1. Introduction to Fluid Mechanics
Chapter 6
Incompressible Inviscid Flow

2. Main Topics Momentum Equation for Frictionless Flow: Euler’s Equation
Euler’s Equation in Streamline Coordinates
Bernoulli Equation – Integration of Euler’s 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: Euler’s Equation
Continuity

4. Momentum Equation for Frictionless Flow: Euler’s Equation
Rectangular Coordinates

5. Momentum Equation for Frictionless Flow: Euler’s Equation
Cylindrical Coordinates

6. Euler’s Equation in Streamline Coordinates
Along a Streamline (Steady Flow, ignoring body forces)

7. Euler’s Equation in Streamline Coordinates
Normal to the Streamline (Steady Flow, ignoring body forces)

8. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow
Euler’s Equation in Streamline Coordinates (assuming Steady Flow)

9. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow
Integration Along s Coordinate

10. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow
No Friction
Flow Along a Streamline
Incompressible Flow

11. Bernoulli Equation
Derivation Using Rectangular Coordinates

12. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow
Static, Stagnation, and Dynamic Pressures (Ignore Gravity)
Stagnation
Static
Dynamic

13. Bernoulli Equation – Integration of Euler’s Equation Along a Streamline for Steady Flow
Pitot Tube

14. The Bernoulli Equation Interpreted as an Energy Equation

15. The Bernoulli Equation Interpreted as an Energy Equation
Basic Equation
No Shaft Work
No Shear Force Work
No Other Work
Steady Flow
Uniform Flow and Properties

16. The Bernoulli Equation Interpreted as an Energy Equation
Hence
Assumption 6: Incompressible
Assumption 7:

17. The 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

18. Energy Grade Line and Hydraulic Grade Line
Energy Equation
H is the total head of the flow; it measures the total mechanical energy in units of meters or feet.

19. Energy Grade Line and Hydraulic Grade Line
Energy Grade Line (EGL)
Hydraulic Grade Line (HGL)

20. Energy Grade Line and Hydraulic Grade Line

21. Irrotational Flow
Irrotationality Condition
Irrotational flow

22. Irrotational Flow
Velocity Potential

23. Irrotational Flow
Velocity Potential automatically satisfies Irrotationality Condition

24. Irrotational Flow
2D Incompressible, Irrotational Flow

25. Irrotational Flow The slope of a potential line (a line of constant ϕ)
The slope of a streamline (a line of constant ψ)
Lines of constant ψ and constant ϕ are orthogonal.

26. Irrotational Flow
Elementary Plane Flows

27. Irrotational Flow
Superposition