Is there enough water to cover the surface of a topographically normalized earth?

Is there enough water in the oceans, ice caps, rivers and streams to cover a completely flattened earth, in proportional to land volume and water volume?

• I assume when you say "a completely flat Earth" you are talking about a sphere or better a geoid in which flat means perpendicular to gravity. Commented Apr 14, 2017 at 2:18
• @aretxabaleta provides an answer below, but I think a key part of the question here is "to what depth," because presumably only a few microns would do. If you ask me if there's enough peanut butter to turn a loaf of bread into sandwiches, I need to know not only the size of the loaf and the amount of peanut butter in the jar, but how thickly you think the peanut butter should cover the bread. Commented Apr 14, 2017 at 16:49
• What do you mean by in proportional to land volume and water volume?
– gerrit
Commented Apr 18, 2017 at 13:55

Here is a very simplistic approximation: The total volume of the oceans (no lakes, rivers, water vapor) is around $1.3\ 10^9$ cubic kilometers. The surface area of Earth is around $5\ 10^8$ square kilometers. Dividing the volume by the area, we get a depth of 2.5 kilometers. The fresh water contribution is about 3% of the volume of salt water.