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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