Sometimes the obvious escapes me, and it’s only due to some chance observation that I realize the same fundamental principles are everywhere.

A short time ago, I created a simple hydraulic network in MapleSim, and after experimenting with some of the parameters, found it gave the same behaviour as an electric circuit I’d modeled earlier.

 It dawned on me that the hydraulic and electric circuit looked pretty similar; both contained either a source of fluid or charge, and both contained resistances to flow (either in the form of pipes or resistors), all in the same configuration.

I then realized that both models were simple balances.  In the hydraulic circuit, the flowrate in the pipes is governed by balancing the pressure of the fluid source against friction in the pipes. Similarly, the current throughout the circuit is dictated by a balance between the voltage source and the resistors.

After experimenting with the parameters I found that doubling the pressure or voltage doubled the flowrate or current throughout the system, while tripling the pressure or voltage tripled the flowrate or current throughout the system.  Hmmm….interesting….

I then made a connection between otherwise disparate parts of my formal education. I wrote down the following equations, carefully extracted from long dormant parts of my hippocampus.

 I found it interesting that a linear relationship applied across all three domains – in each case the output was simply a constant times the input, giving me the behaviour I’d noticed earlier.

Then, something pretty fundamental (and obvious) struck me; each equation was just a relationship between

1. a driving force, which is a relative change in a quantity (voltage, pressure or temperature) over a spatial dimension,
2. and a conserved quantity (charge, mass, or heat)

This crystallized something I’d always known at some level - there are grand, unifying principles that connect multiple scientific and engineering fields, and if you’re familiar with one discipline, you can at least understand the physics of others by analogy:

Pressure is to flowrate what voltage is to current

Temperature is to heat flow what pressure is to flowrate

Voltage is to current what temperature is to heat flow

This in itself is no revelation – but it took software to lead me through a thought process, and make the obvious…well…obvious.

This prompts a deeper question; are we giving students and practicing engineers the skills to reconcile disparate pools of knowledge from multiple fields, and understand their unifying principles.

Most engineering education is domain specific - my degree in chemical engineering concentrated solely on pressures and flowrates, temperatures and heat. It was only my professional experience in supporting math and simulation software that propelled me to explore other fields.

The emerging engineering challenges are, however multidomain, and engineers will need to understand the unifying principles between physical domains.

This, I think, calls for greater interdisciplinary education at an earlier stage (something I would have appreciated as an undergraduate), and the tools and methods to support this training.