14.1.2. Energy Conservation Principles

The conservation of momentum which is required for you to know it, how the fluid particles are moving it, what could be the force exerting on that, what could be the velocity. Similar way, we can understand the energy conservation which plays a major role for us when the fluid comes from one location to other locations, how much of work is done by the fluid or into the fluid.

This chunk introduces the concept of energy conservation as it relates to fluids. It explains that as fluid particles move from one location to another, they exert forces and have velocities that are important to understanding energy conservation. The work done by the fluid, in terms of energy conservation, refers to the energy transfer that occurs as fluids interact with their surroundings or move through different states.

Imagine a river flowing from a higher elevation to a lower one. As the water moves downstream, it has potential energy due to its height, which gets converted into kinetic energy as it speeds up. This exchange illustrates energy conservation in action, where the total energy remains constant but transforms as the fluid flows.

To summarise this, that means, we all know that there are three energy conservation principles that we follow in solid mechanics when you consider as a system. Same concept also we can use at the system levels to solve the problems, conservation of mass, conservation of linear momentum which is Newton’s law, and the conservation of energy which is the first law of thermodynamics.

This chunk summarizes the three fundamental principles of conservation relevant to fluid mechanics: conservation of mass, conservation of linear momentum, and conservation of energy. The conservation of mass states that mass cannot be created or destroyed; it must remain constant. The conservation of linear momentum relates to how a fluid maintains its motion unless acted upon by an external force, as described by Newton's laws. Lastly, the conservation of energy aligns with the First Law of Thermodynamics, which states that energy cannot be created or destroyed, only transformed.

Think of energy conservation like a bicycle ride. When you pedal uphill, you use energy to change potential energy as you gain height, but as you ride downhill, that potential energy converts back into kinetic energy, and you speed up. Just like the bicycle, fluids maintain their energy and momentum as they flow, obeying these principles along their path.

Now, let me define two types of properties that we have; one is called extensive property and the other is the intensive property. The extensive property which is considered as proportional to the amount of mass.

In this section, the difference between extensive and intensive properties is clarified. Extensive properties depend on the amount of substance present; examples include mass, momentum, and energy. As the amount of mass increases or decreases, so do the extensive properties. Intensive properties, on the other hand, do not depend on the mass – they remain the same regardless of how much substance you have. Examples include temperature and pressure. For instance, while the energy of a system increases with added mass, the temperature (an intensive property) does not change.

Consider a glass of water. If you fill it halfway, it has a certain temperature and mass. If you then fill it all the way, the temperature stays the same (intensive property), but the mass and total energy increase (extensive properties). This illustrates how extensive and intensive properties function differently in a real-world scenario.

Let us understand the Reynolds transport theorem which establish the relationship between the conservation law at the system level and the conservation at the control volume level.

The Reynolds transport theorem is a critical concept that connects the conservation laws at the system level (the larger context of fluid mechanics) to those at the control volume level (specific areas within that system). It allows for the evaluation of changes in extensive properties over time, contributing to understanding how fluid properties evolve when considering a specific section of space or fluid (the control volume). This theorem is fundamental for deriving the equations governing mass, momentum, and energy in fluid systems.

Think of the Reynolds transport theorem like tracking your morning coffee. If you consider yourself (the system) and your cup (the control volume), you can observe how the amount of coffee (mass) you pour in changes over time while also thinking about how the total amount of coffee in the pot (the system) remains constant unless something is added or taken out. This analogy helps in illustrating the dynamic changes in properties within a defined space.

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