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ES 202 Fluid and Thermal Systems Lecture 7: Mechanical Energy Balance (12/16/2002) Assignments • Reading: – Cengel & Turner Section 11-4 – ES 201 notes • Homework: – 11-5, 11-6 in Cengel & Turner – notion of combined efficiency Road Map of Lecture 7 • Final attempt on curved surfaces • Steady state devices – revisit energy and entropy equation – nozzle, diffuser, turbine, compressor, heat exchanger • function • design assumption • modeling assumption • Close examination of energy equation – – – – means of transport zero production mechanical energy vs thermal energy flow work, kinetic energy, potential energy • Bernoulli’s equation Final Attempt on Curved Surfaces • Compare the hydrostatic forces acted on Surface AB (not the bottom of the tank) in the following configurations: A A B A B B Major Conclusions • For inclined submerged surfaces (plane or curved) with same end points: – total horizontal force is the same – total vertical force differs (depending on the weight of fluid above/below the surface) End of Hydrostatics Revisit Energy Equation • Mean of transport: – heat transport – work transport – mass transport • Enthalpy: h = u + p / r consists of internal energy and flow work (Do not double count flow work in Wout !) • Internal energy is a measure of molecular activities at the microscopic level (strongly dependent on temperature) while kinetic and potential energies are measures of bulk fluid motion Revisit Entropy Equation • Mean of transport: – heat transport – mass transport • There is no entropy transport associated with work, i.e. work transport of energy is entropy-free. This is the major difference between the two energy transfer modes: work and heat. Work is better! • Entropy production is always non-negative! Steady-State Devices • List the purpose (function) for the following devices: – – – – – nozzle diffuser turbine pump, compressor, blower, fan heat exchanger Turbine • • • • Steam turbine Water turbine (hydro-electricity) Wind turbine (hill slopes) Gas turbine engine – – – – compressor combustor turbine good power to weight ratio (multiple rotor-stator stage) Steady-State Devices (cont’d) • What does the energy equation reduce to for the following devices: – – – – – nozzle diffuser turbine compressor, fan, blower, pump heat exchanger Close Examination of Energy Equation • Energy equation again • Energy components • Components of mechanical energy – flow work (pressure energy in C & T) – kinetic energy – potential energy • Thermal energy – thermodynamic property u Mechanical Energy Vs Thermal Energy • Mechanical energy vs thermal energy – mechanical energy can freely change its form among various components – mechanical energy can be converted to work completely (without loss) if the system is reversible – example: spring-mass system in simple harmonic motion – thermal energy cannot be converted to work completely (the second law of thermodynamics imposed limitation to the conversion) – example: spring-mass system under influence of friction – the first law of thermodynamics (conservation of energy) does not differentiate the different forms of energy but the second law does – mechanical energy is a “higher quality” form of energy Energy Equation in Steady State • Assumptions – – – – steady adiabatic no shaft work or friction small changes in thermal energy relative to mechanical energy (good for low speed flows) • Conservation of mechanical energy – Interpretation: interchange of mechanical energy among its various forms Bernoulli’s Equation • Traditional derivation is based on momentum equation • Warning: Its simplicity may often lead to incorrect application • Remember the assumptions (limitations) – – – – – steady no shaft work or friction small change in thermal energy constant density along flow direction • Examples: application to nozzle and diffuser