Creating a waterfall from a roof slope.

[zarch]

I am an architect and I am wanting to create a water feature where the rain water falls directly off of the sloped roof on to the ground 31 feet below. Similar to a waterfall. The problem is that I need to have a hard surface or some type of trench for the water to hit on the ground. This way it can be collected. How can I calculate all of this? I understand that this trench will most likely be large in size due to width of the roof and varying rain amounts. A small rain will fall directly off of the roof where a heavy rain may shoot some distance off of the roof as it falls to the ground.

The roof is a rectangular with no cuts in or out and is 222’ x 74’ giving it a surface area of 16,428 sqft. The roof slopes in only one direction (222’ in length) and the slope of the roof is ½” per 1’. I believe this comes to .041667. The project location is in Dallas, TX where there is a 7” per hour precipitation rate. The roofing material is called a single ply membrane which a rolled on sheet and is not very rough. The roof is 31’ above the ground, the location where the trench will be.

I have looked into the Manning Equation but this seems to only calculate water in a channel at a specific water level. Does anyone have any thoughts?

 

[Bob S]

The roof on this building is a series of open channels, and created rather spectacular waterfalls during heavy rains:

http://history.fnal.gov/meson.html

Bob S

 

[Frostfire]

I am an architect and I am wanting to create a water feature where the rain water falls directly off of the sloped roof on to the ground 31 feet below. Similar to a waterfall. The problem is that I need to have a hard surface or some type of trench for the water to hit on the ground. This way it can be collected. How can I calculate all of this? I understand that this trench will most likely be large in size due to width of the roof and varying rain amounts. A small rain will fall directly off of the roof where a heavy rain may shoot some distance off of the roof as it falls to the ground.

The roof is a rectangular with no cuts in or out and is 222’ x 74’ giving it a surface area of 16,428 sqft. The roof slopes in only one direction (222’ in length) and the slope of the roof is ½” per 1’. I believe this comes to .041667. The project location is in Dallas, TX where there is a 7” per hour precipitation rate. The roofing material is called a single ply membrane which a rolled on sheet and is not very rough. The roof is 31’ above the ground, the location where the trench will be.

I have looked into the Manning Equation but this seems to only calculate water in a channel at a specific water level. Does anyone have any thoughts?

Interesting, I believe you will, as you have probably guessed dealing with a basic parabolic trajectory, My suggestion would be to install some sort of blocker near the end of the roof, to slow the water so it falls straight, or close to, if not it will shoot off quite far, you can look up basic kinematic equations of projectile motion to calculate the distance it launches off. I am unaware of a way to directly calculate the distance via the water quanity, it would be a fluid dynamics question, However I think if you use water density to calculate mass, you can calculate the maiximum distance it would travel from the building with kinematics and use that distance as a parameter

 

[m.e.t.a.]

Despite your detailed data, I suspect that it would be very difficult to attempt to calculate (on paper) the impact zone of the falling water. A computer simulation might be more appropriate here. I'm not knowledgeable in fluid dynamics, but my intuition says that there will be a non-linear relationship between the heaviness of the rainfall and the terminal velocity of the roof-water flow—both as it slides down the roof and as it falls to the ground. There would then be a non-linear, and possibly complex, relationship between the heaviness of the rainfall and the impact zone of the roof-water.

A light rainfall will result in a slow roof-water flow, made even slower by the texture and roughness of the roof material. In heavy rainfall, the roof-water flow will tend to flow more like a river; and the roughness of the roof will do little to slow the flow.

Also, in light rainfall, the stream of water flowing off the roof will be largely composed of droplets. The droplets, having a large surface area to mass ratio, will obviously fall more or less vertically downwards off the roof, and will be easily blown by the wind. Conversely, in heavy rainfall, the river-like torrent of water flowing off the roof will have a low surface area to mass ratio, and will plough easily through the air, carving a more parabolic curve.

I would have no idea how to incorporate these (or other, for I'm sure there are others) fluid phenomena into some grand equation for your roof. For my opinion, I would say that the surest way of marking out your trough zone is to build the roof first and the trench much later (if time allows). This way, you will have plenty of time to observe the roof-water flow in different rain conditions, and then you can simply lay down markers where the roof-water hits the ground. Let Nature be your mathematician ;)

 

[Bob S]

The maximum rainfall on the roof (7" per hour) is about 2.66 cubic feet per second. Using Manning equation from

http://www.lmnoeng.com/manning.htm

with a wetted perimeter of 74' and with a Manning n=0.010 (smooth roofing or concrete) from

http://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Mannings_n_Tables.htm

A = 1.3 square feet, and the horizontal velocity falling off the roof is about 2.06 feet per second. Since the time for the water to fall to the ground from 31' is about 1.39 seconds, the waterfall will hit the ground about 2.86 feet offset from a vertical drop. For 3.5" per hour rainfall, the horizontal velocity is about 1.55 feet per second, and the horizontal offset at the ground is about 2.2 feet.

Bob S

 

[zarch]

Thank you all for your responses.

I knew that this would be a difficult question to answer and that many factors would need to be considered. After reading all of the posts, I have begun to calculate some of the equations referenced and also consider other possibilities to better control the water flow.