In this chapter, we will delve into the world of fluid mechanics. We begin will defining what a fluid actually is and then progress into other topics such as density, bernoulli’s equation, and turbulence.
20.1 Understanding Fluids: Liquids and Gases
In the realm of physics, we define a fluid as a substance that deforms continuously under the application of shear stress, regardless of how small that stress might be. This encompasses both gases and liquids, as both of them conform to the shape of their containers and flow when subjected to external forces.
The core difference between gases and liquids lies in their compressibility. Liquids are nearly incompressible, meaning their volume remains relatively constant under pressure, whereas gases are highly compressible and expand to fill their containers.
20.2 Fluid Density
A fundamental property of any fluid is its density (
), defined as its mass per unit volume:
where 
is the mass of the fluid and 
is its volume. The units of density are typically kilograms per cubic meter 
in the International System of Units (SI).
20.3 Exploring Pressure in Fluids
Pressure 
is a scalar quantity related to the force exerted by a fluid on a surface per unit area. In fluids, pressure is isotropic, meaning it acts equally in all directions. The general equation for pressure is:
where 
is the force applied and 
is the area over which it is distributed.
20.3.1 Depth and Pressure in a Fluid
In a fluid at rest, the pressure increases with depth due to the weight of the fluid above. This increase in pressure can be calculated using:
where 
is the pressure at the surface of the fluid, is the fluid density, 
is the acceleration due to gravity, and 
is the depth below the surface of the fluid.
20.4 Dynamics of Fluid Flow
Fluid dynamics is the study of how fluids behave when they flow. In this section, we’ll introduce the concepts of laminar and turbulent flow, and then dive into the Bernoulli’s equation.
20.4.1 Laminar and Turbulent Flow
Fluid flow can be characterized as either laminar or turbulent. Laminar flow is smooth and orderly, with fluid particles moving in parallel layers, or “streamlines”. Turbulent flow, on the other hand, is chaotic and unpredictable, characterized by eddies, swirls, and rapid changes in pressure and velocity.
20.4.2 Bernoulli’s Equation
Bernoulli’s equation is a principle of fluid dynamics that describes how the pressure of a fluid changes with its speed and elevation. The equation is:
where 
is the fluid pressure, is the fluid density, 
is the speed of the fluid, is the acceleration due to gravity, and is the height above a reference point.
20.5 Turbulence in Fluid Mechanics
While viscosity typically helps in maintaining laminar flow by damping out disturbances, under certain conditions, a fluid’s flow can become unstable and exhibit irregular motion, referred to as turbulence. Turbulence is characterized by eddies and swirls that mix fluid elements and enhance the rate of energy dissipation.
The transition from laminar to turbulent flow depends on the Reynolds number (
), a dimensionless quantity defined as:
where is the fluid density, is the fluid velocity, 
is a characteristic length (such as the diameter of a pipe), and 
is the dynamic viscosity of the fluid.
For 
, the flow is generally laminar, while for 
, the flow is generally turbulent. The range 
is a transition range where the flow can be either laminar or turbulent.
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Continue to Chapter 21: Buoyancy and Archimedes’ Principle
Back to Chapter 19: Thermal Energy
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