Mechanical Properties of Solids

9.1 Introduction

This chapter introduces the fundamental physical properties of fluids, which include liquids and gases. Fluids are distinct from solids primarily because they can flow and do not have a fixed shape. Instead, their shape is determined by the container that holds them. Both liquids and gases are classified as fluids due to this property. While solids and liquids have a fixed volume, gases expand to fill their containers entirely. The volume of solids, liquids, and gases can change under applied stress or pressure, but solids and liquids are much less compressible compared to gases. Another key difference is that fluids offer very little resistance to shear stress, meaning their shape changes easily under such forces, unlike solids which resist shear stress strongly. This chapter aims to explore these properties and understand the behavior of fluids under various conditions.

• Fluids include liquids and gases, characterized by their ability to flow.
• Fluids have no definite shape; their shape depends on the container.
• Solids and liquids have fixed volume; gases fill the entire container volume.
• Solids and liquids have low compressibility compared to gases.
• Fluids offer negligible resistance to shear stress compared to solids.
• Understanding fluid properties is essential due to their prevalence in nature and technology.
• 📌 Fluid: A substance that can flow and does not have a fixed shape.
• 📌 Compressibility: The measure of how much a substance's volume decreases under pressure.
• 📌 Shear stress: A force that causes layers of a material to slide past each other.

9.2 Pressure

Pressure is defined as the force exerted per unit area on a surface. Everyday experiences illustrate that the effect of a force depends not only on its magnitude but also on the area over which it is applied. For example, a sharp needle pierces the skin because it applies force over a very small area, resulting in high pressure, whereas a blunt object does not. Similarly, an elephant stepping on a man’s chest can cause injury due to the large force applied over a relatively small area, but placing a wooden plank distributes the force over a larger area, reducing pressure and preventing injury. In fluids at rest, the force exerted by the fluid on any surface is always perpendicular (normal) to that surface. This is because any tangential component would cause the fluid to flow, which contradicts the assumption of fluid at rest. Pressure is a scalar quantity, representing the magnitude of the normal force per unit area. It is measured in pascals (Pa) in the SI system, where 1 Pa = 1 N/m². Other units include atmosphere (atm), bar, and torr. The density of a fluid, defined as mass per unit volume, is an important property influencing pressure variations in fluids. Liquids are largely incompressible, so their density remains nearly constant under pressure, while gases show significant density changes with pressure variations.

• Pressure = Force/Area; smaller area leads to higher pressure for the same force.
• Fluid exerts force normal to any surface in contact when at rest.
• Pressure is a scalar quantity with SI unit pascal (Pa).
• Density (ρ) = mass/volume; important in fluid pressure calculations.
• Liquids are nearly incompressible; gases are compressible.
• Common pressure units: Pa, atm (1 atm = 1.013 × 10^5 Pa), bar, torr.
• 📌 Pressure: Force exerted per unit area, acting normal to surface.
• 📌 Density (ρ): Mass per unit volume of a fluid.
• 📌 Pascal (Pa): SI unit of pressure, equal to one newton per square meter.