What you were describing with 3" bottom drain gravity feeding though 3 tanks is essentially what I have.
Except the first tanks is a 110 gal conical vortex tank and I have 3500 gph pump in the last tank.
There will always be a certain amount of drop down from one tank to the next, and any mechanical filtration that restricts flow will cause more severe drop down to the point of causing the water to drop down enough in the final tank that the pump starts sucking air. Of course once it does that it becomes airlocked and stops pumping water at it's usual rate and the water level will rise in the barrel and very likely the pump will prime itself again (depending on the pump and it's exact location). Of course until the restriction is cleared the water will drop again and the cycle will continue to repeat itself. Although this is not ideal and can be hard on the pump it is unlikely the pump will burn out right away.
I have an overflow off the pond itself, During normal operating conditions there is no way for the tanks to overflow, however. I did install an overflow on my large conical tank. The reason being that in the winter I change my plumbing around and close off the two 55 gal blue tanks and only have the water flowing through the bottom drain into the large conical vortex tank and directly back into the pond via the 1" skimmer line. This keeps some ongoing circulation in the pond and allows oxygen into the pond water via the vortex tank which never freezes. But the pond does completely freeze over, and snow accumulates on the the pond ice which weighs down the ice and effectively raises the pond water level, but because the pond overflow is frozen over the water level can increase in the vortex tank and it can overflow on the sides, so I installed a small overflow pipe to allow the excess water to drain down into the open ground below the tank instead of spilling over the sides of the tank and onto the floor of my pump room.
The overflow line
BTW having a gravity fed system through several tanks like that is far superior and safer to having the pump fed direct by the bottom drain.
Except the first tanks is a 110 gal conical vortex tank and I have 3500 gph pump in the last tank.
There will always be a certain amount of drop down from one tank to the next, and any mechanical filtration that restricts flow will cause more severe drop down to the point of causing the water to drop down enough in the final tank that the pump starts sucking air. Of course once it does that it becomes airlocked and stops pumping water at it's usual rate and the water level will rise in the barrel and very likely the pump will prime itself again (depending on the pump and it's exact location). Of course until the restriction is cleared the water will drop again and the cycle will continue to repeat itself. Although this is not ideal and can be hard on the pump it is unlikely the pump will burn out right away.
I have an overflow off the pond itself, During normal operating conditions there is no way for the tanks to overflow, however. I did install an overflow on my large conical tank. The reason being that in the winter I change my plumbing around and close off the two 55 gal blue tanks and only have the water flowing through the bottom drain into the large conical vortex tank and directly back into the pond via the 1" skimmer line. This keeps some ongoing circulation in the pond and allows oxygen into the pond water via the vortex tank which never freezes. But the pond does completely freeze over, and snow accumulates on the the pond ice which weighs down the ice and effectively raises the pond water level, but because the pond overflow is frozen over the water level can increase in the vortex tank and it can overflow on the sides, so I installed a small overflow pipe to allow the excess water to drain down into the open ground below the tank instead of spilling over the sides of the tank and onto the floor of my pump room.
The overflow line
BTW having a gravity fed system through several tanks like that is far superior and safer to having the pump fed direct by the bottom drain.
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