# I need some formula for raining time --> flood height

I want to make a story in our world, where there is a sudden rain everywhere, and this rain is pretty average but it's permanent. (This is not a raining cycle, because the origin of the rain is surnatural. The amount of water is actually added, everywhere, not transfered.) What I'd like to know is how much time is needed for the rain to actually fill the sewers and become a flood ? Especially in a university (main place of story). There's a lot of concrete and roads in there, not so much grass fields.

Then, more importantly, how much would the flood height increase in 24H of raining ? Is there a formula about this? That would be perfect.

The amount of rain falling on a certain area is usually expressed in mm, or if you are referring to the rain rate, mm/hour.

Multiplying that value for the surface on which the rain is pouring, you get the volume of water falling as rain.

For example 10 mm of rain falling in 1 hour over a surface of 1 square meter would amount to 1 liter of water per hour, since $$0.01 dm \times 100 dm^2 = 1 dm^3 = 1 liter$$

Sewers have a certain maximum flow that they can carry before bursting, and any clogging will lower that number.

In principle the amount of water deposition rate on a certain area can be approximated with $$WDR = Rate_{rain} - Rate_{Outflow}$$.

If WDR is negative you don't have water accumulation, because more water is going out than is coming in, the contrary when WDR is positive.

Knowing the rate you can get how long will it take for the water to reach a certain height. Keep in mind that any obstruction will affect the outflow rate.

• Also worth noting that porous substances like grass/soil have low outflow rates but can act asa buffer and soak up (very) large volumes of water, depending on the exact composition. – Joe Bloggs Sep 16 at 13:05