Page 23 - Fluid Mechanics and Thermodynamics of Turbomachinery

4 Fluid Mechanics, Thermodynamics of Turbomachinery
newton (N), defined as that force which, when applied to a mass of 1 kilogram,
2
gives an acceleration to the mass of 1 m/s . The recommended unit of pressure is
the pascal (Pa) which is the pressure produced by a force of 1 newton uniformly
distributed over an area of 1 square metre. Several other units of pressure are in wide-
spread use, however, foremost of these being the bar. Much basic data concerning
properties of substances (steam and gas tables, charts, etc.) have been prepared in SI
units with pressure given in bars and it is acknowledged that this alternative unit of
pressure will continue to be used for some time as a matter of expediency. It is noted
5
5
2
that 1 bar equals 10 Pa (i.e. 10 N/m ), roughly the pressure of the atmosphere at
sea level, and is perhaps an inconveniently large unit for pressure in the field of
turbomachinery anyway! In this book the convenient size of the kilopascal (kPa) is
found to be the most useful multiple of the recommended unit and is extensively
used in most calculations and examples.
In SI the units of all forms of energy are the same as for work. The unit of energy
is the joule (J) which is the work done when a force of 1 newton is displaced through
1
2
a distance of 1 metre in the direction of the force, e.g. kinetic energy ( mc ) has the
2
2
2
2
dimensions kg ð m /s ; however, 1 kg D 1Ns /m from the definition of the newton
given above. Hence, the units of kinetic energy must be Nm D J upon substituting
dimensions.
The watt (W) is the unit of power; when 1 watt is applied for 1 second to a system
the input of energy to that system is 1 joule (i.e. 1 J).
The hertz (Hz) is the number of repetitions of a regular occurrence in 1 second.
Instead of writing c/s for cycles/sec, Hz is used instead.
The unit of thermodynamic temperature is the kelvin (K), written without the °
sign, and is the fraction 1/273.16 of the thermodynamic temperature of the triple
point of water. The degree celsius ( ° C) is equal to the unit kelvin. Zero on the
celsius scale is the temperature of the ice point (273.15 K). Specific heat capacity,
or simply specific heat, is expressed as J/kg K or as J/kg ° C.
1
1
Dynamic viscosity, dimensions ML T , has the SI units of pascal seconds, i.e.
M kg N.s 2
D D Pa s.
2
LT m.s m. s
Hydraulic engineers find it convenient to express pressure in terms of head of a
liquid. The static pressure at any point in a liquid at rest is, relative to the pressure
acting on the free surface, proportional to the vertical distance of the free surface
above that point. The head H is simply the height of a column of the liquid which
3
can be supported by this pressure. If is the mass density (kg/m ) and g the local
2
gravitational acceleration (m/s ), then the static pressure p (relative to atmospheric
2
pressure) is p D gH, where H is in metres and p is in pascals (or N/m ). This is
left for the student to verify as a simple exercise.

Dimensional analysis and performance laws
The widest comprehension of the general behaviour of all turbomachines is,
without doubt, obtained from dimensional analysis. This is the formal procedure
whereby the group of variables representing some physical situation is reduced