© fox, mcdonald & pritchard introduction to fluid mechanics chapter 5 introduction to...

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Introduction to Fluid Mechanics

Chapter 5

Introduction to Differential Analysis of

Fluid Motion

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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

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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 forTwo-Dimensional

Incompressible Flow

Two-Dimensional Flow

Stream Function

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Stream Function forTwo-Dimensional

Incompressible Flow

Cylindrical Coordinates

Stream Function (r,)

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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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Motion of a Fluid Particle (Kinematics)

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Motion of a Fluid Particle (Kinematics)

Fluid Translation: Acceleration of aFluid Particle in a Velocity Field

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Motion of a Fluid Particle (Kinematics)

Fluid Translation: Acceleration of aFluid Particle in a Velocity Field

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Motion of a Fluid Particle (Kinematics)

Fluid Translation: Acceleration of aFluid Particle in a Velocity Field

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Motion of a Fluid Particle (Kinematics)

Fluid Translation: Acceleration of aFluid 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