13.1.2. System versus Control Volume Concept

Now, let us come to what is a system and what is a control volume. A system is defined as a set of fluid particles, or more specifically, a set of virtual fluid balls. In motion, they change position, velocity, and pressure vectors. In contrast, a control volume refers to a fixed region of space that can have fluid particles moving in and out.

Here, the section differentiates between 'system' and 'control volume'. A system consists of fluid particles, which can change over time and space. For instance, when you think of a flowing river, the water particles in that river represent a system. On the other hand, a control volume is a specific region in space that doesn’t change – think of it as an invisible box that can contain fluid but doesn’t itself move. Imagine drawing a rectangle around a section of that river; that rectangle is your control volume, and you look at what enters or leaves this defined area.

Consider a water bottle. The water inside represents a system since its quantity and properties can change as you drink. However, the bottle itself represents a control volume; it has defined dimensions, and while the water can enter or exit, the bottle's size and shape stay the same.

The system can change over time, meaning fluid particles can displace and rearrange, while maintaining the same mass. In contrast, while the control volume remains fixed, the fluids can flow in and out through its surfaces. The primary focus at the control volume level is the change in velocity field, mass flux, pressure gradient, and energy exchange, not the individual fluid particles.

This chunk explains how systems are dynamic, meaning that they can experience changes in their properties or the location of their particles over time. In contrast, the control volume remains static, and we look at how fluids behave as they enter and exit this defined space. For instance, consider a pumping system – while the liquid inside the pump (the system) is moving and changing, we observe how that liquid interacts at the boundaries of the pump (the control volume) without worrying about the specifics of every individual particle inside it.

Imagine a busy restaurant's kitchen as a control volume. The kitchen space itself doesn’t change size or shape, but the chefs (fluid particles) are busy coming in and out, cooking, and serving. The focus for the manager (the observer) isn’t on the details of each chef but on how well the kitchen runs with the flow of people and food as they come in and out.

Control volumes can be classified into three types: fixed control volume, movable control volume, and deformable control volume. A fixed control volume stays the same through time, while a movable control volume moves with the fluid, and a deformable control volume changes its dimensions to fit the space occupied by the fluid.

This part discusses the different kinds of control volumes used in fluid mechanics. A fixed control volume could be a section of a pipe where fluid flows in but the section itself does not change. A movable control volume may be a ship moving through the water where we have to account for the ship's motion while considering the water flow around it. A deformable control volume refers to situations such as a piston in an engine, where the space occupied by the gas expands or contracts, changing the volume and behavior of the gas inside.

Think of a balloon filled with air as a deformable control volume – as you squeeze it, the shape changes based on the pressure inside. A fixed control volume could be a reservoir that holds water but isn’t going anywhere. A movable control volume could be a watercraft navigating through water – its position and how it interacts with waves changes, just like the fluid does around it.

The laws of conservation apply to systems and can be summarized as follows: conservation of mass, conservation of momentum, and conservation of energy. When considering isolated systems composed of virtual fluid balls, we can analyze the interactions with the control volume to calculate changes in mass, velocity, and energy.

Lastly, this section lays out the fundamental conservation laws that govern fluid mechanics. Conservation of mass ensures that the mass of fluid within a system remains constant unless it leaves the system. Conservation of momentum states that the momentum of the fluid can change due to external forces acting upon it. Lastly, the conservation of energy asserts that energy in the system is exchanged in forms such as work or heat. These principles help define fluid behavior in various applications, from pumps to turbines.

Think of a public water supply system. The water being transported represents the conservation of mass, as the total amount of water remains constant despite pressures and flows. The momentum conservation can be observed during peak usage times when the pressure changes are experienced throughout the pipes. Energy conservation is evident when pumps are used – they provide energy to push the water, changing its kinetic energy as it moves through the system.

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