03 Dinamika Fluida Persamaan Bernoulli Part3 MEKFLU

Introduction

This tutorial focuses on the principles of fluid dynamics as explained through Bernoulli's equation, particularly related to inviscid flow and Newton's laws along a streamline. Understanding these concepts is essential for engineering applications involving fluid mechanics, such as aerodynamics and hydrodynamics.

Step 1: Understand Inviscid Flow

• Definition: Inviscid flow refers to fluid motion where viscosity is negligible. In this scenario, the fluid does not experience internal friction.
• Importance: This concept simplifies the analysis of fluid motion, allowing for easier application of Bernoulli's equation.

Step 2: Apply Newton's Second Law Along Streamlines

• Concept: Newton's second law can be applied to fluid particles moving along a streamline. It states that the force acting on a fluid particle is equal to the rate of change of momentum.
• Mathematical Representation:
  • For a fluid particle, the forces can be described by:
    • ( F = ma )
    • Where ( F ) is the net force, ( m ) is mass, and ( a ) is acceleration.
• Key Consideration: Ensure that the forces considered are those acting tangential and perpendicular to the streamline.

Step 3: Explore Bernoulli’s Equation

• Formulation: Bernoulli's equation relates pressure, velocity, and height in a flowing fluid. The general form is:
  • ( P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} )
  • Where:
    • ( P ) = static pressure
    • ( \rho ) = fluid density
    • ( v ) = fluid velocity
    • ( g ) = acceleration due to gravity
    • ( h ) = height above a reference point
• Interpretations:
  • Stagnation Pressure: The pressure when fluid velocity is zero.
  • Static Pressure: The pressure in the fluid when it is at rest.
  • Dynamic Pressure: The pressure associated with the fluid's motion.

Step 4: Recognize the Physical Interpretation of Bernoulli's Equation

• Pressure Types:
  • Stagnation Pressure: Total pressure at a point where the fluid comes to rest.
  • Static Pressure: The pressure felt by a stationary observer in the fluid.
  • Dynamic Pressure: Represents the kinetic energy per unit volume of the fluid.
• Applications: This understanding is crucial in various applications, such as calculating lift in airfoils or predicting flow behavior in pipes.

Step 5: Identify Limitations of Bernoulli's Equation

• Flow Assumptions: Bernoulli's equation is applicable under certain conditions:
  • The flow must be steady.
  • The fluid must be incompressible.
  • Viscous effects are negligible (inviscid).
• Common Pitfalls: Applying Bernoulli's equation in scenarios where these conditions are violated can lead to inaccurate results.

Conclusion

In this tutorial, we've covered the fundamentals of Bernoulli's equation and its application in fluid dynamics, specifically regarding inviscid flow and Newton's laws along streamlines. Understanding these principles is vital for engineers working with fluid systems. For further exploration, consider practical applications of Bernoulli's equation in real-world engineering problems, such as fluid transport in pipelines or aerodynamics in vehicle design.