How constant do you think it is over what time period. It is commonly believed that before the flood the earth's atmosphere was thick with water. The whole earth was more like a giant terrarium which is why tropical vegetation existed way up north, like Siberia.
The science is squirrelly. Don't make a science argument here. A miracle would be an appropriate answer. Think of how high up mountains are. To flood everything in sitting water, think about 30,000 feet above sea level filled with water around the globe. It didn't happen with science. I am not insulting you as to say God couldn't have done it as a miracle, and then dissapeared the water, but the volume of water just doesn't exist, even in a humid atmosphere. There is only so much water air can hold. Not 30,000 feet high across the entire surface of the planet.