Why Conventional Engineering Laws should be Abandoned, and the New Laws that will Replace them

Abstract

There are three reasons why laws such as q = hΔT and σ = Eε, and parameters such as h and E, should be abandoned. 1. The laws are analogs of y = (y/x)x and, if y is a nonlinear function of x, analogs of (y/x) (such as h and E) are extraneous variables that greatly complicate problem solutions. 2. Parameters such as h and E were created by assigning dimensions to numbers, in violation of the modern view that dimensions must not be assigned to numbers. 3. The laws purport to describe how the numerical value and dimension of parameters are related when, in fact, equations can rationally describe only how the numerical values of parameters are related. When conventional engineering laws are abandoned, they will be replaced by new laws described by the following: 1. They are dimensionless because parameter symbols in equations represent only numerical value. 2. They are analogs of y = f{x}. 3. They contain no analogs of y/x, and consequently they contain no extraneous variables. 4. They make it possible to abandon analogs of y/x (such as modulus and heat transfer coefficient), greatly simplifying the solution of nonlinear problems by reducing the number of variables. 5. They have no parameters that were created by assigning dimensions to numbers. 6. They are inherently dimensionally homogeneous because parameter symbols in equations represent only numerical value. 7. They state that the numerical value of parameter y is always a function of the numerical value of parameter x, and the function may be proportional, linear, or nonlinear.