[Comic title: Delta-P; alt text: If you fire a Portal gun through the door of the wardrobe, space and time knot together, which leads to a frustrated Aslan trying to impart Christian morality to the Space sphere.]
There's nothing I can say of XKCD's various artistic failures which hasn't been said millions of times already. So, let's criticize Randy's most valued thing in the world: his precious science, his physics, or more precisely his grasp of fluid mechanics(breast milk not included- let's leave that one to Rob). [Nice. -Ed.]
Now, I'm an undergraduate of physics. I took a course of fluid mechanics with one of the world's premier physicists. I only mention this to stress that when I say I had no idea how the fuck Randall got the formula he uses in this one, I know what I'm talking about. But, eventually, I found out the horrible truth:
Randall begins with Q=A*v, which says that the flow equals the area of opening times the speed of the water relative to the wardrobe. This is wrong, but compared with his future follies this is actually still pretty acceptable. Only now Randy needs to calculate that speed, and here he fails tremendously.
Randy assumes conservation of energy, which is usually a fine thing to assume when doing physics. He takes the initial, purely potential energy of the wardrobe as Ei=mgd .He takes the final, purely kinetic energy as Ef=1/2 mv^2 .Because he assumes conservation of energy, both quantities are equal and so he extracts v from that and finally gets Q=A*√(2gd).
Now, his whole process is rife with errors(the Q=A*v thing assumes both laminar flow and and an opening that is two-dimensional, none of which occur here,) but let's narrow it down to just two of the most obscene ones:
- There is no conservation of energy here, you dumb fuck. Friction with water is a substantial, non-conservative force which does not allow you to use even actual fluid mechanics stuff such as Bernoulli's principle, let alone the high-school-level conservation-of-energy calculations shown above which Randy tries to pass off as science. If this was true, it could lead to all sorts of shit: a cylinder that is moving in such a liquid as Randall suggests would never come to a stop or even slow down, which is obviously a nonsensical result. This is what was known historically as Stokes' Paradox, this is why the concept of viscosity was introduced, and to top it off, this was all well known for 150 years or so. Do try and keep up, Randy. This would be okay, though, had Randy tried to find the speed of the wardrobe as it hit the water, but
- Randy doesn't know how to use the concept of potential energy. This is some really elementary stuff. This is high-school level stuff, and Randy fails at it miserably. Randy tries to calculate the wardrobe's speed on the moment of impact with the water. He takes the potential energy as mgd, when d is the ocean depth. . To find the speed of impact he should take the height of the wardrobe relative to the sea level, and what he takes is the height of the wardrobe relative to the ocean floor. Therefore, the speed he would extract using the method shown above is not the speed of the wardrobe upon impact. What he gets is the speed of the wardrobe when it reaches depth d under the sea level, and even that is assuming friction with water is just as negligible as friction with air. This gives him a nonsensical result: Randy says that the deeper the ocean is, the more water would flow into the wardrobe- as d grows, so does the root of d. At the limit where the ocean depth approaches infinity, an infinite amount of water would flow into the wardrobe as soon as it hits the water. This is hideously, preposterously wrong. I really cannot stress out just how asinine this error is. No wonder this guy was kicked out of NASA.
Now, a real physicist would've said 'gee, this result is ridiculous, I'd better check out where I've gone wrong.' What Randy said was 'gee, this result is ridiculous, I'd better publish it.'