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Introduction to Fluid Mechanics. Chapter 5 Introduction to Differential Analysis of Fluid Motion. Main Topics. Conservation of Mass Stream Function for Two-Dimensional Incompressible Flow Motion of a Fluid Particle (Kinematics) Momentum Equation. Conservation of Mass.

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introduction to fluid mechanics

Introduction to Fluid Mechanics

Chapter 5

Introduction to Differential Analysis of Fluid Motion

main topics
Main Topics
  • Conservation of Mass
  • Stream Function for Two-Dimensional Incompressible Flow
  • Motion of a Fluid Particle (Kinematics)
  • Momentum Equation
conservation of mass
Conservation of Mass
  • Basic Law for a System
conservation of mass1
Conservation of Mass
  • Rectangular Coordinate System
conservation of mass2
Conservation of Mass
  • Rectangular Coordinate System
conservation of mass3
Conservation of Mass
  • Rectangular Coordinate System

“Continuity Equation”

conservation of mass4
Conservation of Mass
  • Rectangular Coordinate System

“Del” Operator

conservation of mass5
Conservation of Mass
  • Rectangular Coordinate System
conservation of mass6
Conservation of Mass
  • Rectangular Coordinate System

Incompressible Fluid:

Steady Flow:

conservation of mass7
Conservation of Mass
  • Cylindrical Coordinate System
conservation of mass8
Conservation of Mass
  • Cylindrical Coordinate System
conservation of mass9
Conservation of Mass
  • Cylindrical Coordinate System

“Del” Operator

conservation of mass10
Conservation of Mass
  • Cylindrical Coordinate System
conservation of mass11
Conservation of Mass
  • Cylindrical Coordinate System

Incompressible Fluid:

Steady Flow:

stream function for two dimensional incompressible flow
Stream Function forTwo-DimensionalIncompressible Flow
  • Two-Dimensional Flow
  • Stream Function y
stream function for two dimensional incompressible flow1
Stream Function forTwo-DimensionalIncompressible Flow
  • Cylindrical Coordinates
  • Stream Function y(r,q)
motion of a fluid particle kinematics
Motion of a Fluid Particle (Kinematics)
  • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
  • Fluid Rotation
  • Fluid Deformation
    • Angular Deformation
    • Linear Deformation
motion of a fluid particle kinematics2
Motion of a Fluid Particle (Kinematics)
  • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
motion of a fluid particle kinematics3
Motion of a Fluid Particle (Kinematics)
  • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
motion of a fluid particle kinematics4
Motion of a Fluid Particle (Kinematics)
  • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field
motion of a fluid particle kinematics5
Motion of a Fluid Particle (Kinematics)
  • Fluid Translation: Acceleration of aFluid Particle in a Velocity Field (Cylindrical)
motion of a fluid particle kinematics9
Motion of a Fluid Particle (Kinematics)
  • Fluid Deformation:
    • Angular Deformation
motion of a fluid particle kinematics10
Motion of a Fluid Particle (Kinematics)
  • Fluid Deformation:
    • Angular Deformation
motion of a fluid particle kinematics11
Motion of a Fluid Particle (Kinematics)
  • Fluid Deformation:
    • Linear Deformation
momentum equation
Momentum Equation
  • Newton’s Second Law
momentum equation1
Momentum Equation
  • Forces Acting on a Fluid Particle
momentum equation2
Momentum Equation
  • Forces Acting on a Fluid Particle
momentum equation3
Momentum Equation
  • Differential Momentum Equation
momentum equation4
Momentum Equation
  • Newtonian Fluid: Navier-Stokes Equations
momentum equation5
Momentum Equation
  • Special Case: Euler’s Equation