Book cover for Thermodynamics: An Engineering Approach

Thermodynamics: An Engineering Approach

Yunus A. Cengel, Michael A. Boles

ISBN #9781259822674

9th Edition

2,694 Questions

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59,300 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter on Mass and Energy Analysis of Control Volumes provides a comprehensive approach to understanding and applying the principles of mass and energy conservation in various flow systems. Through detailed examination of steady and unsteady flow processes, key variables such as mass flow rate, volume flow rate, flow work, and enthalpy are explained. Engineers learn how to set up energy balances for devices including nozzles, diffusers, turbines, compressors, and more. Mastery of these concepts is critical for solving practical engineering problems in fluid mechanics and thermodynamic system analysis.

Learning Objectives

1

Explain the principles of mass and energy conservation using control volume analysis.

2

Differentiate between steady-flow and unsteady-flow processes and apply the appropriate analysis methods.

3

Define and compute key parameters such as mass flow rates, volume flow rates, flow work, and enthalpy.

4

Set up energy balances for various engineering devices including nozzles, diffusers, turbines, compressors, throttling valves, mixing chambers, heat exchangers, and pipe/duct flows.

5

Analyze practical problems in fluid mechanics and thermodynamics using the established conservation principles.

Key Concepts

CONCEPT

DEFINITION

Control Volume

An imaginary or physical boundary used to analyze mass and energy flows into and out of a system.

Mass Flow Rate

The mass of fluid passing through a cross-sectional area per unit time, typically expressed in kg/s.

Volume Flow Rate

The volume of fluid passing through a section per unit time, often expressed in m³/s.

Flow Work

Work done by or against fluid forces as it enters or exits a control volume, accounting for pressure and volume change.

Enthalpy

A thermodynamic quantity representing the total heat content of a system, combining internal energy with flow work (P·V).

Energy Balance

An analysis tool that ensures all energy entering a system equals the energy leaving, adjusted for work and heat interactions.

Kinetic and Potential Energy

Energy forms associated with the motion (kinetic) and position (potential) of the fluid, which must be accounted for in energy analyses.

Example Problems

Example 1

Name four physical quantities that are conserved and two quantities that are not conserved during a process.

Example 2

Define mass and volume flow rates. How are they related to each other?

Example 3

Does the amount of mass entering a control volume have to be equal to the amount of mass leaving during an unsteady-flow process?

Example 4

Consider a device with one inlet and one outlet. If the volume flow rates at the inlet and at the outlet are the same, is the flow through this device necessarily steady? Why?

Example 5

The ventilating fan of the bathroom of a building has a volume flow rate of $30 \mathrm{~L} / \mathrm{s}$ and runs continuously. If the density of air inside is $1.20 \mathrm{~kg} / \mathrm{m}^{3},$ determine the mass of air vented out in one day.
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Step-by-Step Explanations

QUESTION

How do you determine the mass flow rate of a fluid entering a control volume?

STEP-BY-STEP ANSWER:

Step 1: Identify the density (ρ) of the fluid at the inlet.
Step 2: Measure or determine the cross-sectional area (A) through which the fluid flows.
Step 3: Determine the velocity (V) of the fluid as it enters.
Step 4: Calculate the mass flow rate using the formula: mass flow rate = ρ × A × V.
Final Answer: The mass flow rate is given by ρ × A × V (kg/s).

Mass Flow Rate Calculation

QUESTION

How can you set up an energy balance for a nozzle using control volume analysis?

STEP-BY-STEP ANSWER:

Step 1: Define the control volume encompassing the nozzle.
Step 2: Write the energy balance equation accounting for enthalpy, kinetic energy, and potential energy entering and exiting the nozzle.
Step 3: Include flow work as part of the enthalpy term.
Step 4: Recognize that for an ideal nozzle, changes in potential energy are often negligible.
Step 5: Solve the equations to relate inlet conditions to outlet conditions.
Final Answer: The energy balance equates the sum of the inlet enthalpy and kinetic energy to the outlet enthalpy and kinetic energy (plus any work interactions if applicable).

Energy Balance for Nozzles

QUESTION

How is the conservation of mass principle applied in steady-flow processes?

STEP-BY-STEP ANSWER:

Step 1: Define the control volume and assume steady state conditions (no accumulation of mass).
Step 2: Write the mass balance: mass flow rate in = mass flow rate out.
Step 3: Identify all inlet and outlet streams.
Step 4: Ensure that the sum of mass flow rates in all inlets equals the sum of mass flow rates at all outlets.
Final Answer: The conservation of mass is validated if the total mass flow rate into the system equals the total mass flow rate exiting the system.

Conservation of Mass in Steady-Flow

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Common Mistakes

  • Confusing mass flow rate with volume flow rate without considering fluid density.
  • Neglecting kinetic and potential energy contributions in energy balances, particularly in high-speed or elevation-change systems.
  • Incorrectly assuming that all processes are steady-flow and overlooking the need for different analyses in unsteady-flow situations.
  • Failing to account for flow work as part of the enthalpy term when setting up energy balances.