4. Mechanics of fluids

Introduction

• Ideal Fluids:
• Ideal fluids represent a theoretical concept where fluid behaviour is simplified for analytical purposes (too perfect for real fluids).
• Characteristics:
• No friction or internal forces: Ideal fluids flow without any resistance or internal friction, allowing smooth motion.
• Volume remains constant: They cannot be compressed or expanded, maintaining a constant volume under any conditions.
• Zero viscosity: Ideal fluids have no internal friction between layers, enabling perfect flow without any loss of kinetic energy.
• Ideal fluids serve as a useful theoretical model for understanding fluid dynamics in simplified scenarios.
• Real Fluids:
• Real fluids are the fluids we encounter in everyday life, which deviate from the idealized behavior due to various factors.
• Characteristics:
• Compressible: Real fluids can be compressed or expanded under pressure, unlike ideal fluids, which maintain a constant volume.
• Viscous in nature: Real fluids exhibit viscosity, meaning they offer resistance to flow and show internal friction between layers.
• Certain amount of resistance: Due to viscosity, real fluids encounter resistance when flowing, leading to energy losses.
• Real fluids, while more complex in behavior compared to ideal fluids, accurately represent the behavior of most fluids encountered in practical situations.
• Density of Fluids:
• Density (symbolized by ρ) is a fundamental property of fluids that quantifies how much mass is packed into a certain volume.
• Formula: Density (ρ) equals the change in mass (Δm) divided by the change in volume (Δv), expressed as ρ = Δm / Δv.
• Density plays a crucial role in determining various fluid characteristics, including buoyancy, pressure, and flow behavior.
• Hydrostatic Pressure:
• Hydrostatic pressure refers to the pressure exerted by a fluid at rest at a specific point within the fluid due to the force of gravity.

• It arises from the weight of the fluid above the given point, pressing down uniformly in all directions.
• Hydrostatic pressure increases linearly with depth and is influenced by fluid density, gravitational acceleration, and depth. It can be calculated using the formula P = ρgh, where P is the hydrostatic pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid column.
• Archimedes force
• Archimedes' Principle: Buoyancy Explained
• Archimedes' Principle is a fundamental law of fluid mechanics that explains the buoyant force acting on an object submerged in a fluid (liquid or gas). It states: