Speed of Water Through a Culvert

I get a velocity of about 23 m/s both coming and going...actual results could vary...

excellent. thank you

Oh sorry I read that wrong....~30 m/s... 10% drop 10' vs 10° drop = 17.6'

The 100' culvert is rough concrete

There's a calculator here, where you can enter more detailed information:

http://onlinecalc.sdsu.edu/onlineculvert.php

I looked at this last night and came up with a figure of 23.5 ft depth at the end of the culvert for a drop of 17.5 ft over the culvert length, because the equations were simplified to discount velocity. The relationship between flow velocity and depth is interesting! That is, depth increases more than velocity... discussed on page 8 of this pdf, which also gives a handy table of Manning coefficients for different materials on page 10.

http://www.dartmouth.edu/~cushman/books/EFM/chap15.pdf

Manning's equation is used to calculate discharge velocity for supercritical flow, but another equation is given for subcritical flow calculation here:

https://wisconsindot.gov/rdwy/fdm/fd-13-15.pdf

Thank you for the Table and chart

What does g and H stand for in the velocity formula?

As usual, I have come to the right place for technical answers. Thank all of you.

I think that means gravity and height....

ok

It depends upon whether or not the <...lake...> is infinite or not.

• If it is not infinite, then the level will fall with time, which means the velocity will fall with time also.

It depends upon whether the <...river...> is infinite or not.

• If it is not infinite, then its level will rise with time. Once the level in the river exceeds the level of the bottom of the culvert, the flow will reduce with time.

It depends upon the roughness of the <...culvert...>.

• The rougher it is, the more resistance there will be to flow.

It depends upon whether or not the <...culvert...> is straight.

• The straighter it is, the less resistance there will be to flow.

The <...culvert...> as depicted is not the full story. There has to be some device to reduce or even stop the flow at some point in it, otherwise a non-infinite lake will drain to the bottom of the culvert and flow will stop.

• The further open the device is, the less resistance there will be to flow.

It will also depend upon temperature:

• The viscosity and density of water vary with temperature, viscosity strongly and density less so. In particular, below 0degC, the features in the illustration can be expected to have ice in them, which will affect the flow.

Kudos for working through the problem with all its changes. If I read you right, there is just a trickle coming out of the pipe (or gushing out of the pipe) on the other end ?

That seemed surprising, since the comment about depth increasing instead of velocity seemed to suggest otherwise. But I may be mistaken. I also completely missed the loss of depth just inside the culvert, but definitely got the impression that these problems are so complex given real world situations that they are usually measured and adjusted in the field in order to address site specifics.

The way I look at it it's the entrance to the culvert from the lake that limits the flow, and everything flows (pun intended!) from there. Obviously the flow is constant at any section of the culvert (not pipe) so there is 6.3m³/s coming out the end (if my calcs are correct).

The very steep slope accounts for the increase in velocity/decrease in depth going down the culvert. I integrated the gradually-varied conditions equation (using Mathcad) and trying various depths at or near the end of the culvert till the calculated length came to about the 100' specified.

BTW, the mixed units is because the OP wanted it, not my choice!

That makes sense to me. Bearing in mind I have no practical experience in this area, no reason I wouldn't expect to be surprised.

Flow in open channels can have a wide range of characteristics, depending on eg flow rate, bottom slope, length, inlet and outlet arrangements etc etc.

Drainage design is increasingly interesting, due to the risk of higher precip events. There are a lot of open storm drains in my area, with culverts passing under people's driveways. It is hilly so the slopes vary but those ditches have been quite filled by the heavier rain we've had - and we've been lucky so far. A few minor road washouts or shoulder damage at worst. We just haven't had the extreme amount that is happening on the continent.. yet.

https://www.youtube.com/watch?v=rsgi_F4Z-GE

As the velocity increases, the depth decreases. In this video example, the depth goes from ~6' deep at the start and is ~2' deep at the end.