Flood drainage outflow rate from horizontal 1500m drainpipe at sump

[morrobay]

TL;DR Summary

If a flood drainage 2m diameter ,1500m long pipe with no fall/gradient is 1. is above sump water level. 2. Is below sump water level what kind of drainage from sump to outflow will there be ?

This 1500 m long , 2m diameter , 1m below flooded road surface from point at right side to sump at left side is horizontal.
My understanding for sufficient drainage is a minimum fall, 1:100 required. Then with a gradient of .01 a pipe of this length should have a 15m fall. There is grating above concrete gutter, above junctions ( about 2m wide gap) in plastic drainpipes where flood water enters system. The question is about what kind of flow rate would be present where the pipe enters the sump that is continuous with the outfall that is at base level of sump ( with not much fall ) Two situations: 1 sump water level below end of horizontal drainpipe. 2 sump water level above end of pipe ?

 

[jrmichler]

If I understand correctly, a simplified side view of your system is as follows:

Water flows into a sump, and from there to open water (lake, ocean, or river) through an outfall pipe. If so, some statements can be made:

1) The difference in water level between the water in the sump and the open water is the total head.
2) If the outfall pipe is completely under water, the slope does not matter. Only the total head matters.
3) The resistance to flow is calculated from the length, diameter, and wall roughness of the outfall pipe.
4) If the sump water level is below the top of the outfall pipe, you have open channel flow. Rivers are open channel flow.
5) If the outfall pipe is in open channel flow, the slope of the pipe does not matter. Only the total head matters.
6) The resistance to flow is calculated from the length, diameter, water level, and wall roughness of the outfall pipe. This calculation is more complex than the case of the pipe running full.

As a side note, the Mississippi River in the US has no trouble flowing south to the Gulf of Mexico. It has an average gradient of less than 20 cm per kilometer.

 

[morrobay]

Thanks for the information @jrmichler about the flow from sump to bay outflow. My original question was on the drainage from the 1500 horizontal drainpipe and what kind of flow would be at the sump. In the top diagram the 1500m drain pipe with no gradient and flood water entering at street level(dotted line) is below water level in sump. In the lower diagram the drainpipe is above sump water level. So what if any difference would there be in the two cases. * Since these cases are both free flowing with no pump station i am surprised that the water in the 1500m drain pipe would flow to the sump , especially in the lower case, but i guess the outflow water level an the bay is also a factor. This side view is more clear! Also the rectangle at sump deck is the outflow channel.

 

[256bits]

Since these cases are both free flowing...

Wouldn't the flow in the drainage be either flooded flow, or open channel flow, the same as for the outflow pipe?
For case 2, there could be both types of flow within the drainage depending upon distance from the sump, and the amount of water accumulating on the street and passing into the drainage.

 

[morrobay]

Wouldn't the flow in the drainage be either flooded flow, or open channel flow, the same as for the outflow pipe?
For case 2, there could be both types of flow within the drainage depending upon distance from the sump, and the amount of water accumulating on the street and passing into the drainage.

This 1500m, 2m diameter pipe is horizontal with no gravity fall. Then is it only the difference in the 1500m pipe elevation and the sump water level that is the force causing the flow from right to left in diagrams as well as the outflow into bay?

 

[256bits]

This 1500m, 2m diameter pipe is horizontal with no gravity fall. Then is it only the difference in the 1500m pipe elevation and the sump water level that is the force causing the flow from right to left in diagrams as well as the outflow into bay?

With channel flow, the usual method of determining the flow is with to assume the top surface follows the same gradient as the bottom surface, over the majority of its length until near the exit.

In this horizontal pipe, with no gradient, that will not be the case, thus, so while the bottom surface of the pipe is horizontal, the top surface of the water open to atmosphere will still have a slight gradient. That would be the driving "force" moving the water along. Needless to say, the flow would not be very fast.

You could of course assume a very mild gradient, S, over the length of the pipe, assume the open surface follows this bottom pipe surface so that the water depth does not change along the length of the channel, and then use your equations for channel flow.

As I mentioned, depending upon the amount of water accumulation on the street, a part of the pipe could be flooded.and part channel flow. In addition, for the channel section of the pipe, the wetted surface will vary with the filling being greater than half full, or less than half full. Hence, the width of the channel becomes a variable to take into account as the pipe in circular rather than having a continuous sloping banks such as that for a river or constant banks such as for a rectangular channel.

For the horizontal pipe, channel flow, you most likely would have to do some sort of iterative calculation since there is not a given S slope of the bottom surface. Yet the top surface should have some sort of slope to drive the flow. Tat top surface is what you would need to calculate to detemine the flow rate Q in the pipe.

For your horizontal pipe, the task becomes more difficult, as there is water entering all along the pipe from the drainage areas, making the Q, not constant but changing along the pipe length.

Are you a civil engineering student, or just interested in the flow of this particular pipe?
If a student, has this not been brought up in your studies?

 

[morrobay]

Just a resident in seaside resort in Thailand where this drain project was just completed. Thanks for information. The engineer in post #2 referred to the total head as the driving force for flow from sump to outfall. From your reply then the total head between the level of horizontal pipe and sump is not applicable as driving force ? And it is only atmospheric pressure causing flow in this horizontal pipe. Yes that would be a very slow flow rate then. I should add that there have been major failed drain projects here, and this one looks questionable.

 

[jrmichler]

It's not quite as bad as it first appears. When the horizontal pipe is running full, the total head starts at just below the street surface, and extends to either the bottom of the pipe or the water surface in the sump.

A less obvious problem is that, when the horizontal pipe is not running full, there will be low velocity in it as mentioned in Post #6. That will be the case in most rain events. With low velocity, dirt and sand in the runoff water settles to the bottom of the pipe. If the horizontal pipe is not cleaned at regular intervals, it will eventually get plugged.

 

[256bits]

Just a resident in seaside resort in Thailand where this drain project was just completed. Thanks for information. The engineer in post #2 referred to the total head as the driving force for flow from sump to outfall. From your reply then the total head between the level of horizontal pipe and sump is not applicable as driving force ? And it is only atmospheric pressure causing flow in this horizontal pipe. Yes that would be a very slow flow rate then. I should add that there have been major failed drain projects here, and this one looks questionable.

I think you mis-read or misinterpret.
For one, Post #2 is correct.

For two, one has to be correct in what head one is talking about.
The sump head ( difference of the water level in between the sump and the lake ) provides the pressure for the outflow.
The head in the horizontal pipe -
- if that exits above the sump water level, then the two heads ( sump head and horizontal pipe head ) do not contribute to one another - the water from the horizontal pipe is exiting to atmospheric pressure. We just have the situation as above paragraph.
- if that exits below the sump water level, then an extra "back pressure" hinders the flow in the horizontal pipe, which will most likely be flooded along its entire length. That would be a normal situation if there is a great accumulation of water from the street. For a 2 meter diameter pipe, that is a lot of rainfall.
Whatever the situation, as I do not know if the outflow from the sump can keep up with, or is greater than, the inflow from the horizontal pipe. The sump could have a varying level dependent upon precipitation.

And it is only atmospheric pressure causing flow in this horizontal pipe

No. It is gravity.

I should add that there have been major failed drain projects here, and this one looks questionable.

Don't know the terrain, nor the level of precipitation for the area, so I really cannot comment fully on that, except that what has been done is a solution, even if it might or might not be a 100% effective at all times.
Just because they tried to do something does not make it a complete failure, if it reduces the frequency of flooding from that beforehand. Isn't that a plus?
I suspect it is a fairly level area, which are usually difficult at the best of times.

Especially, for central North America, where with expansive flat areas, with spring runoff, or heavy rains, the surrounding areas can be flooded for miles and miles around, several feet deep. There really is at times no simple engineering solution that is cost effective.
We sometimes have to live with what we got, which is living on local flood plains, or deltas.
The topography of the Earth is given to us, and we adapt the best we can, or re-settle someplace else.