Overview of the new engineering

Engineering phenomena

Engineering phenomena are cause and effect processes:

· Electromotive force E causes electric current I.

· Temperature difference DT causes heat flux q.

· Stress s causes strain e.

Cause and effect parameters in modern engineering

In modern engineering, cause and effect parameters are combined in ratios that are assigned names and symbols:

· E/I is assigned the name “electrical resistance”, and the symbol R

· q/DT is assigned the name “heat transfer coefficient”, and the symbol h

· s/e is assigned the name “material modulus”, and the symbol E

Cause and effect parameters in the new engineering

In the new engineering, cause and effect parameters are never combined in ratios. They are kept separate in order to simplify the solution of problems. (Just as in mathematics, x and y are kept separate to simplify the solution of problems.)

In the new engineering, parameters such as R, h, and E are found only in history books, just as phlogiston and caloric fluid are now found only in history books.

Describing the behavior of engineering phenomena without using R, h, E

In the new engineering, behavior is described with the cause and effect parameters separated—ie without parameters such as R, h, and E. Equations that describe behavior are in the form of Eqs. (1) to (3).

E = f{I} (1)

q = f{DT} (2)

s = f{e} (3)

Note that Eqs. (1) to (3) are directly analogous to Eq. (4), the fundamental equation of pure mathematics. Also note that the “laws” on which modern engineering is based bear no resemblance to Eq. (4).

y = f{x} (4)

Symbolism and homogeneity in modern engineering

In modern engineering, parameter symbols represent parameters, and rational equations must be dimensionally homogeneous. Eqs. (1) to (3) are dimensionally inhomogeneous and therefore they are deemed irrational in modern engineering. For example, the left side of Eq. (1) is electromotive force, the right side is electric current. Since the dimensions of these two parameters differ, Eq. (1) is inhomogeneous. And similarly for Eqs. (2) and (3).

Symbolism and homogeneity in the new engineering

In the new engineering, parameter symbols represent the numerical values of parameters in dimensions specified in the nomenclature that identifies the symbols. In other words, symbols represent pure numbers.

For example, if the nomenclature states that the symbol “I” is the numerical value of electric current in amperes, then I is a pure number. In this case, the equation “I = 3” states that “the numerical value of electric current in amperes equals 3”. It would be inappropriate to write “I = 3 amperes” because “amperes” would be redundant.

(The symbolism used in the new engineering is not new. It was widely used in mid twentieth century in what were called “dimensional equations”. For example, see the nomenclature on page 467 of Perry’s Chemical Engineers’ Handbook, Third Edition (1950), published by McGraw-Hill. Note that the symbol dimensions are specified in the nomenclature.)

Since symbols represent pure numbers in the new engineering, Eqs. (1) to (3) are rational in the new engineering. For example, Eq. (1) states

The numerical value of E (in the dimension specified in the identifying nomenclature) is a function of the numerical value of I (in the dimension specified in the identifying nomenclature).

Note that Eqs. (1) to (3) are homogeneous because they contain only pure numbers. However, no significance is attached to homogeneity because all rational equations contain only pure numbers, and therefore are inherently homogeneous.

Equations used to solve problems: new vs modern engineering

In modern engineering, equations such as Eqs. (5) and (6) are used in the solution of problems.

R_parallel = 1/SR_i^-1 (5)

U = (1/h₁ + t_wall/k_wall + 1/h₂)^-1 (6)

Note in Eq. (5) that the cause and effect parameters E and I are combined and implicit in R_parallel and R_i. Note in Eq. (6) that the cause and effect parameters q, DT, and dT/dx are combined and implicit in U, h₁, h₂, and k_wall.

In the new engineering, cause and effect parameters are always separate, and Eqs. (5) and (6) are altogether replaced by Eqs. (5a) and (6a):

I_parallel = SI_i (5a)

DT_total = DT₁ + DT_wall + DT₂ (6a)

It is important to note the following:

· Eqs. (5) and (5a) are identical. Equation (5a) is readily obtained from Eq. (5) by substituting E/I for R, then separating E and I.

· Eqs. (6) and (6a) are identical. Eq. (6a) is readily obtained from Eq. (6) by substituting q/ΔT for h and U, substituting qt_wall/ΔT for k, and then separating q and ΔT.

· Any problem that can be solved with Eq. (5) can be solved with Eq. (5a).

· Any problem that can be solved with Eq. (6) can be solved with Eq. (6a).

· If a problem concerns proportional behavior, the solution is simple and direct using Eqs. (5) and (6), or using Eqs. (5a) and (6a).

· If a problem concerns nonlinear behavior, the solution is much simpler using Eqs. (5a) and (6a).

· Equations such as Eqs. (5) and (6) have no place in the new engineering. They are found only in history books.