Fluid Mechanics Principles and Flow Dynamics

Archimedes' Principle

Archimedes' Principle: Any body immersed in a fluid suffers an apparent weight loss equal to the weight of the liquid displaced (evicted).

Pressure Concepts

Pressure: It is the force exerted per unit area.

Atmospheric Pressure: Pressure exerted by the atmospheric layer above the Earth.

Hydrostatic Pressure: Is the pressure exerted by a column of fluid at the bottom of the tank that contains it.

Pascal's Principle

Pascal's Principle: All fluid enclosed in a tank, when subjected to pressure, exerts this in all directions with equal intensity.

Flow Characteristics

• Steady-flow: When the particles of a fluid passing a given point of the pipe keep the speed constant.
• Incompressible-flow: Liquids are considered incompressible because their density does not vary during movement. Gases are considerably compressible; however, in some special situations, they can be considered incompressible.
• Irrotational-flow: The flow in which fluid particles have a net angular velocity equal to 0; otherwise, it is rotational flow.

Current Lines

These lines represent the trajectory of particles in a steady flow.

Conservation Laws and Bernoulli

Principle of Conservation of Mass: The total mass of the universe remains constant; it is neither created nor destroyed, but can be transformed into energy.

Bernoulli's Principle: For steady, incompressible flow without internal friction, the summation of pressure energy, kinetic energy, and potential energy in any part of the pipe is constant.

Venturi Tube and Output Speed

Venturi Tube: It is a device that permits determining the speed of the pipe.

Output Speed: For a hole in a tank open to the atmosphere.

Torricelli's Theory: The liquid behaves as a solid in free fall when it leaves a hole in a tank open to the atmosphere.

Viscosity and Fluid Behavior

Viscosity: A liquid can support compression efforts but no traction. The fluid particles are subjected to intermolecular forces called cohesion; as they move in relation to each other, friction forces are generated due to these forces of cohesion.

Technical Notes

1. In an ideal fluid, u = 0.
2. In a real fluid, u ≠ 0.
3. The dynamic viscosity varies with temperature: if the temperature rises, the viscosity increases in gases and decreases in liquids, but in both cases, it is practically independent of pressure.
4. The kinematic viscosity varies with pressure and temperature in gases. In liquids, it varies with temperature.
5. The kinematic viscosity depends on the density and, therefore, the inertial forces.

Theory of Models

To test the model and prototype so they are dynamically similar, the Reynolds numbers must be equal.

Note: If the Reynolds number (RE) is:

• RE > 20,000: Turbulent flow in a pipe.
• RE > 10: Turbulent flow with an obstacle.

Flow Types

Laminar flow: The fluid particles follow known trajectories that resemble sheets.

Turbulent flow: Fluid particle trajectories are unknown; it causes a mess (disorder).