LECTURE 15
15.1 Reversible Steady-Flow Work


Derivation of Reversible Steady-Flow Work

For a steady-flow device undergoing an internally reversible process,

When the changes in kinetic and potential energies are negligible,

 

Note
reversible work associated with an internally reversible process in a steady-flow device
reversible work in closed systems

 

For an Incompressible Fluid

Bernoulli Equation

If , then we have

Bernoulli equation holds for incompressible flows that involve no irreversibilities such as friction or shock waves.

Note:

The larger the specific volume, the larger the reversible work produced or consumed by the steady-flow device.

To minimize the work input during a compression process
- to keep the specific volume of the working fluid as small as possible.

To maximize the work output during an expansion process
- to keep the specific volume of the working fluid as large as possible.

Steam Power Plants
Gas Power Plants
Pump handles liquid water (small specific volume)
Turbine handles vapor (large specific volume) 		Compressor handles air
(large specific volume)

 
15.2 Minimizing the Compressor Work


Two Ways of Minimizing the Compressor Work
1. To approach an internally reversible process as much as possible by minimizing the irreversibilities such as friction, turbulence, and non-quasi-equilibrium compression.

2. To keep the specific volume of the gas as small as possible by maintaining the gas temperature as low as possible during the compression process.

This requires that the gas be cooled as it is compressed.

Consider an isentropic process (no cooling), a polytropic process (some cooling), and an isothermal process (plenty of cooling) operate between the same pressure levels in an internally reversible manner.

Isentropic Process ( constant)
Polytropic Process (constant)
Isothermal Process (pv = constant)

 

 
15.3 Isentropic Efficiency for Steady-Flow Devices


Isentropic efficiency is defined as the ratio of the actual performance of a device to the performance that would be achieved by undergoing an isentropic process for the same inlet state and the same exit pressure.

 
15.3.1 Turbines


Turbines
Actual Turbine Work

Rate of Entropy Production
(per unit mass)
Isentropic Turbine Work
Isentropic Efficiency

 

 
15.3.2 Compressors


Compressors
Actual Compressor Work
Isentropic Compressor Work
Isentropic Efficiency

 
15.3.3 Nozzles

Nozzles
Isentropic Efficiency