The video, shot and posted Monday, shows an older gentleman spraying the woman who was sitting on the sidewalk in front of him, seemingly minding her business. Unclear if the woman was homeless, but you can see right off the bat, he's going to town with the water -- letting it run on her for several seconds.

You can also hear the woman screaming in protest, apparently asking him to stop. Eventually, he does, and tells her to move down the block.

Never mind the fact it's been rainy and cold in SF these past few days ... this act looks cruel and unnecessary, and as you can imagine -- it's gotten a lot of pissed off people online calling for accountability, as well as the identity of the sprayer.

Some thought he was associated with the bar behind him, but the business is distancing itself ... reps say they don't know the dude, or condone his behavior.

Now, we're told cops did respond, but no one was cited or arrested.

SFPD tells TMZ they responded to this incident -- described to them as a possible assault -- but say when they arrived, neither the man or the woman sought any further police action. So, unfortunately for those who wanted this guy in cuffs ... absolutely nothing came of it.