Fluids Wk 5 Tuesday Lecture Bernoulii Examples, Nozzles, Cavitation

Assumptions
- Inviscid Flow: No viscous effects considered.
- Incompressible Fluid: Fluid density is constant and does not vary with pressure changes.
- Steady Flow: Fluid properties at a point do not change over time.
- Flow Along a Streamline: Bernoulli's equation is applied along a streamline only; improper orientation leads to incorrect results.

The equation is derived from the principles of energy conservation in a fluid system.
Derived under the assumption of incompressibility, where density remains a constant value.
General form:
- Bernoulli's Equation: ( P + \frac{1}{2}\rho v^2 + \rho gh = constant )
- Relates pressure (P), dynamic pressure (( \frac{1}{2}\rho v^2 )), and potential energy per unit volume (( \rho gh )).
Pitot Static Tube: Used for measuring velocity based on pressure difference; idealized conditions assume constant density.

Confined Flow:
- Fluid constrained by boundaries (e.g., pipes).
- Pressure cannot be determined solely by atmospheric pressure due to isolation from the environment.
- Conservation of mass principle, represented as the Continuity Equation:
  - Mass flow rates must remain constant between two points: ( m_1 = m_2 ) or ( \rho_1 A_1 v_1 = \rho_2 A_2 v_2 ).
Velocity and Cross-Section Area Relationship:
- When pipe area reduces (e.g., nozzle), flow velocity increases to conserve mass.
- Definition of flow rate (Q):
  - ( Q = A v ), often used in practical applications for fluid systems.

Vertical Flow Considerations: Analyze how acceleration affects pressure changes; using Bernoulli's equation here facilitates understanding of upward/downward flow transitions.
Practical Problem-Solving: Using Bernoulli’s and continuity principles together to derive relationships between variables while considering assumptions.
- Know the context of each variable; ensure showing streamlines and clear identification of pressures and velocities.

Cavitation occurs when pressure drops below the saturation vapor pressure of the fluid, leading to the formation of vapor bubbles.
Boiling Point Reference: At atmospheric pressure, water boils at 100°C; lowering pressure allows boiling at lower temperatures.
Bubble Formation Process:
- Bubbles form due to low pressures (e.g., through nozzles); once they exit constricted areas and enter zones of higher pressure, the bubbles collapse.
Destructive Effects:
- Cavitation can damage piping systems and impeller blades due to the intense pressures experienced during bubble collapse.
Practical System Design:
- When designing fluid systems, assess potential for cavitation by evaluating pressures at various operational points, modifying designs to prevent adverse conditions.