4.1 Thermodynamic Analysis of Control Volumes

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‚ Ẇ = 0: Heat exchangers typically involve no work interactions.‚ KE PE 0: Changes in these forms of energy are usually negligible.Pipe and Duct Flow:The transport of liquids or gases in pipes and ducts is of great importance in many engineeringapplications. When flow through pipe or ducts is analyzed, the following points should be considered:‚ Q . 0: Under normal operating conditions, the amount of heat gained or lost by the fluid canbe very significant, particularly if the pipe or duct is long and not insulated.‚ Ẇ 0: If the control volume involves a heating section (electric wires, a fan, or a pump (shaft),the work interaction should be considered.‚ KE 0: For constant-diameter pipes/ducts, this energy term is usually negligible.‚ PE 0: Potential energy consideration are important when a fluid is pump through greatelevation changes.4.4 Unsteady-Flow ProcessesMany processes of engineering interest involve changes within the control volume with time.Such processes are called unsteady-flow, or transient-flow processes.Important point!The steady-flow relations developed in the previous sections are not applicable tothese processes!When an unsteady-flow process is analyzed, it is important to keep track of the mass and energycontents of the control volume as well as the energy interactions across the boundary. Some familiarunsteady flow processes are the charging of rigid vessels from supply lines, discharging a fluid from apressure vessel, inflating tires or balloons, and even cooking with an ordinary pressure cooker. Unlikesteady-flow processes, unsteady-flow processes start and end over a finite time period ∆t. Anotherdifference between steady and unsteady-flow processes is that steady-flow systems are fixed in space, insize, and in shape. Unsteady -flow systems, however, are not. They are usually stationary, but involvemoving boundaries (boundary work!)Conservation of Mass:Unlike the case of steady-flow processes, the amount of mass within the control volume doeschange with time during an unsteady-flow process. The degree of change depends on the amount ofmass entering and leaving the control volume during the process. The conservation of massprinciple for unsteady-flow processes is mathematically stated as ...ENGS205--Introductory Thermodynamics page 39
m i − m e = m CVTotal mass entering Total mass leaving Net change in massCV during ∆t CV during ∆t within CV during ∆t(4.4.1)If all the terms in Eq. (4.4.1) are divided by ∆t and taking the limit as t 0 gives ..(4.4.2)where dm CV / dt is the time rate of change of mass contained within the control volume.Conservation of Energy:Unlike the steady-flow process, the energy content of a control volume changes with time duringan unsteady-flow process. The degree of change depends on the amount of energy transfer across thesystem boundaries as heat and work as well as on the amount of energy transported into and out of thecontrol volume by mass during the process. That is, we have to keep track of the energy flowing into andout of the control volume for the duration of the unsteady process ∆t. The conservation of energyprinciple for a control volume undergoing an unsteady process for a time interval ∆t isQ − W + i − e = E CVTotal energy crossing Total energy trans- Total energy trans- Net change in energyboundary as heat and ported by mass into ported by mass out of of CV during ∆twork during ∆t CV during ∆t CV during ∆tIf all the terms in Eq. (4.4.3) are divided by ∆t and taking the limit as t 0 gives ...(4.4.3)(4.4.4). .where i and e are the rates at which energy is transported with mass into and out of the controlvolume respectively, and dE CV / dt is the time rate of change of energy within the control volume.In Eq. (4.4.3), the heat and work terms (Q and W) can be determined by external measurements.The total energy of the control volume at the beginning and end states of the process (E 1 and E 2 ) can beeasily determined by measuring the relevant properties of the substance at these two states. The totalenergy transported into or out of the control volume (Θ i , Θ e), however, is not as easy to determine sincethe properties of the mass at each inlet or exit may be changing with time as well as over thecross-section. Thus, the only way to determine the energy transport through an opening as a result ofmass flow is to consider sufficiently small differential masses δm that have uniform properties and add totheir total energies.Total mass, mdivided up intonumerousdifferential masses,δmENGS205--Introductory Thermodynamics page 39
Page 2 and 3: Mass and Volume Flow Rates:The amou
Page 4 and 5: The conservation of mass principle
Page 6 and 7: CompressorShaftWork (-)TurbineShaft
Page 10: The total energy of a flowing fluid

4.1 Thermodynamic Analysis of Control Volumes

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