The prior version of the duck pond filter did not quite function well, primarily because the pipe I was using was too small and did not provide enough flow rate.
The pipe provided enough flow rate when I made a hydroponic garden last year, but that connection was set as a parallel connection rather than a serial connection.
According to this website https://www.wpsexpert.com/calculators/how-much-water-can-flow-through-a-pipe-by-size-and-gpm-or-gph/ the 1/2" pipe will provide 420 gallons per hour, and because I set it up as 3 outlets, I had 420x3 = 1260 GPH effective flow.
However when connecting as a serial connection, the flow rate is 420 period and because the water pump had a much higher output, water overflow the filter bucket.
Flow Rate
The website listed different flow rates, the chart above shows relationships between the flow rate and the size of the pipe. It looks non-linear, and I noticed that there is a big increase in flow rate as the pipe gets wider.
This relationship makes sense because the flow rate should be proportional to the area of cross section of the pipe. When I calculate the area, by taking the square of the diameter of the pipe, then the relationships become linear (row panel).
Equipped with this knowledge, I decided to obtain a PVC pipe of 2" in diameter, which is rated to provide 3,300 GPH of flow, which should be more than enough flow rate considering some loss in efficiency from clogging. The water pump from VIVOSUN is rated to lift 850GPH of water, it will be less given water need to be lifted around 1 to 1.5 meters off the pond. Either way, a 2" pipe should provide a sufficient flow rate.
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It makes me smile, when I see it.