Chapter Two - Philadelphia University. Basic.pdfChapter Two Laith Batarseh Basic Thermodynamics,...
Transcript of Chapter Two - Philadelphia University. Basic.pdfChapter Two Laith Batarseh Basic Thermodynamics,...
Chapter Two
Laith Batarseh
Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency
Basic Thermodynamics, Fluid Mechanics
The equation of continuity
Most analyses in this book are limited to one-dimensional steady flows where the velocity and density are regarded as constant across each section of a duct or passage
Basic Thermodynamics, Fluid Mechanics
The first law of thermodynamics internal energy
The first law of thermodynamics states that if a system is taken through a
complete cycle during which heat is supplied and work is done,
heat supplied to the system during the cycle
work done by the system during the cycle
Internal energy change
Basic Thermodynamics, Fluid Mechanics
The steady flow energy equation
specific enthalpy
kinetic energy per unit mass
Potential energy per unit mass
Basic Thermodynamics, Fluid Mechanics
The steady flow energy equation
Assume:
1. The level difference between the entrance and the existence of turbo
machine is negligible : g(z1 – z2) is neglected.
2. stagnation enthalpy
3. Adiabatic process
For work producing machines (turbines)
For work absorbing machines (compressors)
Basic Thermodynamics, Fluid Mechanics
The momentum equation Newton’s second law of motion
Force in x-direction
Velocity in x-direction
Velocity at the entrance
Velocity at the existence
Euler’s equation of motion
Basic Thermodynamics, Fluid Mechanics
The momentum equation Newton’s second law of motion
Bernoulli’s equation
For an incompressible fluid
stagnation pressure
Basic Thermodynamics, Fluid Mechanics
Moment of momentum
sum of the moments
Sum of moments (torque)
Mass
tangential velocity
For one-dimensional steady flow
Euler’s pump and turbine equations
Basic Thermodynamics, Fluid Mechanics
work done on the fluid per unit mass or specific work
pump or compressor
turbine
Basic Thermodynamics, Fluid Mechanics
Rothalpy
This relationship is true for steady, adiabatic and irreversible flow in compressor or in pump impellers.Substitute the definition of stagnation enthalpy and rearrange the above equation
Rothalpy
Basic Thermodynamics, Fluid Mechanics
The second law of thermodynamics entropy
for a system passing through a cycle involving heat exchanges
Absolute temperature
element of heat transferred
If all the processes in the cycle are reversible then dQ =dQR
entropy, for a finite change of state, is
defined as
For an incremental
change of state
Mass of the system
Basic Thermodynamics, Fluid Mechanics
The second law of thermodynamics entropy
Isentropic process
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Efficiency of turbines
isentropic efficiency or hydraulic efficiency
overall efficiency
mechanical efficiency
Compressible flow Incompressible flow
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Steam and gas turbines
actual turbine work/unit mass
stagnation enthalpy
change
Ideal turbine work/unit massStagnation enthalpy change
during the isentropic process
The most important information here is
the exit kinetic energy is usefully
employed or is wasted
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Steam and gas turbines
adiabatic efficiency or the total-to-total efficiency when exhaust kinetic energy is usefully employed
total-to-static efficiency
When the exhaust kinetic energy is not usefully employed and entirely wasted, therelevant adiabatic efficiency is the total-to-static efficiency
Hydraulic turbines
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Efficiency of compressors and pumps
isentropic efficiency of a compressor or the hydraulic efficiency of a pump
the overall efficiency of the compressor or pump
The mechanical efficiency
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Efficiency of compressors and pumps
the incremental work input
For a complete adiabatic compression process
reversible adiabatic compression process
for an adiabatic process in a compressor
Assume zero elevation
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Efficiency of compressors and pumps
incompressible flow
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Small stage efficiency for a perfect gas
isentropic efficiency
Polytropic efficiency
ideal compression
Ideal Actual
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Example 2.1
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Example 2.1
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency
Basic Thermodynamics, Fluid Mechanics
Definitions of efficiency