Rebuilding Science in a Magic World

It's been another month, and the quarry and houses are coming along well enough.  I've gotten about half the stone out of the quarry that I intend to remove.  It's become quite sizeable now, and the goblins actually have to travel up and down stairs in the quarry to remove stone that I've cut.  I'm actually a little concerned about the surplus of stone now.  Realistically, we've already excavated more stone that I'll need to build all the houses, workshops, roads, and walls for the goblin village.  It also seems like I'm not going to finish the quarry before the snow melts at this rate.

If my math is right, then the reservoir will hold about five days of regular water flow, which frankly is very little.  Some very rudimentary tests for the stream flow over the last few months have given me an average flow rate of about 3/4 of a cubic foot per second.  I honestly thought it would be higher, but the slope here is so low that the velocity of the stream is quite slow.  I recall during the spring rains from before, that the stream was running at a greater depth and velocity, so my estimates for an average are probably quite low.  The levee itself has a cross section of 16 square feet, compared to the ten it used to be. Even if flow rate stayed the same, it could handle fifteen times the flow, but the velocity should speed up during a flood, which would drastically increase capacity.

The quarry is being chiseled out of the hillside directly, deepening a small natural valley in the hillside.  If it didn't have a natural valley here, the reservoir capacity would be significantly smaller than it will be.  Soon I'll start using stone from the quarry to build the dam for the reservoir as well, which will be a good use for the remaining stone.

I wish I had the ability to stress test the stone to actually do the math on the reservoir dam, to make sure it'll hold up to the pressures it's going to be under, but instead, I'm just going to have to be sure that it's extra strong to handle the pressure of the water.  It'll end up looking like a mix between a buttress and gravity dam most likely. I'll of course attach it entirely to the stone bedrock through the area as well, which should increase its strength drastically.

I recall the romans were able to make relatively watertight plug valves from stone, and they made them by hand, so I hope that I can make them with the help of magic.  I'll probably want to use lightstone for them though, rather than any run of the mill stone from the area.  The top of the dam will have a regular spillway to prevent topping of the dam.  Then at various heights down the dam, I want to make walkways to valve handles so that the water in the dam can be lowered to any height by opening these valves.  I'll have to size the valves accordingly so that the goblins don't accidentally flood their own village as well.

The equation for the volumetric flow of liquid draining through an outlet is approximately Volumetric flow = Area*(2*gravitational acceleration*height)^1/2.  Which actually means I actually should determine what the acceleration of gravity is here.  Which is a bit of a diversion, but a necessary one.

As long as I define my length of feet using a single ruler for sizing both the valves and the acceleration of gravity, the math will balance out.  I think the saying goes, it'll be precise, but not accurate.  I start by using a foot ruler that I made before, to use as the baseline.  Thankfully, I have an area that I already leveled with a water level before, namely the pavilion floor.  I use stone shaping on some stone from the stockpile to make a brick that is six inches tall.  Then I make a seven foot long slightly curved ramp, and set everything up on the pavilion floor such that the top of the ramp is at six inches after modifying the brick somewhat to rest the ramp on.

By rolling a ball down the ramp, I can calculate the acceleration down the ramp, and by applying the ratio of the ramp's slope to that acceleration, get an approximation for gravity.  Of course, at this point, my mana is already starting to recharge, so I'll just run trials when I get the chance, and average them out to get a close approximation for gravitational acceleration.

Well, after a few days of running trials in my free time, I think I've got a number that should be good enough to use.  Approximately 29.2 feet per second per second.  Slightly less than Earth had.  I changed the ramp heights at times, and adjusted its length a few times, so I'm fairly confident in my number.  Now by applying the depth of the reservoir at various heights, I can calculate how big the valves' cross sectional areas should be.  I've also realized that the risk of the goblins flooding their village will have to be communicated with them, because there is no way to make one valve size fit all for various heights in the dam.  They'll just have to progressively open the next valve in the line to prevent the valves from eroding due to high velocities if they open a valve too deep.  

If I put the valves every five feet of depth, then the cross section would need to be about a half a square foot, or a circle with diameter of 0.8.  Which would give a flow rate of between 8.5 cubic feet per second and 3.8 feet per second depending on how deep the water above each valve is.  Which I think is completely doable, they might need some gears to turn them though.  The deeper the valve is, the thicker the valve needs to be as well, which will make it heavier.  Yeah, those bottom valves are definitely going to need gears to open.

Well, all of that will be something to deal with when I actually start building the dam.  Which is a little ways away yet, since I've still got houses to build, along with roads and a workshop for Kaga.  Thinking about it that way, I would really prefer to spend my time up at my mountain cave once I can, so the dam and reservoir might have to wait until next year.  I'm pretty sure the snow will probably start melting soon, as it has started to feel a little warmer in the afternoons.  So I think I'll focus my efforts on finishing construction in the village, and put the reservoir on halt.

Fifteen days have passed since I started focusing on just building the goblin village, and it's clear that the snow has started to melt on the mountain.  The stream is now both deeper and faster flowing now.  It's only running at about a foot deep compared to the three foot levee walls, and flowing at 6 cubic feet per second, with a velocity of nearly double what it used to be.  The effect of this has been less than ideal.  The dirt I had piled along the levee edges has started to slowly wash away.  The previous soil had plants helping hold it in place, and was packed down.  When I refilled the dirt by hand when I built the stone walls to form the levee, I didn't factor this in.

Which means if I get the opportunity, I need to do something about it.  That something will likely be coating the dirt in a small layer of stone to waterproof it.  It's not ideal, because it'll mean that there won't be plant life along the stream any longer, but it does mean that the stream will be more manageable.

Stone lining the levee has taken a lot longer than I thought it would.  I've only fixed it through the length of the village, and halted all other construction to handle it.  Tomorrow Zaka is going to go summon new imps.  I'm going to go along again, but only to clean up and then come back to finish the pressing construction here.  I haven't really checked to see how viable food is up on the mountain this time of year either, so giving it an extra month might be a good idea anyway.

We returned two days later with three more goblins.  It seems like the buildings at the cave entrance held up fine to the snow as well, which is good.  I'll need to work extra hard for this next month to get the houses, roads, wall, kaga's workshop, and the remainder of the levee finished.

Well, another month has passed, and we're supposed to go back up the mountain to summon goblins tomorrow.  I haven't quite finished everything I wanted to finish, but I think it's in a good enough state that I can leave the remaining work for next winter.  There is a little bit of everything that needs finished actually, except for the levee.  The walls aren't quite at their full height yet, and I haven't put closable gates in yet.  I've also only completed thirty-two of the forty houses, and I've only made basic tools for kaga to work with in his workshop.  The roads also don't reach to the openings in the walls yet.  I was maybe going to stay for an extra month to work on things, but two days ago I ticked over to level 99, so I'd like to be back up on the mountain when I max my level out.  

<UNCOMMON LESSER EARTH DEMON>
Level: 99
HP: 2149/2149
MP: 902/902
Traits: Mana Affinity, Earth Manipulation
Magic: Improved Stone Shaping, Tectonic Sense, Earth Spike