© Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 5 Introduction to Differential Analysis of Fluid Motion

© Fox, Pritchard, & McDonald Main Topics Conservation of Mass Stream Function for Two-Dimensional Incompressible Flow Motion of a Fluid Particle (Kinematics) Momentum Equation

© Fox, Pritchard, & McDonald Conservation of Mass Basic Law for a System

© Fox, Pritchard, & McDonald Conservation of Mass Rectangular Coordinate System

© Fox, Pritchard, & McDonald Conservation of Mass Rectangular Coordinate System

© Fox, Pritchard, & McDonald Conservation of Mass Rectangular Coordinate System “Continuity Equation”

© Fox, Pritchard, & McDonald Conservation of Mass Rectangular Coordinate System “Del” Operator

© Fox, Pritchard, & McDonald Conservation of Mass Rectangular Coordinate System

© Fox, Pritchard, & McDonald Conservation of Mass Rectangular Coordinate System Incompressible Fluid: Steady Flow:

© Fox, Pritchard, & McDonald Conservation of Mass Cylindrical Coordinate System

© Fox, Pritchard, & McDonald Conservation of Mass Cylindrical Coordinate System

© Fox, Pritchard, & McDonald Conservation of Mass Cylindrical Coordinate System “Del” Operator

© Fox, Pritchard, & McDonald Conservation of Mass Cylindrical Coordinate System

© Fox, Pritchard, & McDonald Conservation of Mass Cylindrical Coordinate System Incompressible Fluid: Steady Flow:

© Fox, Pritchard, & McDonald Stream Function for Two-Dimensional Incompressible Flow Two-Dimensional Flow Stream Function 

© Fox, Pritchard, & McDonald Stream Function for Two-Dimensional Incompressible Flow Cylindrical Coordinates Stream Function  (r,  )

© Fox, Pritchard, & McDonald 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

© Fox, Pritchard, & McDonald Motion of a Fluid Particle (Kinematics)

© 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

© 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)

© Fox, Pritchard, & McDonald Motion of a Fluid Particle (Kinematics) Fluid Rotation

© Fox, Pritchard, & McDonald Motion of a Fluid Particle (Kinematics) Fluid Rotation

© Fox, Pritchard, & McDonald Motion of a Fluid Particle (Kinematics) Fluid Rotation

© Fox, Pritchard, & McDonald Motion of a Fluid Particle (Kinematics) Fluid Deformation: Angular Deformation

© Fox, Pritchard, & McDonald Motion of a Fluid Particle (Kinematics) Fluid Deformation: Angular Deformation

© Fox, Pritchard, & McDonald Motion of a Fluid Particle (Kinematics) Fluid Deformation: Linear Deformation

© Fox, Pritchard, & McDonald Momentum Equation Newton’s Second Law

© Fox, Pritchard, & McDonald Momentum Equation Forces Acting on a Fluid Particle

© Fox, Pritchard, & McDonald Momentum Equation Forces Acting on a Fluid Particle

© Fox, Pritchard, & McDonald Momentum Equation Differential Momentum Equation

© Fox, Pritchard, & McDonald Momentum Equation Newtonian Fluid: Navier-Stokes Equations

© Fox, Pritchard, & McDonald Momentum Equation Special Case: Euler’s Equation

© Fox, Pritchard, & McDonald Computational Fluid Dynamics Some Applications

© Fox, Pritchard, & McDonald Computational Fluid Dynamics Discretization