They close the Narrows for 24 hours when the flow rate is above 150 cubic feet per second (CFS). You can look up the real-time Narrows CFS at https://waterdata.usgs.gov/ut/nwis/uv/?site_no=09405500&PARAmeter_cd=00065,00060,00010,00095,72020. Regardless, before tackling the Narrows you should check-in at the visitor center. The best time to hike the Narrows is in June.
Best bet is to call the visitor center. They'll have the most up to date info
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