Introduction to Fluid Mechanics

1
Introduction to Fluid Mechanics

• Chapter 5
• Introduction to Differential Analysis of Fluid
  Motion

2
Main Topics

• Conservation of Mass
• Stream Function for Two-Dimensional
  Incompressible Flow
• Motion of a Fluid Particle (Kinematics)
• Momentum Equation

3
Conservation of Mass

• Basic Law for a System

4
Conservation of Mass

• Rectangular Coordinate System

5
Conservation of Mass

• Rectangular Coordinate System

6
Conservation of Mass

• Rectangular Coordinate System

Continuity Equation
7
Conservation of Mass

• Rectangular Coordinate System

Del Operator
8
Conservation of Mass

• Rectangular Coordinate System

9
Conservation of Mass

• Rectangular Coordinate System

Incompressible Fluid
Steady Flow
10
Conservation of Mass

• Cylindrical Coordinate System

11
Conservation of Mass

• Cylindrical Coordinate System

12
Conservation of Mass

• Cylindrical Coordinate System

Del Operator
13
Conservation of Mass

• Cylindrical Coordinate System

14
Conservation of Mass

• Cylindrical Coordinate System

Incompressible Fluid
Steady Flow
15
Stream Function forTwo-DimensionalIncompressible
Flow

• Two-Dimensional Flow

• Stream Function y

16
Stream Function forTwo-DimensionalIncompressible
Flow

• Cylindrical Coordinates

• Stream Function y(r,q)

17
Motion of a Fluid Particle (Kinematics)

• Fluid Translation Acceleration of aFluid
  Particle in a Velocity Field
• Fluid Rotation
• Fluid Deformation
• Angular Deformation
• Linear Deformation

18
Motion of a Fluid Particle (Kinematics)
19
Motion of a Fluid Particle (Kinematics)

• Fluid Translation Acceleration of aFluid
  Particle in a Velocity Field

20
Motion of a Fluid Particle (Kinematics)

• Fluid Translation Acceleration of aFluid
  Particle in a Velocity Field

21
Motion of a Fluid Particle (Kinematics)

• Fluid Translation Acceleration of aFluid
  Particle in a Velocity Field

22
Motion of a Fluid Particle (Kinematics)

• Fluid Translation Acceleration of aFluid
  Particle in a Velocity Field (Cylindrical)

23
Motion of a Fluid Particle (Kinematics)

• Fluid Rotation

24
Motion of a Fluid Particle (Kinematics)

• Fluid Rotation

25
Motion of a Fluid Particle (Kinematics)

• Fluid Rotation

26
Motion of a Fluid Particle (Kinematics)

• Fluid Deformation
• Angular Deformation

27
Motion of a Fluid Particle (Kinematics)

• Fluid Deformation
• Angular Deformation

28
Motion of a Fluid Particle (Kinematics)

• Fluid Deformation
• Linear Deformation

29
Momentum Equation

• Newtons Second Law

30
Momentum Equation

• Forces Acting on a Fluid Particle

31
Momentum Equation

• Forces Acting on a Fluid Particle

32
Momentum Equation

• Differential Momentum Equation

33
Momentum Equation

• Newtonian Fluid Navier-Stokes Equations

34
Momentum Equation

• Special Case Eulers Equation