Fluid flow involves a few basic properties and rules that help explain how liquids and gases behave. Knowing these properties is really important for understanding different situations in fluid mechanics.

First, let’s talk about density. Density is the amount of mass in a certain volume. It's usually shown by the Greek letter $\rho$. Density helps us figure out things like buoyancy and how fluids behave in different places. For example, in fluids that are layered (like oil and water), each layer can have a different density, which causes them to flow in different ways.

Next is viscosity. Viscosity tells us how thick or sticky a fluid is and how well it flows. It helps us know if the flow is smooth (laminar) or rough (turbulent). The dynamic viscosity is shown by the letter $\mu$. It affects how fluids move around each other and against surfaces. Think of honey; it flows slowly because it has high viscosity. Water flows quickly because it has low viscosity. The Reynolds number, which is calculated using $Re = \frac{\rho vD}{\mu}$, helps us understand the type of flow based on viscosity, density, and speed.

Another important property is pressure. Pressure measures how much force the fluid puts on a certain area. When there’s a difference in pressure, fluids will move from areas of high pressure to low pressure. The Bernoulli equation, shown as:

$$P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$$

helps explain this relationship. It connects pressure (P), the energy from movement ($\frac{1}{2} \rho v^2$), and the energy from height ($\rho gh$).

Temperature also plays a big part in how fluids act. It can change both density and viscosity, which means it affects how fluids flow. In cooling systems, keeping the temperature steady is really important for smooth fluid movement and good performance.

We should also think about compressibility, especially when talking about gases. Compressibility is about how much a fluid’s volume changes when pressure changes. Most liquids are incompressible, meaning their density stays pretty much the same. But gases can change a lot when pressure and temperature vary, making compressibility a key factor, especially in things like planes and engines.

Finally, surface tension and capillarity are important when fluids interact with solid surfaces. Surface tension happens because of the strong forces at the surface of a liquid, affecting things like how droplets form. This is really important in small-scale applications like inkjet printing and oil recovery.

In summary, by looking at these basic properties—density, viscosity, pressure, temperature, compressibility, and surface tension—we can understand and predict how fluids behave. Mastering these concepts helps students and professionals in fluid mechanics handle real-world challenges, from how airplanes move through the air to how water flows in pipes, improving our grasp of fluid dynamics.