Chapter Two. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency. Laith Batarseh
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1 Chapter Two Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency Laith Batarseh
2 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
3 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
4 The steady flow energy equation specific enthalpy kinetic energy per unit mass Potential energy per unit mass
5 The steady flow energy equation Assume: 1. The level difference between the entrance and the existence of turbo machine is negligible : g(z 1 z 2 ) is neglected. 2. stagnation enthalpy 3. Adiabatic process For work producing machines (turbines) For work absorbing machines (compressors)
6 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
7 The momentum equation Newton s second law of motion Bernoulli s equation For an incompressible fluid stagnation pressure
8 Moment of momentum sum of the moments tangential velocity Mass Sum of moments (torque) For one-dimensional steady flow Euler s pump and turbine equations
9 work done on the fluid per unit mass or specific work pump or compressor turbine
10 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
11 The second law of thermodynamics entropy for a system passing through a cycle involving heat exchanges element of heat transferred Absolute temperature If all the processes in the cycle are reversible then dq =dq R Mass of the system entropy, for a finite change of state, is defined as For an incremental change of state
12 The second law of thermodynamics entropy Isentropic process
13 Definitions of efficiency Efficiency of turbines overall efficiency isentropic efficiency or hydraulic efficiency mechanical efficiency Compressible flow Incompressible flow
14 Definitions of efficiency Steam and gas turbines actual turbine work/unit mass Ideal turbine work/unit mass stagnation enthalpy change Stagnation enthalpy change during the isentropic process The most important information here is the exit kinetic energy is usefully employed or is wasted
15 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, the relevant adiabatic efficiency is the total-to-static efficiency Hydraulic turbines
16 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
17 Definitions of efficiency Efficiency of compressors and pumps the incremental work input For a complete adiabatic compression process reversible adiabatic compression process Assume zero elevation for an adiabatic process in a compressor
18 Definitions of efficiency Efficiency of compressors and pumps incompressible flow
19 Definitions of efficiency Small stage efficiency for a perfect gas isentropic efficiency Polytropic efficiency ideal compression Ideal Actual
20 Definitions of efficiency Example 2.1
21 Definitions of efficiency Example 2.1
22 Definitions of efficiency
23 Definitions of efficiency
24 Definitions of efficiency
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