#dimensional analysis

[math-memes]

physics nerds i have a question for you

so pressure is measured in kg/m^2. this makes sense because pressure is applied over a two-dimensional area

acceleration is measured in m/s^2. I know this is a shorthand for “m/s every second”, but that s^2 in the denominator is enticing me. is there a way we can visualize acceleration as distance being applied to a two-dimensional time surface? what would that look like? what even are units?

[manorinthewoods]

Out of curiosity, I've been puzzling through dimensional analysis mainly by referring to Wikipedia and writing down the very basic SI constructions, and then constructing simpler relations of the closely related units (ex: coulumb, watt, ampere, volt, for electricity - probably forgetting one or two there, I do not really get electricity that well). It's reasonably entertaining. Metric is very fun to work with.

...I still remember that one time I was at a Scout camp against my will and cleaning dishes and debating units with another dishwasher, and he said that Imperial units were better because they were smaller. I tried to explain that this is a completely nonsensical argument to make, fundamentally units don't work like that, but I'm less eloquent in speaking and I didn't have a super good familiarity with the nature of metric anyway. But now I am learning. Wonderful units! So... so many units... it all reduces, it's incomprehensible...

One time my brother was mentioning to me some sort of three C joke system for dimensional analysis. Speed of light and centimeter or something. I don't remember. He rambles much worse than me. Looking this up in various ways just now returned mostly nonsense, and I've not really got the inclination to bug him about it.

[hyperoperationfractallisation]

Dimensional analysis my beloved

[nobodywasneverhere]

these dimensions are getting weird

[er-cryptid]

Patreon

[andmaybegayer]

bitsow also mentions that Energy is Pressure × Volume which is fun because it means you can express Pressure as Energy per Volume, which works out pretty nicely since one kilopascal is equal to one Joule Per Liter.

[pervocracy]

Let’s Fix Knives Out

I went to see Knives Out last night, and I want to say first of all, it’s a great movie.  The plotting, performances, cinematography, art direction - all amazing.  I highly recommend seeing it and I do not recommend reading the rest of the post if you haven’t.  It’s a mystery with a lot of twists and it’s more fun unspoilered.

But I went to see it with another nurse, and she also loved it, but we both had some technical issues with a certain plot point.

MAJOR SPOILERS FOLLOW 

KNIVES OUT SPOILERS AFTER THIS POINT

In the key scene of the film, Marta gives Harlan two IV medications, and accidentally switches them.  (Fortunately for her, they had already been maliciously exchanged and she’s switching them back to the correct medications, but this only comes out later.)  The medication vials are shown and the dosages are stated onscreen, so we know exactly what happened.

Harlan was prescribed 100mg ketorolac and 3mg morphine for pain after a shoulder injury.  The ketorolac comes in a 30mg/mL concentration and the morphine in a 5mg/mL concentration.

Therefore, Marta should have given him 3.3mL ketorolac and 0.6mL morphine to deliver the correct doses.  But because she switched them, she (supposedly) gave him incorrect dosages: only 18mg ketorolac, but 16.5mg morphine.

However, she exclaims in horror that she gaveit Harlan 100mg morphine.  This is not possible; it would have required 20mL of solution and there wasn’t that much in the whole vial.  Also, a 20mL syringe is gigantic and we don’t see Marta using one anywhere near that large.  I think what happened is the filmmakers worked out how this med error could occur with the same number of milligrams, but disregarded the different concentrations, even though they’re clearly shown onscreen.

Some other problems with this scenario:

- 100mg ketorolac is too high a dose.  A normal dose would be 30mg or at most 60.  100mg ketorolac isn’t likely to kill someone, but it’s not good for your kidneys.  I give ketorolac a lot at my job and I’ve never given someone 100mg in one dose.

- Neither of these meds has to be given IV.  Ketorolac can be given orally or as an intramuscular injection and morphine can be given orally or sublingually.  There’s no reason to put the patient through the hassle/pain/risks of daily home IV injections.

- What doctor prescribed morphine for a week after a shoulder sprain so mild that Harlan doesn’t even need a sling?  Even the ketorolac is probably overkill.  Realistically he’d probably get an oral NSAID and maybe a muscle relaxant.

- IV morphine works fast.  There’s no way Harlan would have ten minutes of full consciousness to work out a harebrained scheme with Marta.  (Well, he didn’t really get overdosed.  But there’s no way Marta would have seen his total lack of symptoms and not thought “maybe I didn’t OD him after all.”)

–

But fortunately, with the help of a fellow nurse, Epocrates, Allagash White, and a pink margarita cocktail described as tasting like “the opposite of cough syrup” and “a headache in a bottle,” I have fixed this!  Here’s an alternate scenario I worked out:

- Instead of a shoulder sprain, Harlan is under hospice care for lung cancer with bone metastases.  (This would also address some other plot issues: why he changed his will only a week earlier, and why he accepts death so readily.)  This better justifies him being on morphine.

- He is prescribed 30mg oral prednisolone for airway inflammation, and 10mg oral morphine for bone pain.  Both are given as liquids because as a late-stage cancer patient he has difficulty swallowing pills.

- The prednisolone comes in a concentration of 15mg/5mL, so his dose would be 10mL.

- The morphine comes in a concentration of 20mg/mL, so his dose would be 0.5mL.

- In switching them, giving 10mL morphine and 0.5mL prednisolone, Marta accidentally gives Harlan only 1.5mg prednisolone, but a whopping 200mg morphine. (or would have, if that dastardly Ransom hadn’t switched them)

- Normally, these two medications are dyed different colors.  But Harlan has a food dye allergy so he has gotten a compounding pharmacy to make him clear solutions.  He also doesn’t like the taste of the medications (which are both pretty awful), so he has Marta mix them in juice for him, obscuring any difference in flavor, consistency, or odor.

- Because he took the morphine orally, it’ll take longer to take effect, making it more plausible that he doesn’t just immediately pass out.

This scenario isn’t perfectly plausible and still requires a little reaching, but at least the math works out.

[avery-acrylic]

05.07.2019 10:37 AM

Day one of summer physics review. My baby succulents are my pride and joy. 

Day 001/100