ES 202 Fluid and Thermal Systems Lecture 7: Mechanical Energy Balance (12/16/2002)

1. ES 202Fluid and Thermal SystemsLecture 7:Mechanical Energy Balance (12/16/2002)

2. Assignments • Reading: • Cengel & Turner Section 11-4 • ES 201 notes • Homework: • 11-5, 11-6 in Cengel & Turner • notion of combined efficiency

3. Road Map of Lecture 7 • Final attempt on curved surfaces • Steady state devices • revisit energy and entropy equation • nozzle, diffuser, turbine,compressor, heatexchanger • 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

4. Compare the hydrostatic forces acted on Surface AB (not thebottom of the tank) in the following configurations: A A A B B B Final Attempt on Curved Surfaces

5. 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)

6. End of Hydrostatics

7. Revisit Energy Equation • Mean of transport: • heat transport • work transport • mass transport • Enthalpy: h = u + p / r consists of internalenergy 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

8. 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!

9. Steady-State Devices • List the purpose (function) for the following devices: • nozzle • diffuser • turbine • pump, compressor, blower, fan • heat exchanger

10. 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)

11. 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

12. Close Examination of Energy Equation • Energy equation again • Components of mechanical energy • flow work (pressure energy in C & T) • kinetic energy • potential energy • Thermal energy • thermodynamic property u • Energy components

13. 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 workcompletely (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

14. 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

15. 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