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Introduction to Fluid Mechanics

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Title: Introduction to Fluid Mechanics


1
Introduction to Fluid Mechanics
  • Chapter 6
  • IncompressibleInviscid Flow

2
Main Topics
  • Momentum Equation for Frictionless Flow Eulers
    Equation
  • Eulers Equation in Streamline Coordinates
  • Bernoulli Equation Integration of Eulers
    Equation Along a Streamline for Steady Flow
  • The Bernoulli Equation Interpreted as an Energy
    Equation
  • Energy Grade Line and Hydraulic Grade Line

3
Momentum Equation for Frictionless Flow Eulers
Equation
  • Eulers Equation
  • Continuity

4
Momentum Equation for Frictionless Flow Eulers
Equation
  • Rectangular Coordinates

5
Momentum Equation for Frictionless Flow Eulers
Equation
  • Cylindrical Coordinates

6
Eulers Equation inStreamline Coordinates
  • Along a Streamline(Steady Flow, ignoring body
    forces)
  • Normal to the Streamline(Steady Flow, ignoring
    body forces)

7
Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
  • Eulers Equation in Streamline Coordinates
    (assuming Steady Flow)

8
Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
  • Integration Along s Coordinate

9
Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
  • Bernoulli Equation
  1. Steady Flow
  2. No Friction
  3. Flow Along a Streamline
  4. Incompressible Flow

10
Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
  • Static, Stagnation, and Dynamic Pressures(Ignore
    Gravity)

11
The Bernoulli Equation Interpreted as an Energy
Equation
12
The Bernoulli Equation Interpreted as an Energy
Equation
  • Basic Equation
  1. No Shaft Work
  2. No Shear Force Work
  3. No Other Work
  4. Steady Flow
  5. Uniform Flow and Properties

13
The Bernoulli Equation Interpreted as an Energy
Equation
Hence
Assumption 6 Incompressible
Assumption 7
14
The Bernoulli Equation Interpreted as an Energy
Equation
  • Energy Equation
  1. No Shaft Work
  2. No Shear Force Work
  3. No Other Work
  4. Steady Flow
  5. Uniform Flow and Properties
  6. Incompressible Flow
  7. u2 u1 dQ/dm 0

15
Energy Grade Line and Hydraulic Grade Line
  • Energy Equation

16
Energy Grade Line and Hydraulic Grade Line
  • Energy Grade Line (EGL)
  • Hydraulic Grade Line (HGL)

17
Energy Grade Line and Hydraulic Grade Line
18
Irrotational Flow
  • Irrotationality Condition

19
Irrotational Flow
  • Velocity Potential

20
Irrotational Flow
  • Velocity Potential automatically satisfies
    Irrotationality Condition

21
Irrotational Flow
  • 2D Incompressible, Irrotational Flow

22
Irrotational Flow
  • Elementary Plane Flows

23
Irrotational Flow
  • Superposition
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