Air flows at 1.42 kg / s through a 100 -mm-diameter duct. At...

Air flows at $1.42 \mathrm{kg} / \mathrm{s}$ through a 100 -mm-diameter duct. At the inlet section, the temperature and absolute pressure are $52^{\circ} \mathrm{C}$ and $60.0 \mathrm{kPa} .$ At the section downstream where the flow is choked, $T_{2}=45^{\circ} \mathrm{C}$. Determine the heat addition per unit mass, the entropy change, and the change in stagnation pressure for the process, assuming frictionless flow.

Key Concepts

Conservation of Energy in Open Systems

In open systems, the conservation of energy principle governs how energy is converted from one form to another as a fluid flows through a control volume. This involves accounting for the heat added to or extracted from the fluid, the work interactions, and the changes in internal, kinetic, and potential energy. In compressible flows, such as those in ducts, the energy equation is central to predicting changes in temperature and pressure due to heat addition or expansion and compression processes.

Compressible Flow Dynamics

Compressible flow dynamics deals with fluid flows where changes in density are significant, typically happening at high velocities or under conditions with large temperature and pressure variations. Key aspects include the variation in static and stagnation properties, the speed of sound, and the presence of phenomena such as choking, where the flow reaches sonic conditions and the mass flow rate becomes limited by the geometry and thermodynamic state.

Choked Flow

Choked flow is a condition in which the mass flow rate through a duct or nozzle reaches a maximum limit, typically when the flow velocity at some section becomes sonic (Mach 1). This phenomenon is crucial in the analysis of gas flows as it determines the upper bound on the mass flow rate and plays an important role in the design and safety of fluid systems handling compressible gases.

Stagnation Properties

Stagnation properties, namely stagnation temperature and stagnation pressure, represent the thermodynamic state a fluid would achieve if brought to rest isentropically. They are key parameters in compressible flow analysis because they remain invariant in adiabatic, reversible flows, and any deviations from these invariances point to the effects of heat addition, friction, or other thermodynamic processes.

Entropy Change in Thermodynamic Processes

Entropy change is a measure of the irreversible portion of a thermodynamic process. In the context of open and compressible flow, assessing the entropy change helps to quantify the irreversibilities introduced by heat addition, mixing, or other non-ideal effects. Even in frictionless flows, when heat is added or removed, the overall entropy of the system will change, making this concept essential for evaluating the second law efficiency of a process.

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