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Mass and Energy Analysis of Control Volumes – Part 2. Chapter 5b. So far…. We’ve developed a general energy balance We’ve developed a general material balance We’ve only actually looked at systems that are steady state Now we are going to do more complicated problems

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## Mass and Energy Analysis of Control Volumes – Part 2

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**Mass and Energy Analysis of Control Volumes – Part 2**Chapter 5b**So far…**• We’ve developed a general energy balance • We’ve developed a general material balance • We’ve only actually looked at systems that are steady state • Now we are going to do more complicated problems • Ones that change with time**We need to make some assumptions**• Uniform flow • The system can change with time, but the inlet conditions are constant • Everything in the system is in the same state • Fluid exiting the system is at the same state as the system**We need to look at our balances again**We aren’t using the rate form of the balances here. Why?**Usually, they both equal 0**This is the kinetic energy of the system This is the potential energy of the system**Inlet and Exit conditions, assuming only a single inlet and**a single exit stream Time 1 and time 2 Usually both the kinetic energy and potential energy of thefluidare zero too**Consider a bottle filling problem**• What happens to the temperature when you fill an empty tank with air?**Consider a bottle filling problem**• What happens to the temperature when you fill an empty tank with air? • The air gets hot • Why? • It takes energy to push the air into the tank (flow work). That energy is converted into internal energy**For our bottle filling problem…**hi is bigger than ui, so… u2 is bigger than ui That means the temperature in the tank is higher than the inlet temperature**Try an example**• Example 5-12 page 248 • Charging of a rigid tank • Note that the inlet conditions stay constant throughout the process • There is no exit term**Try a harder example**• Example 5-13 page 250 • Cooking with a pressure cooker • Because the system is two phase and constant pressure, the exiting steam is always at the same conditions • There is no inlet term**What if…**• How would we handle inlet or exit conditions that change with time? • The best we can do at this point is to take the average • If we knew more, we could integrate over time**For example…**• What happens to the temperature of the container when you use a bottle of canned air? • The bottle gets cold. • Why? • It takes energy to push the air out of the can (flow work) • That energy comes from the energy of the air that remains in the can**But….**• The air coming out of the can gets colder with time • That means the exit conditions are not constant What conditions should you use for he?**SummaryControl Volumes**• A control volume differs from a closed system in that it involves mass transfer. Mass carries energy with it, and thus the mass and energy content of a system change when mass enters or leaves.**SummaryMass and Energy Balance**• The mass and energy balances for any system undergoing any process can be expressed as :**SummaryRate form of the mass and energy balance**• The mass and energy balances for any systemundergoing any processcan be expressed in the rate form as**SummaryMass flow rates**• Mass flow through a cross section per unit time is called the mass flow rate and is denoted m. It is expressed as .**SummaryVolumetric flow rates**• The mass and volume flow rates are related by**SummaryTypes of Control Volume problems**• Thermodynamic processes involving control volumes can be considered in two groups: • steady-flow processes and • unsteady-flow processes.**SummarySteady Flow Equations**• Taking heat transfer to the system and work done by the system to be positive quantities, the conservation of mass and energy equations for steady-flow processes are expressed as where the subscript i stands for inlet and e for exit. These are the most general forms of the equations for steady-flow processes. for each exit for each inlet**SummarySteady Flow equations for a single inlet and single**exit system • For single-stream (one-inlet--one-exit) systems such as nozzles, diffusers, turbines, compressors, and pumps, the steady flow equations simplify to:**SummaryUniform Flow Process**• During a uniform-flow process, • the state of the control volume may change with time, but it may do so uniformly. • Also, the fluid properties at the inlets are assumed to remain constant during the entire process. • The fluid properties of the exit streams are the same as the fluid properties of the system**SummarySimplified Energy Balance for the Uniform Flow Case**• When the kinetic and potential energy changes associated with the control volume and the fluid streams are negligible, the conservation of energy equation for a uniform-flow process simplifies to

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