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 B A B A 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 /  consists of internal energy and flow work (Do not double count flow work in W out !) 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 Components of mechanical energy –flow work (pressure energy in C & T) –kinetic energy –potential energy Thermal energy –thermodynamic property u Energy equation again Energy components

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