Dimensional Consistency

Now that we have reviewed some background material concerning units and dimensions, we can immediately make use of this information in a very practical and important application . A basic principle exists that equations must be dimensionally
consistent. What the principle requires is that each term in an equation must have the same net dimensions and units as every other term to which it is added or subtracted or equated . Consequently, dimensional considerations can be used to help identify the dimensions and units of terms Or quantities in terms in an equation.
Groups of symbols may be put together, either by theory or experiment, that have no net units. Such collections of variables or parameters are called dimensionless or nondimensional groups. One example is the Reynolds number (group) arising in fluid mechanics.
We also need to mention something about the accuracy and precision of numbers as used in practice. Accuracy refers to how close a measured value is to its true value; precision refers to the degree of dispersion (or deviations) of
measurements from their true values . In this book you will encounter integers such as 1, 2, 3 and so on, which are in some cases exact (2 reactors, 3 input streams) but in other cases are shortcut substitutes for presumed measurements in problem solving (3 moles , 10 kg).