While the drawings of plumbing details are interesting, I think the first order of importance is to look at energy levels.
Plants of all sorts need certain things to grow. If you want more plants you need more of all the things they need. It does not matter if they live under water or above, or if you are harvesting them to eat or for sale. If your system gives them all they need they will grow. If your system lacks something, then the plants will not grow.
In designing a system like this, lets break it down to its most basic components. Draw a circle. This is the water flow. Put 3 tubs in the circle.
1) Grow plants to eat.
2) Grow fish and plants
3) Pump/filter/equipment etc.
Now put some arrows going into and out of each tub.
Tub 1) Input needs to be fertilizers and light (CO2 from the air).
Output is plants to eat. Every plant you remove from the system removes a certain amount of nitrogen, phosphorus, potassium and so on.
Tub 2) Input needs to be fish food and oxygen for the fish, and fertilizer for the plants (could be fish food), perhaps CO2 for the plants, light for the plants.
Output needs to be anything that is toxic to the fish (nitrogen, primarily), and organic waste that create conditions that can lead to diseased fish. Output might also be fish (to eat or sell), which means a loss of the materials that make up fish- Nitrogen etc.
Tub 3) Is a place to balance it all. I am including your sumps, pumps, and all other equipment in this 'tub'. The waste from the aquariums is collected, the water flow is modified for optimum oxygen for the fish, heater or chiller would be linked in and so on.
Looking at the first 2 tubs in the system, you want to balance the fish (or other animals) with the plants (both aquatic and above water). The fish act only to decompose fish food, and turn it into fertilizer in the simplest view. If you have enough fish then you will be adding enough fish food to supply most of the plant needs for N, P, K etc. Perhaps not all, but corrections are small. If you do not have enough fish then you can grow fewer plants or add more fertilizers right before the vegetable part of the cycle.
If you just follow nitrogen as representative of all the nutrients through the cycle you can figure out if you have enough, need to add more, or need faster removal.
You add nitrogen in the form of fish food protein. Fish and microorganisms digest the food and send it on its way to the plants. Some plants are in the fish tanks and remove some of the nitrogen right there. The remaining nitrogen goes on to the vegetable beds and is used by the plants growing there. Some nitrogen is in the form of solids that you are collecting. (Are you reusing these? or is this a loss to the system?). When you harvest the crops you are removing nitrogen from the system. If you eat the fish or are raising ornamental fish for sale you are removing their nitrogen etc from the system.
So, the big question is: Are you adding enough nitrogen (and all other nutrients) to support the removal in the form of vegetables
ornamental plants (perhaps you are giving away or selling the trimmings to other aquarium keepers?)
fish to eat
ornamental fish to give away or sell
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OK, so back to your drawing:
1) If you are going to this much work, drill the tanks. Do not depend on the PVC overflow.
2) Do not need 4 sumps with 'hamster tubes'. One sump collects all the water from all the tanks. This sump IS the swirl chamber. Water is removed from the upper (clean) area for sending on to the vegetables. You could use a manifold here to direct different amounts to each bed depending on what each needs to grow, if this is needed. There are different styles of beds for growing things and they may need different water flows.
The fish tanks will be high enough up that the swirl/sump can be gravity fed via an overflow through a bulkhead. (There are ways to set this up so the debris from the bottom of the fish tank is removed) The swirl aspect is accessible to clean the accumulated debris, perhaps a pipe and ball valve that leads off to the side. You can attach a hose and fill a bucket with the solids. This swirl-sump can be on a low platform, just a few inches, to accommodate some plumbing.
Remember that there is a lot of water weight in all of this, so build strong tables to support things, or else use the floor or ground and pump the water from place to place. Ultimately you will need to pump the water uphill at least once, even if everything else is downhill, gravity feed. You then need strong structures to support the weight of the water in the higher and middle containers. If you break this into sections, keep each part at the same level, and put a pump between each section each pump will be smaller.
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rininger, you will need to heat the system, or else only run it in mild to warm weather. I am having a really hard time trying to get just solar heat to work in my greenhouse here in 'sunny' California.