Units and dimensions

Introductory remark:

Any physical quantity has a twofold value. It has one component with a dimensional significance and another with a numerical significance. Both components are equally important , and should be specified together. 

Mathematical manipulation of numbers leads to quantitative answers to problems of engineering interest. For these answers to be correctly interpreted without difficulty by all concerned it is essential to have a system of units which is adhered to by all. 

Dimensions:

Five fundamental dimensions , namely ;

• Mass(M)  
• Length(L) 
• Time(T) 
• Quantity of heat interaction(H) 
• Temperature(Θ)     

were used in classical thermodynamics. The dimensions of all other thermodynamic quantities were expressed in terms of these five.   

Systems of units:

Out of the many systems of the units available to us , two deserve special mention :

• The British (or imperial) system
• The international (SI) system 

The British System has four basic mechanical units , namely ;

• Pound (mass)   'lb'
• Foot (length)   'ft'
• Second (time)   's'
• Pound-Force (force)   'lbf'

One pound-force is the force necessary to give one pound of matter and acceleration of 32.174 ft/s². Familiarity with this system is still important because of its continued use in a few industrialized countries , especially the USA.

Pressure:

In engineering practice pressures are measured by instruments such as manometers , Bounder pressure gauges and pressure transducers which give an indication of the difference between the measured pressure and the atmospheric pressure. The pressure reading given by the instrument is called the gauge pressure , so that ;

Absolute pressure(p) = Gauge pressure(p_g) + Atmospheric pressure(p_a)

Absolute pressures which are less than atmospheric are specified in terms of vacuum , which is defined by ;

Vacuum(p_v) = Atmospheric pressure(p_a) - Absolute pressure(p)

When giving the values of pressures it is extremely important to specify whether they are absolute values(by writing abs after the number and unit) or gauge values or a vacuum (by writing either gauge or vac after the unit). Where the nature of the quantity is not specified , it may be assumed to be the gauge or the absolute value , depending on what the reader is used to. Where a large number of pressure values need to be given , it is convenient to declare at the beginning that all values are absolute(or gauge).