What is the purpose of the one foot capped copper pipes on the utility sink.

If I understand you correctly... these 1 foot capped pipes are "bumpers" or shock absorbers for the utility sink... here, the capped pipes are used to reduce noise or "water hammer" in the system by nature of the air that is captured in the "bumpers" when the system is filled. In theory, you would have to drain the system periodically so the bumpers can refill with air as the air is displaced over time with water and the bumpers loose their effectiveness.

Here, in Massachusetts, bumpers or shock absorbers are illegal now (plumbing code)... it has been suggested that bacteria gather in these bumpers and could potentially lead to an unhealthy water system. Most people leave the old bumpers... just do not install any more on future work... they really don't do much anyway... unless you really have a water hammer issue... then you can install REAL water hammer arrestors to deal with that (sold at local home supply stores... usually threaded).. hope this helps... :)

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