Slide 1Slide 2CONSERVATION OF MASSMass and Volume Flow RatesConservation of Mass PrincipleSlide 6Slide 7Mass Balance for Steady-Flow ProcessesSpecial Case: Incompressible FlowFLOW WORK AND THE ENERGY OF A FLOWING FLUIDTotal Energy of a Flowing FluidEnergy Transport by MassENERGY ANALYSIS OF STEADY-FLOW SYSTEMSMass and Energy balances for a steady-flow processSlide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36SummaryCHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMESLecture slides byMehmet KanogluCopyright © The McGraw-Hill Education. Permission required for reproduction or display.Thermodynamics: An Engineering Approach 8th EditionYunus A. Çengel, Michael A. BolesMcGraw-Hill, 20152Objectives•Develop the conservation of mass principle.•Apply the conservation of mass principle to various systems including steady- and unsteady-flow control volumes.•Apply the first law of thermodynamics as the statement of the conservation of energy principle to control volumes.•Identify the energy carried by a fluid stream crossing a control surface as the sum of internal energy, flow work, kinetic energy, and potential energy of the fluid and to relate the combination of the internal energy and the flow work to the property enthalpy.•Solve energy balance problems for common steady-flow devices such as nozzles, compressors, turbines, throttling valves, mixers, heaters, and heat exchangers.•Apply the energy balance to general unsteady-flow processes with particular emphasis on the uniform-flow process as the model for commonly encountered charging and discharging processes.3CONSERVATION OF MASSConservation of mass: Mass, like energy, is a conserved property, and it cannot be created or destroyed during a process. Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries, and so we must keep track of the amount of mass entering and leaving the control volume.Mass m and energy E can be converted to each other according towhere c is the speed of light in a vacuum, which is c = 2.9979  108 m/s. The mass change due to energy change is negligible.4Mass and Volume Flow RatesDefinition of average velocityVolume flow rateMass flow rate5Conservation of Mass PrincipleThe conservation of mass principle for a control volume: The net mass transfer to or from a control volume during a time interval t is equal to the net change (increase or decrease) in the total mass within the control volume during t.These equations are often referred to as the mass balance and are applicable to any control volume undergoing any kind of process.6the time rate of change of mass within the control volume plus the net mass flow rate through the control surface is equal to zero.General conservation of mass in rate form78Mass Balance for Steady-Flow ProcessesDuring a steady-flow process, the total amount of mass contained within a control volume does not change with time (mCV = constant). Then the conservation of mass principle requires that the total amount of mass entering a control volume equal the total amount of mass leaving it.For steady-flow processes, we are interested in the amount of mass flowing per unit time, that is, the mass flow rate.Multiple inlets and exitsSingle streamMany engineering devices such as nozzles, diffusers, turbines, compressors, and pumps involve a single stream (only one inlet and one outlet).9Special Case: Incompressible FlowThe conservation of mass relations can be simplified even further when the fluid is incompressible, which is usually the case for liquids.Steady, incompressibleSteady, incompressible flow (single stream)There is no such thing as a “conservation of volume” principle.For steady flow of liquids, the volume flow rates, as well as the mass flow rates, remain constant since liquids are essentially incompressible substances.10FLOW WORK AND THE ENERGY OF A FLOWING FLUIDFlow work, or flow energy: The work (or energy) required to push the mass into or out of the control volume. This work is necessary for maintaining a continuous flow through a control volume.11Total Energy of a Flowing FluidThe total energy consists of three parts for a nonflowing fluid and four parts for a flowing fluid.h = u + PvThe flow energy is automatically taken care of by enthalpy. In fact, this is the main reason for defining the property enthalpy.12Energy Transport by MassWhen the kinetic and potential energies of a fluid stream are negligibleWhen the properties of the mass at each inlet or exit change with time as well as over the cross section13ENERGY ANALYSIS OF STEADY-FLOW SYSTEMSSteady-flow process: A process during which a fluid flows through a control volume steadily.14Mass and Energy balances for a steady-flow processMass balanceEnergy balance15Under steady operation, shaft work and electrical work are the only forms of work a simple compressible system may involve.Energy balance relations with sign conventions (i.e., heat input and work output are positive)when kinetic and potential energy changes are negligibleThe units m2/s2 and J/kgare equivalent.At very high velocities, even small changes in velocities can cause significant changes in the kinetic energy of the fluid.16SOME STEADY-FLOW ENGINEERING DEVICESMany engineering devices operate essentially under the same conditionsfor long periods of time. The components of a steam power plant (turbines,compressors, heat exchangers, and pumps), for example, operate nonstop formonths before the system is shut down for maintenance. Therefore, these devices can be conveniently analyzed as steady-flow devices.A modern land-based gas turbine used for electric power production. This is a General Electric LM5000 turbine. It has a length of 6.2 m, it weighs 12.5 tons, and produces 55.2 MW at 3600 rpm with steam injection.17Nozzles and DiffusersNozzles and diffusers are commonly utilized in jet engines, rockets, spacecraft, and even garden hoses. A nozzle is a device that increases the velocity of a fluid at the expense of pressure. A diffuser is a device that increases the pressure of a fluid by slowing it down. The cross-sectional area of a nozzle decreases in the flow direction for subsonic flows and increases for supersonic flows. The reverse is true for diffusers.Energy balance for a nozzle or diffuser:18Deceleration of Air in a