First law of thermodynamics (fluid mechanics)

The First Law of Thermodynamics, when applied to fluid mechanics, is a statement of energy conservation. It states that energy can neither be created nor destroyed; it can only be transformed from one form to another. In the context of fluid flow, this law is often expressed as a balance equation relating the changes in various forms of energy within a control volume to the energy entering and leaving the control volume.

The general form of the First Law for a fluid system can be expressed as:

ΔE = Q - W

Where:

• ΔE is the change in the total energy of the system. This includes changes in internal energy (due to temperature variations), kinetic energy (due to velocity changes), and potential energy (due to elevation changes).
• Q is the heat added to the system. Heat transfer can occur through conduction, convection, or radiation. A positive Q indicates heat is added to the system, while a negative Q indicates heat is removed.
• W is the work done by the system. Work can be done by the fluid on its surroundings (e.g., expansion against a pressure) or work can be done on the fluid (e.g., by a pump). A positive W indicates work done by the system, while a negative W indicates work done on the system.

In differential form, the First Law is often written to describe the energy balance at a specific point or within a small control volume in the fluid.

The First Law is a fundamental principle in fluid mechanics, essential for analyzing a wide range of problems, including pipe flow, turbomachinery, heat exchangers, and compressible flows. When combined with the continuity equation (conservation of mass) and the momentum equation (Newton's Second Law), it provides a complete set of governing equations for fluid flow.

Different forms of the First Law are used depending on the specific application and assumptions made. For example, in steady-state, steady-flow processes (where properties at a point do not change with time), the First Law simplifies significantly. Often, enthalpy (H = U + pV, where U is internal energy, p is pressure, and V is volume) is used as a convenient property to express energy changes in flowing systems. The energy equation can then be written in terms of enthalpy, kinetic energy, and potential energy changes.