Air is drawn isentropically into the pipe at V1=640 m / s, T1=80^∘ C, and absolute pressure

step 1 We're given that air enters with a initial velocity of 640 meters per second with a temperature

Air is drawn isentropically into the pipe at V1=640 m /...

Air is drawn isentropically into the pipe $\underline{\text { at }}$ $V_{1}=640 \mathrm{~m} / \mathrm{s}, \quad T_{1}=80^{\circ} \mathrm{C},$ and absolute pressure of $p_{1}=250 \mathrm{kPa}$. If it exits the pipe having a speed of $470 \mathrm{~m} / \mathrm{s}$ determine the amount of heat per unit mass that the pipe supplies to the air.

Air is drawn isentropically into the pipe $\underline{\text { at }}$ $V_{1}=640 \mathrm{~m} / \mathrm{s}, \quad T_{1}=80^{\circ} \mathrm{C},$ and absolute pressure of
$p_{1}=250 \mathrm{kPa}$. If it exits the pipe having a speed of $470 \mathrm{~m} / \mathrm{s}$ determine the amount of heat per unit mass that the pipe supplies to the air.

Key Concepts

Steady Flow Energy Equation

This principle applies to systems where fluid flows steadily through a control volume and the energy balance accounts for changes in enthalpy, kinetic energy, potential energy, work, and energy added or removed as heat. It is particularly useful in open system analyses to relate the energy at the inlet and outlet conditions, enabling calculation of heat transfer when the kinetic energy and enthalpy differences are known.

Enthalpy in Ideal Gases

Enthalpy, defined as the sum of internal energy and the product of pressure and specific volume, is a key property in thermodynamics, especially for ideal gases where it depends solely on temperature. In energy balances, changes in enthalpy directly reflect temperature changes that occur in the fluid, allowing for the translation of thermal energy differences into measurable quantities.

Kinetic Energy Changes

In a flowing fluid, kinetic energy per unit mass, given by the square of the flow speed divided by two, represents the energy due to the motion of the fluid. Differences in kinetic energy between inlet and outlet states are crucial in the energy balance of flow processes and must be accounted for when evaluating the net heat transfer in systems where fluid speeds vary.

Isentropic Process

An isentropic process is one where the entropy remains constant, implying no heat transfer across the system boundaries and an ideal reversible adiabatic process. Recognizing when and how a process deviates from isentropic conditions is important, as it affects the energy balance and the interpretation of changes in thermal and mechanical energy in a flowing system.

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