Page 22 - Fluid Mechanics and Thermodynamics of Turbomachinery

Introduction: Dimensional Analysis: Similitude 3
absent or present respectively in the flow through the rotor. In an impulse machine
all the pressure change takes place in one or more nozzles, the fluid being directed
onto the rotor. The Pelton wheel, Figure 1.1(f), is an example of an impulse turbine.
The main purpose of this book is to examine, through the laws of fluid mechanics
and thermodynamics, the means by which the energy transfer is achieved in the
chief types of turbomachine, together with the differing behaviour of individual
types in operation. Methods of analysing the flow processes differ depending upon
the geometrical configuration of the machine, on whether the fluid can be regarded
as incompressible or not, and whether the machine absorbs or produces work. As
far as possible, a unified treatment is adopted so that machines having similar
configurations and function are considered together.

Units and dimensions
The International System of Units, SI (le Syst` eme International d’Unit´ es)
is a unified self-consistent system of measurement units based on the MKS
(metre kilogram second) system. It is a simple, logical system based upon decimal
relationships between units making it easy to use. The most recent detailed
description of SI has been published in 1986 by HMSO. For an explanation of
the relationship between, and use of, physical quantities, units and numerical values
see Quantities, Units and Symbols, published by The Royal Society (1975) or refer
to ISO 31/0-1981.
Great Britain was the first of the English-speaking countries to begin, in the
1960s, the long process of abandoning the old Imperial System of Units in favour
of the International System of Units, and was soon followed by Canada, Australia,
New Zealand and South Africa. In the USA a ten year voluntary plan of conversion
to SI units was commenced in 1971. In 1975 US President Ford signed the Metric
Conversion Act which coordinated the metrication of units, but did so without
specifying a schedule of conversion. Industries heavily involved in international
trade (cars, aircraft, food and drink) have, however, been quick to change to SI for
obvious economic reasons, but others have been reluctant to change.
SI has now become established as the only system of units used for teaching
engineering in colleges, schools and universities in most industrialised countries
throughout the world. The Imperial System was derived arbitrarily and has no
consistent numerical base, making it confusing and difficult to learn. In this book
all numerical problems involving units are performed in metric units as this is more
convenient than attempting to use a mixture of the two systems. However, it is
recognised that some problems exist as a result of the conversion to SI units. One
of these is that many valuable papers and texts written prior to 1969 contain data
in the old system of units and would need converting to SI units. A brief summary
of the conversion factors between the more frequently used Imperial units and SI
units is given in Appendix 1 of this book.
Some SI units
The SI basic units used in fluid mechanics and thermodynamics are the metre
(m), kilogram (kg), second (s) and thermodynamic temperature (K). All the other
units used in this book are derived from these basic units. The unit of force is the