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I have a proposed stormwater design which will necessitate some very large diameter pipe installed near the surface to minimize constructability issues. However, near the end of the run, it will be necessary to install a structure to allow the stormwater to drop its elevation more than 7', which I'm concerned will risk erosive forces scouring out the bottom due to the fall. Based on the standard equation of standard equation of v=a*t, the vertical velocity is in the range of 21.4 feet/second upon impact with the bottom of the structure.

Generally, I'd like velocities for pipe flows to be less than 15 feet/second to prevent scouring and 10 preferable (though not always feasible). This scenario where water is falling is a little different, but given the quantities being on the order of approximately 170 CFS for the 25-year design storm, I don't want to neglect the kind of erosive potential this could have on the structure's bottom.

To mitigate this issue, I'd like to propose a sump at the bottom of the structure to help dissipate some of the energy. However, I can't figure out how deep to spec this sump area.

I've reviewed my state's Soil Erosion Control Manual, but it doesn't really specify measures for this kind of circumstance. Is there an alternative equation or source I can use to size the sump area for something like this?

Sketch for clarification:

enter image description here

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  • $\begingroup$ If someone could create tags for 'scour' and 'erosion', I think they'd also be suitable for this question. $\endgroup$ Sep 20 at 20:32
  • $\begingroup$ Have you proposed this to the senior engineer? What was the response? $\endgroup$
    – Solar Mike
    Sep 20 at 20:41
  • $\begingroup$ can you sketch a profile? Why not simply have a vertical drop into the sump? $\endgroup$
    – mart
    Sep 20 at 20:53
  • $\begingroup$ @SolarMike I have, but the unique situation of having it be within a storm structure is creating a unique situation that my colleagues haven't been able to come up with a comparable situation that they've dealt with. $\endgroup$ Sep 20 at 21:13
  • $\begingroup$ @mart I made some edits to clarify my intent and added a sketch to better illustrate. $\endgroup$ Sep 20 at 21:25
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I suspect the sump will fill up and be ineffective when the water levels with the flow.

Usually, they use an open channel shoot with a stepped ending to break the flow of the stream of water and by creating turbulence and hydraulic jumps dissipate the energy of the flow passively while turning most of the energy into foaming flow.

The profile is designed to accommodate the variable volume of the flow.

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Wiki source.

stepped spillway

Edit

Reviewing the comments of OP, one can offer this alternative view.

If we need to change the velocity of the flow we can use the flow continuity. First, we check the speed of the flow exiting the pipe using Manning's equation for gravity fall in a sloped pipe,

$$v = (kn / n) R_h^{2/3} S^{1/2} $$

  • v = cross-sectional mean velocity (ft/s, m/s)

  • kn = 1.486 for English units and kn = 1.0 for SI units

  • n = Manning coefficient of roughness - ranging from 0.01 (a clean and smooth channel) to 0.06 (a channel with stones and debris, 1/3 of vegetation)

-Rh = hydraulic radius (ft, m)

-S = slope - or gradient - of pipe (ft/ft, m/m)

Hydraulic radius can be expressed as

  • $R_h = A / P_w $

where

  • $A =$ cross sectional area of flow (ft2, m)

  • $P_w =$ wetted perimeter (ft, m)

Then we add the extra speed due to free fall

  • $v_{fall}=\sqrt{2gh}$

Now we can plug in the mass continuity eq.

$$\dot m_{inlet}=\dot m_{outlet} \rightarrow A_1v_1= A_2v_2$$

$$A_2=A_1(v_1/v_2)$$

So in order to get less outlet speed, we need to make it wider. And there is no need for a sump reservoir, the fact that the downstream channel is wider will cause a hydraulic jump at the bottom of the fall and take the needed energy out of the flow to make it go slower.

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    $\begingroup$ Why would the sump filling up render it ineffective? I need it to be full most of the time in order to dissipate the energy of the falling water so that it doesn't erode the bottom of the structure. $\endgroup$ Sep 20 at 22:29
  • $\begingroup$ If you have mix of solids, like sand and dirt washed down they are going to require regular cleaning. depending on the climate they may get clogged and damaged under icing and freezing. the sump is not a fault proof system whil a stepped open channel or even rocky apron is. $\endgroup$
    – kamran
    Sep 21 at 0:06
  • $\begingroup$ Annual cleaning of inlets is required for stormwater structures in this system. Additionally, even if the sump were to fill with sediment then the erosion wouldn't be happening to the bottom of the inlet, it would be happening to the sedimentation which is acceptable in this instance. $\endgroup$ Sep 21 at 3:12
  • $\begingroup$ Also, this answer is indicative of a solution that's applicable for an actual open channel. As I indicated in the question, this is proposed within a stormwater structure experiencing a vertical drop. It's open channel flow in the sense that the flow is not pressurized. $\endgroup$ Sep 21 at 3:17
  • $\begingroup$ The horizontal velocity I've calculated is already based upon the Manning's equation, which is based upon the design storm which will occur infrequently at best (worst?). But that's not the issue I'm having. The issue I'm having is the velocity of falling water, which I determined based upon the original physics equations v=gt and d=1/2*at^2. The force of this falling water will occur with a great deal of regularity more than the design storm. $\endgroup$ Sep 21 at 13:29
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To prevent/minimize erosion by thrust is to line the bottom of the plunging pool with rocks. The linked article provides some useful information.

enter image description here https://www.usbr.gov/ssle/damsafety/risk/BestPractices/Presentations/D1-ErosionOfRockAndSoilPP.pdf

This article may also help. https://www.nap.edu/read/17612/chapter/4#15

enter image description here enter image description here

It might be helpful to modify the configuration at the plunge pool - downstream channel to create a small jump to exhaust some energy from the rapid flow caused by the thrust.

enter image description here

ADD:

Below are two materials that will help you to determine the plunge pool depth. Both are based on the USDA method.

Also, if you want to calculate the thrust force due to the water jet, it simply equals the mass flow rate times exit velocity.

Excel WorkSheet - Browse through the file index and select the "Riprap Lined PLunged Pool for Cantilever Outlet (DN-6).

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  • $\begingroup$ I think I had found the DN-6 document you added, but it was heavily dependent upon a d50 determination to be a functional calculation. Do you know how it would be modified to assume a scenario of no rocks and specifically just depend on a sump area at the bottom of the structure? $\endgroup$ Sep 28 at 13:33
  • $\begingroup$ I think you can model the thrust from a water jet on the concrete basin. Mainly treat it likes force exerted on slab on grade to determine its thickness and reinforcing. Try to follow every best practice suggestion you can find on abrasion and surface preparation of hydraulic structures. You can minimize the impact by designing a deeper reservoir to absorb some of the energy from the thrust. $\endgroup$
    – r13
    Sep 29 at 0:33

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