Consistent Systems of Units

Except where otherwise noted here or in the text, either consistent system of units (SI or U.S. customary) may he used. Only SI units may he used for electrical quantities, since no comparable electrical units exist in the U.S. customary system. When special units are used, they are noted at the point of use. 

Equations 4-102 through 4-105 are valid in any consistent system of units. 

Formula 4-323 is valid for any consistent system of units and is applicable to vertical holes. 

Any Consistent System of Units may be Employed in Place of the English Units Specified... 

Any consistent system of units can be used with equation 13.61. 

For any equation to be valid, every term in the equation must have the same physical character, i.e., the same net dimensifons (and consequently the same units in any consistent system of units). This is known as the law of conservation of dimensions (otherwise known as the fruit salad law — you can t add apples and oranges, unless you are making fruit salad ). Let us look further at Eq. (2-6). Since both z and x have dimensifons of length, e.g., [x] = L, [z] = L, it follows from the fruit salad law that the dimensions of a and b must be... 

The conclusion that dimensionless numerical values are universal is valid only if a consistent system of units is used for all quantities in a given equation. If such is not the case, then the numerical quantities may include conversion factors relating the different units. For example, the velocity (F) of a fluid flowing in a pipe can be related to the volumetric flow rate (Q) and the internal pipe diameter (D) by any of the following equations ... 

In equation 1.3, p is the density, p. the dynamic viscosity, and the mean velocity of the fluid d, is the inside diameter of the tube. Any consistent system of units can be used in this equation. The Reynolds number is also frequently written in the form... 

In this chapter all equations are written in a form for which any consistent system of units may be used. The table of nomenclature gives illustrative units in the MKSA system. By definition,... 

For any consistent system of units, NR is a dimensionless number. The linear dimension L may be any length that is significant in the flow pattern. Thus, for a pipe completely filled it might be either the diameter or the radius, and the numerical value of NR will vary accordingly. General usage in this country prescribes L as the pipe diameter. 

This equation makes sense only when all of its terms are expressed in a self-consistent system of units such as the SI system. The appropriate value used for R is... 

With the current trend toward metrication, the question of using a consistent system of units has been a problem. Wherever possible, the authors of this Handbook of Environmental Engineering series have used the British system (fps) along with the metric equivalent (mks, cgs, or SIU) or vice versa. For the convenience of the readers around the world, this book provides a 55-page detailed Conversion Factors for Environmental Engineers. In addition, the basic and supplementary units, the derived units and quantities, important physical constants, the properties of water, and the Periodic Table of the Elements, are also presented in this document. 

Heat-transfer-coefficient correlations are usually presented in terms of dimensionless numbers, which are groups of variables that have no net dimensions when evaluated in any consistent system of units. The most important dimensionless numbers for heat transfer are defined next. 

There are several different consistent systems of units. In most of the world (apart from the US and to some extent the UK) the SI system is standard. It is also used in refereed scientific and engineering journals in these two countries. In practice, it is essential for a chemical engineer to be proficient in the SI system, but to be able to use data in units of other systems and to be able to specify designs in the preferred unit system for the job. 

The development of the metric system, which served as the basis of the International System of Units (Le Systeme International d Unites known as SI), occurred during the French Revolution in the mid-eighteenth century. This coincided with the beginning of the age of modern science, especially chemistry and physics, as the value of physical measurements in the conduct of those pursuits became apparent. As scientific activities became more precise and founded on sound theory, the common nature of science demanded an equally consistent system of units and measurements. The units in the SI have been defined by international accord to provide consistency in all fields of endeavor. The basic units are defined for only seven fundamental properties of matter. All other consistent units are derived as functions of these seven fundamental units. 

Only repeatedly occurring symbols are listed. Symbols occurring in a narrow context only, such as in mathematical proofs or examples are not listed the reader has to follow the context. The notation introduced in Appendices is included only if it occurs in the main text. Physical dimensions are reminded of only if confusion is to be avoided. Concerning the (SI) system of physical units, see Section 2.3, in addition K (Kelvin) for temperature. Of course another consistent system of units can work as well. 

It is an example of a general homogeneous physical equation since the dimensions on either side of the equality sign are [LMT ]. Its physical magnitudes can be expressed using any consistent system of units. Note that a general homogeneous physical equation does not contain a dimensional constant [16]. 

Abcoulomb n The abcouloumb, the emu of charge, is defined as the charge which passes a given surface in 1 s if a steady current of 1 abampere flows across the surface. Its dimensions are, therefore, cm which differ from the dimensions of the statcoulomb by a factor which has the dimensions of speed. This relationship is connected with the fact that the ratio 2K/K must have the value of the square of the speed of light in any consistent system of units. It follows further that... 

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