Title: Introduction to Fluid Mechanics
1Introduction to Fluid Mechanics
- Chapter 6
- IncompressibleInviscid Flow
2Main 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
3Momentum Equation for Frictionless Flow Eulers
Equation
4Momentum Equation for Frictionless Flow Eulers
Equation
5Momentum Equation for Frictionless Flow Eulers
Equation
6Eulers Equation inStreamline Coordinates
- Along a Streamline(Steady Flow, ignoring body
forces)
- Normal to the Streamline(Steady Flow, ignoring
body forces)
7Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
- Eulers Equation in Streamline Coordinates
(assuming Steady Flow)
8Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
- Integration Along s Coordinate
9Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
- Steady Flow
- No Friction
- Flow Along a Streamline
- Incompressible Flow
10Bernoulli Equation Integration of Eulers
Equation Along a Streamline for Steady Flow
- Static, Stagnation, and Dynamic Pressures(Ignore
Gravity)
11The Bernoulli Equation Interpreted as an Energy
Equation
12The Bernoulli Equation Interpreted as an Energy
Equation
- No Shaft Work
- No Shear Force Work
- No Other Work
- Steady Flow
- Uniform Flow and Properties
13The Bernoulli Equation Interpreted as an Energy
Equation
Hence
Assumption 6 Incompressible
Assumption 7
14The Bernoulli Equation Interpreted as an Energy
Equation
- No Shaft Work
- No Shear Force Work
- No Other Work
- Steady Flow
- Uniform Flow and Properties
- Incompressible Flow
- u2 u1 dQ/dm 0
15Energy Grade Line and Hydraulic Grade Line
16Energy Grade Line and Hydraulic Grade Line
- Hydraulic Grade Line (HGL)
17Energy Grade Line and Hydraulic Grade Line
18Irrotational Flow
- Irrotationality Condition
19Irrotational Flow
20Irrotational Flow
- Velocity Potential automatically satisfies
Irrotationality Condition
21Irrotational Flow
- 2D Incompressible, Irrotational Flow
22Irrotational Flow
23Irrotational Flow