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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