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Hey yall
I am working on a project for a PVC based water piston that requires me connecting a three-inch PVC end cap onto a 1.5-inch PVC pipe [schedule 40 for both]. This, in turn, would form the piston head and shaft I need. I need to put it into the open end and make a kind of mushroom looking contraption. The contraption itself will be subject to water, so because of that, I can not use a wood mold. I am mainly stuck on the connection aspect between the piston head [the 3 inch PVC end cap] and the shaft [schedule 40 1.5inch PVC pipe]. Do you guys have any ideas on this topic?
Thanks for reading.

Edit: I know about 3 inch to 1.5 inch adapters, but I have a size constraint on the piston head, and making it twice its current size is not an option, considering I am already cutting down the piston head [end cap] a half-inch.

Edit 2: Here is a more clear picture of what I am working with, and what exact attachment I am looking to make.