Hmm... I personally haven't been sliced across the belly recently, and I'd like to keep it that way. ;D However, I've had my fair share of injuries, which I'll address in a moment.
Personal opinion but I consider a wound that is 2+ inches deep in the skin, an emergency but if it's an inch, there's no reason to treat the injury as such. A stab that's an inch, I wouldn't call it an emergency but a red flag nonetheless. However, a slice, where the blade cuts in only half an inch is nothing, and therefore I can't see anyone passing out from sheer pain. Maybe surprise, since people have phobias of blood, but I certainly don't see an actual person collapsing from intense pain.
Moreover, my first impression of the scene that was described above still seems unrealistic just for that reason; I don't see a person falling unconscious from a slice that's only a half inch deep. Even if it was an inch, I still can't grasp someone responding, like your character. I just don't think the pain would be that intense. People who fall unconscious from severe pain results from life threatening injuries where the pain in gut-wrenching.
Now, about my injuries and why I'm using myself as an example - again, lol. My shins carry many scars. I'm not sure why but injuries follow me like the plague. On my right shin, I have about a half inch scar that's roughly ten years old. How I acquired it was that I was standing on a beaver dam, fishing. I slipped, and fell but a sharp twig (like an arrow) pierced my shin. I'm not entirely sure because it's been a long time, but the stick went about half an inch inside. I remember yelling and cursing, but I stood immediately up and continued to fish. I was down for less than three minutes. It wasn't until about ten minutes later that every mosquito within a radius of five feet engulfed my shin. When I looked down, only then I felt the pain, seeing blood ooze, staining my the edges of my socks and mosquitoes swarm on my skin. At that point, I felt an annoying stabbing sensation but I was more pissed that I had to leave and bandage it, lol.
So, my example with my shin goes back to what I mentioned earlier; everyone has different tolerances with physical pain and for me, it took ten minutes for me to feel anything remotely considered to pain. I probably wouldn't have felt a thing if the mosquitoes didn't attack me. Also, my injury would be considered as a stab wound, since the twig jabbed down, but it was only half and inch.
As for a slice, I collect knives myself. Fortunately in the twelve year span of owning knives, I've only sliced myself seven times. I don't recall ever slicing myself half an inch but I have a couple of nicks on my fingers. The pain was minimal though. Just think of a paper cut, but one with salt or lemon juice mixed in the slice. Not a reason for me to fall unconscious from severe pain but it felt like a stinging sensation; an annoying one if I may say so.
The reason I asked was if a blade is dull (whether you're aware or not) the chances of it slicing half an inch into the stomach is slim to none. At least it wouldn't be a clean slice but rather messy.
Recently, I had to sharpen one of my pocket knives because the blade was so dull, it couldn't cut through twelve lbs. fishing line. That's pathetic! A dull knife would have a difficult time inflicting any type of real damage, unless the attacker grinds good and long enough. Yuck.
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Overall, if the aim is to have a dramatic scene where the character is barely surviving due to an immense blood loss, maybe reevaluate the injury? A stab wound be more life threatening especially if were three inches inwards because the blade could potentially tear through tissue and connect into vital organs. A slice though, if that's the desired direction, to make the scene more jerky, if the blade went an inch and a half in then there might more of a cause for emergency. Slices, depending how deep and the sharpness of the blade, can possibly bleed for a while.
I'll use myself again as an example, lol. I once was tagged by an eight inch Green Moray Eel. Its teeth felt like thin razors slicing through the tips of my index finger; very painful!! I remember yelping for sure. The outcome was I had to keep changing the dressing (similar how I explained above) every ten minutes. There were three tiny, vertical slices, no longer than a quarter of an inch but the wound didn't cease on the bleeding for a good half hour! The pain didn't officially leave me for about three hours.
So, the size of a slice doesn't automatically mean the wound will be painful either. Remember my shin injury? That was a stab wound but I barely felt anything. The eel bite left tiny, tiny slices but oh, God, was it painful!
I believe I've covered enough.
I supplied enough information where I hope I don't give you a headache, Joe. Best of luck with your story!