you remember the last post i made in this community about farming on mars in small greenhouses?
yeah, that rings a bell. i just wanted to know how to construct these plastic tubes sothat they would hold 1 bar of pressure inside. so i did some calculations. they are a real mess, don't look at them:
(r/d is the ratio of the tube radius to the wall thickness btw. r/d = 300 is the point where it tears, so having a thicker wall than that should be fine)
i mostly wrote this down as a reminder for myself sothat i can roughly understand what i did later.
anyways, the results are: basically you can make such a tube with 10cm diameter easily out of polyethylene or any other type of polymer with only a wall strength of 1mm. it will hold, it won't burst. i used some insights from ultimate tensile strength, linear elasticity (Young's modulus) etc.
basically what i did is to assume that the force that the wall material exerts to push to the inside is equal to the gradient in spring-energy that would be stored inside the wall material depending on radius. So dW(r)/dr = F is the force with which the wall material pushes inward, where W(r) is the mechanical stress energy stored in a slice of the tube of 1mm thickness.
ask if you want to know something. i'm tired rn and can't tell what i might have missed.
and as a follow-up calculation, i would do the same thing again, but this time not for small tubes to grow algae in, but instead for large human-sized habitats. i.e. a building for humans inside. i would like to know how much building material it would take, what would have to be the wall thickness, etc.
obviously that's gonna be much thicker than 10cm in diameter, more like 10 meters in diameter! and also not made of plastic, but steel, probably. i'll do the math another day though because i need to process all of this first.