function for

Two
-
Dimensional

Incompressible Flow


Two
-
Dimensional Flow


Stream Function
y

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Stream Function for

Two
-
Dimensional

Incompressible Flow


Cylindrical Coordinates


Stream Function
y
(
r
,
q
)

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Motion of a Fluid Particle
(Kinematics)


Fluid Translation: Acceleration of a

Fluid Particle in a Velocity Field


Fluid Rotation


Fluid Deformation


Angular Deformation


Linear Deformation

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Motion of a Fluid Particle
(Kinematics)

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Motion of a Fluid Particle
(Kinematics)


Fluid Translation: Acceleration of a

Fluid Particle in a Velocity Field

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Motion of a Fluid Particle
(Kinematics)


Fluid Translation: Acceleration of a

Fluid Particle in a Velocity Field

© Fox, Pritchard, & McDonald

Motion of a Fluid Particle
(Kinematics)


Fluid Translation: Acceleration of a

Fluid Particle in a Velocity Field

© Fox, Pritchard, & McDonald

Motion of a Fluid Particle
(Kinematics)


Fluid Translation: Acceleration of a

Fluid Particle in a Velocity Field (Cylindrical)

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Motion of a Fluid Particle
(Kinematics)


Fluid Rotation

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Motion of a Fluid Particle
(Kinematics)


Fluid Rotation

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Motion of a Fluid Particle
(Kinematics)


Fluid Rotation

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Motion of a Fluid Particle
(Kinematics)


Fluid Deformation:


Angular Deformation

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Motion of a Fluid Particle
(Kinematics)


Fluid Deformation:


Angular Deformation

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Motion of a Fluid Particle
(Kinematics)


Fluid Deformation:


Linear Deformation

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Momentum Equation


Newton’s Second Law

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Momentum Equation


Forces Acting on a Fluid Particle

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Momentum Equation


Forces Acting on a Fluid Particle

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Momentum Equation


Differential Momentum Equation

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Momentum Equation


Newtonian Fluid: Navier
-
Stokes Equations

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Momentum Equation


Special Case: Euler’s Equation

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Computational Fluid Dynamics


Some Applications

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Computational Fluid Dynamics


Discretization