the dimensions when the terms are reduced to basic dimensions of mass, 

 length, and time (MLT) or force, length, and time, (FLT) . These two 

 systems, i.e., the MLT and the FLT systems, are interrelated through 

 Newton's law, F = Ma or F = ML/T^. By use of this relation, con- 

 version from one system of units to another can be made. 



The application of the method of dimensional analysis to a particular 

 phenomenon in engineering is based on the assumption that certain vari- 

 ables are independent variables of the problem, and that all the other 

 variables involved, except the dependent variable, are redundant or 

 irrelevant. The listing of the variables, except for simple cases, re- 

 quires considerable insight into the natural phenomenon. Although the 

 application of the principles of dimensional analysis is complicated in 

 some cases, it is simple for a large number of problems and is useful in 

 both analytical and experimental work. Some of these uses are to: 



(a) Aid memory in writing formulas. 



(b) Check the dimensional homogeneity of equations. 



(c) Determine a conversion factor for changing system of 

 units. 



(d) Develop general functional equations of fluid- flow 

 phenomena expressed in terms of dimensionless parameters. 



(e) Obtain partial solutions of complex problems. 



(f) Plan tests and present experimental results in a 

 condensed and systematic manner. 



(g) Provide dimensionless ratios of terms that can be used 

 as the bases for scale-model design and interpreting the test 

 results. 



The details of the methods of dimensional analysis were developed 

 primarily by Rayleigh (1899), Buckingham (1914), and Bridgman (1922). 

 The theory of dimensional analysis has been treated in considerable depth 

 by van Driest (1946), Birkhoff (1950), and Langhaar (1951). Ruark (1935) 

 and Birkhoff (1950) have explained another method, called inspectional 

 analysis, which supplements the dimensional analysis method. Their 

 method is reported to be capable of providing all the information that 

 can be obtained by dimensional analysis and, in certain cases, it can 

 provide more information. The mathematical rigor and the more philo- 

 sophical aspects of the subject are not discussed in this report; however, 

 the above references may be consulted if a detailed study of the methods 

 of dimensional and inspectional analysis is desired. 



The best method of analyzing fluid-flow problems is by direct mathe- 

 matical solution. However, since most problems confronted by the coastal 

 engineer are complex and many variables are involved in the differential 

 equations of motion, direct mathematical solutions are not possible. For 

 these types of problems dimensional analysis can, in many instances, be 

 used to great advantage. The method of dimensional analysis developed 



