How to derive engineering equations

[Zip]

Alright gentlemen I have something very special in mind for those of you new to the BBS, I'm going to show you how to derive virtually all equations you will encounter in engineering.

Step 1:

Define a control volume. Depending on your field and/or problem of interest, this is the region of relevance to your inputs and outputs. Could be mass, light, heat, etc. Pick your coordinate system: cartesian, radial, spherical.

Step 2:

Define the flux, which is the flow rate into the system per unit time, for some quantity of interest. The area is orthogonal to the flow direction. For instance:

Mass: (mass/time)/area
Heat: (energy/time)/area
Moles: (moles/time)/area
Current: (coulombs/time)/area

Draw a diagram of your system, with the flux and control volume. It is convenient to express the flux in differential form if you are deriving an analytical expression. Initially you will be working in one spatial dimension (ℓ) in your control volume, but more general results are analogous using calculus. Here are a few definitions of flux from well-known systems:

Fick's Law: -D(∂c/∂ℓ)
Fourier's Law: -k(∂T/∂ℓ)
Darcy's Law: (-k/u)(∂P/∂ℓ)
Ohm's Law: (-1/R)(∂V/∂ℓ)

Consider momentum and viscosity for additional examples.

Step 3:

Write the overall balance, or conservation equation. For a basic system relative to the control volume, you only have input (I) and output (O). In more complex systems you have to factor in consumption (C), accumulation (A), and generation (G) such that your final equation takes the following form: I - C + G - A = O.

Step 4:

Simplify. If your variables can be defined in terms of more familiar quantities using, for instance, the CGS system, do so. If consumption, accumulation, generation are not present in your system, remove the associated terms from your balance equation.

Step 5:

Solve the equation(s).

[Mantikore]

im going to be doing something like this when university starts for me in a few weeks. do you have any good sources or textbooks that show examples of these?

[Zip]

That depends on what you're studying, you're not going to see Ohm's Law in a textbook on transport phenomena for instance. These are meant to be general guidelines for making engineering topics more accessible when you don't have concise references or in-depth instruction. For instance, using these guidelines, some basic mathematics and the concepts of stress, strain and deformation, you can develop a basic understanding of the finite element method.

[emag]

im going to be doing something like this when university starts for me in a few weeks. do you have any good sources or textbooks that show examples of these?What major are you & what class is it?

[The Jitterskull]

We didn't even cover

Fick's Law: -D(∂c/∂ℓ)
Fourier's Law: -k(∂T/∂ℓ)
Darcy's Law: (-k/u)(∂P/∂ℓ)
Ohm's Law: (-1/R)(∂V/∂ℓ)

^^ in first year physics. The closest was Gauss' law.

[Mantikore]

What major are you & what class is it?

ehh, im doing materials and biomedical engineering. im just doing some regular engineering maths class that all the engineers do