687: Dimensional Analysis

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 Dimensional Analysis Title text: Or the pressure at the Earth's core will rise slightly.

Explanation

This comic makes fun of how scientists (often physicists) use dimensional analysis to quickly check if a given formular can possibly relate to a physical system or if there were some (obvious) mathematicals errors in its derivation. Dimensional analysis here refers to the check if both sides of the equation arrive at the same physical unit if the units of all variables get plugged into the equation. This usually requires knowledge of the system of units and the relation between different physical units.

The comic uses the following equation to make fun of it:

```(Planck energy) / (Pressure at the core of the earth) * (Prius combined EPA gas milage) / (minimum width of the english channel) = pi
```

The right hand side is dimensionless (The constant pi = 3.14... by definition is the relation of two lengths, the circumference and the diameter of a circle). The left hand side requires to plug in the dimensions of the named physical quantities:

```* Plank energy: given in Joule [J]
* Pressure at the core of the earth: Given in Pascal [Pa]
* Prius combined EPA gas milage: miles/gallon, SI units: meters/litres [m/l]
* minimum width of the english channel: meters [m]
```

When plugged into the left hand side this amounts to:

```[J / Pa * (m/l) / m] = [Nm / (N/m²) * (m/m³) / m] = 1
```

Using the following unit relations (this does not reduce units to the seven SI units, but does use some derived units):

```* 1 Joule = 1 Newton-meter  [J] = [Nm]
* 1 Pascal = 1 Newton per square-meter [Pa] = [N/m²]
* 1 cubic-metre = 1000 litres [m³] = 1000 [l]
```

Note that for dimensional analysis constant factors are not taken into account. Here square brackets are used to denote dimensional analysis.

This is another comic in the infrequent My Hobby series.

Transcript

My Hobby: Dimensional Analysis

Discussion

Is it customary to just slap a new contributor after 5 minutes because the page was not done perfectly on the first editing? Now I will NOT research and add the actual numbers you would have to plug into the equation and I will leave this to Dave22. Genius. Stamfest (talk) 09:36, 1 April 2013 (UTC)

We do put those fields there for a reason. Most editors just make a page and leave them incomplete with fields deleted or blank, oftentimes leaving admins with heaps of maintenance work to deal with. I probably *should* have waited for you to finish, but prior experience and me being busy with two simultaneous continuously updating comics led me to treat it like most other incomplete pages. Will wait in the future though, since I know how you edit now. Discussion hidden, as it covers matters outside of the comic. Davidy²²[talk] 10:01, 1 April 2013 (UTC)
And I added the comment of a (very) initial explanation to the initial version. If you only want immediately perfect content, then just say so at page creation-time. This is totally against all wiki rules I have ever experienced. It is also against basic netiquette to call new contributors names upon their first submission. You might consider to change your attitude if you run or are involved with such a project. OTOH, if this is YOUR project, you are free to treat contributors all the way you want, but do not expect them to add more content if you behave like that. But the good thing is: your reaction shifted my attention back to work. Thanks for that. This won't help the page, though. Bad luck, I guess. Also, I only found out now that it is not possible to delete accounts on a wikimedia wiki... Stamfest (talk) 13:10, 1 April 2013 (UTC)
Someone posted that I've been wasting electrons on here. I didn't quite know how to take that, it being true and all. I had the impression that it was the whole point of comics that you waste time on them. Some of us just have too many electrons; obviously. I used Google News BEFORE it was clickbait (talk) 16:33, 27 January 2015 (UTC)
Then they should stop being so negative and get some grounding. Promethean (talk) 13:26, 27 February 2018 (UTC)

This comments should be removed from this topic. --Dgbrt (talk) 20:22, 14 May 2013 (UTC)

I am not sure if this is relevant but I laughed more reading Stamfest vs Daviddy22 then Randall :D but Dgbrt may have a point of removing it. 173.245.62.83ck

Made a minor addition to the explanation as it relates to the "Buckingham Pi" formalization. This may be a 2nd order pun in the comic.Tardyon (talk) 15:05, 3 February 2014 (UTC)

The units only check out if mileage is given in the form liters/100 km. If you use miles/gallon you end up with units of length^-4.108.162.217.5 22:17, 13 November 2014 (UTC)

Or, maybe the Plank Energy will decrease... Mountain Hikes (talk) 04:01, 17 December 2015 (UTC)

Why is he breaking from his usual black and white style? The green was a suprise 162.158.39.207 22:06, 27 November 2016 (UTC)Davy

England is part of the mainland of Britain and can't float anywhere on its own without tearing itself away from the rest of the land. It's like suggesting that California can float away from America. (Maybe that wasn't a good example, what with the San Andreas Fault, and all...) Brenda (talk) 09:52, 15 June 2018 (UTC)