5 ms·
Indeed - the most useful (as in, most-used) models strip out darn near every calculation and boil things down to a very simple rule-of-thumb approximation. For
by reaperman 3y ago
Indeed - the most useful (as in, most-used) models strip out darn near every calculation and boil things down to a very simple rule-of-thumb approximation.
For example, plumbers just ballpark the pressure of water due to elevation to "half a PSI per foot". Their 1/2psi "model" gets them close enough without making them use a calculator. Their 1/2psi "model" gets them close enough, with an appropriate safety factor built-in, without making them use a calculator. Even though really it's much closer to 0.433psi per foot of water column.
But really it's much closer to (((((aT+b)*T+c)*T+d)*T+e)*t+f)/(1+h*T) * g * 0.3048 * 0.453592 psi per foot of water column depending on what the temperature is and what gravity is where you are. And for further precision you'd need to integrate this equation with respect to T and gravity along the height of the water column, or use an even more precise model because the constants a through h are still doing a lot of "heavy-lifting" hiding and abstracting away other hard-to-measure physics phenomena. You'd also have to adjust for impurities in the water, as that will change the density as well at these precisions. It also only applies to water that's not moving, moving water will have a lower psi per foot due to friction.
Obviously plumbers certainly wouldn't find it useful to have to replace their "half-a-psi-per-foot" mantra with something involving an equation to determine the density of water (generally considered incompressible anyways) as a function of its temperature. The amount of situations which need the more complex models are very few and far between.
But we do still need them! A "theory of everything" would be fantastically wonderful for opening up generation and validation of new, useful, rules-of-thumb for many scientists and engineers.
T = temperature of water in C
a=-2.8054253⋅10^-10
b=1.0556302⋅10^-7
c=-4.6170461⋅10^-5
d=0.0079870401
e=16.945176
f=999.83952
g=9.81 m/s^2 (variable depending on where you are on or off the planet)
h=0.01687985
- petsfed 3y agoI'm clearly a physicist through-and-through, I read "half a psi per foot" and wondered if it was ψ or Ψ, and why a plumber would use a Greek letter for anything.
- reaperman 3y agoHaha! Thank you, edited for clarity for a wider audience.
- kwhitefoot 3y agoI'm a European physicist/electronics engineer/software developer and I just wondered what was wrong with 0.1 bar per metre.
- strogonoff 3y agoI’d be the first to admit that “theory of everything” is infinitely compelling to me, but increasingly I think it also deserves caution. It would certainly open many new avenues to explore, and potentially bring lots of innovation. However, to prove it you would need infinite resources and infinite time—in other words, you will never prove it, so within the framework of physics you will not assume it is complete and correct and absolute truth. But there are people who will assume just that, they’ll see how well it works and what progress it brings and say “that’s it guys, we have finally arrived at truth!” When they see something that doesn’t fit in the model (say, consciousness or free will), they will say it doesn’t exist and influence policy decisions based on that. When they see someone using another theory or even suggesting there can be others, they will ridicule them. As map is never the territory, any model is always going to be a local maximum, and a particularly high local maximum followed by a steep trough might make it difficult to reach the next one.