After how many hours water drunk is expelled from the body?
The time from drinking to urination depends mainly on your hydration status and the presence of food in the stomach.

Scenario: You have drunk enough fluid in the previous days, so you are normally hydrated. In the morning, you get up from the bed, urinate, drink 1 liter of water in 5 minutes and eat nothing.

Some water can come through the stomach and can be absorbed in the small intestine in about 5 minutes; the entire liter may need more than 2 hours (sweatscience.com).

When some water is absorbed into the blood it can immediately trigger diuresis - the excretion of the urine through the kidneys into the bladder. It may take about 3 hours for the entire amount of water drunk to be excreted. So, the approximate time span (from start to end of water excretion) could be 5 - 180 minutes. But not likely the entire liter of water will be excreted, because, in the morning, you are in a slightly negative water balance, so some water will stay in your body.

If you are dehydrated before starting drinking, much less urine will be excreted in the first few hours.

If you drink after eating, the food in the stomach can delay water absorption and excretion by more than an hour. This also happens when you drink nutritional fluids, such as milk or juice.

This is from my experience and understanding basic physiology. I'll try to find some references.