bolurins physics

Key Concepts in Fluid Mechanics

Buoyancy and Density

• To solve for buoyancy (b) and pressure (beta), you only need:

  • Density of the object

  • Density of the fluid

  • Gravitational acceleration (g)

• The gravity constant (g) remains the same in these problems.

Understanding Flow Rate

• Flow Rate (Q): A measure of the volume of fluid passing through a surface per time, denoted as Q.

• Flow depends on:

  • Cross-sectional area (A)

  • Velocity of the fluid (v)

• Basic formula to remember: Q = A * v

• For circular cross-sections: Area can be calculated as A = πr²

Continuity Principle

• Applies when fluid is incompressible and flows through varying cross-sectional areas.

• Formula: A₁v₁ = A₂v₂ (for two areas in the flow)

  • Where:

    • A₁ = initial area

    • v₁ = initial flow velocity

    • A₂ = final area

    • v₂ = final flow velocity

• Important to recognize the inverse relationship: If area goes up, velocity goes down (and vice versa).

Bernoulli's Principle

• Explains how pressure varies due to changes in fluid speed and height. Key notes:

  • As fluid speed (v) increases, pressure (P) decreases: P + 1/2ρv² + ρgh = constant.

  • Areas of lower pressure have higher fluid speeds.

• Example: Using a hose: squeezing the end of the hose reduces the area, increasing fluid speed and allowing water to shoot further.

Pressure and Velocity Relationships

• If height is constant and fluids are at the same level: you can eliminate height differences from calculations.

• Keep in mind how fluid travels in vertical scenarios:

  • In pipes, fluid pressure decreases as height increases; thus, more height leads to less pressure.

• In a scenario with two heights (e.g., spigot and water column), consider how pressures might differ.

Practical Applications

• Aerodynamics in Aviation and Automobiles: Understanding how airflow variables can affect lift and drag.

• Medical Procedures: Knowing how fluid dynamics works aids in medical fluid injections and other procedures.

Problem Solving Strategies

• Always identify knowns and unknowns in the problem at hand.

• Be cautious when using pressures or heights – it is key to recognize when you can or cannot eliminate them in your equations.

• Use the correct units consistently (e.g., Pascals for pressure).

• Practice applying these principles through example problems before exams.