what happens when you take water from a 3/4 inch pipe copper to 1/2 inch flexible braided hose through a filter for a 3/4 pipe back through a flexible braided hose 1/2 inch tube to 3/4 inch copper pipe?
Can you say more about your question? You are experiencing more water pressure drop than you expect in your system? Can you upload a sketch (use the "Attach Files" link below the edit window), and give us a rough idea of the pressure in each segment that you are seeing? Is there a vertical drop/climb associated with the system? What are the specs on the filter?
It depends on the rate of flow. Consider the extreme case in which we cap the far end of the last pipe so no water flows: the pressure will be the same everywhere if the piping is all horizontal (if not, the pressure will be higher at the low points).
If the flow is non-zero there will be a pressure drop across the filter and at each of the constrictions; these drops will increase as the flow rate increases.
If you need a quantitative answer (how much pressure drop at a given flow rate) you will have to spend some time with a engineering handbook and the filter specs.
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