Surcharge and Mannings 1

[GoldDredger]

I was hoping someone could confirm my method for capacity calculation under surcharge conditions.

First, when calculating the full or half gravity flow in a sewer pipe, I would use Manning's equation, simple enough. The slope is the physical slope of the sewer pipe.

Now, if we have a surcharge condition (headwater in the manhole), the downstream pipe now becomes a pressure pipe. (Also assuming no tailwater with free outflow, not culvert condition).

Would I calculate the pipe capacity based on the slope created by the surcharge headwater. In other words, the headwater elevation minus discharge elevation, divided by length.

That would give the hydraulic slope, and I would substitute that hydraulic slope into Mannings for the capacity under surcharge.

Does this seem correct to you?

(Also ignoring entrance losses)

 

[RWF7437]

Yep, generally you are correct. The slope (S) in the Manning equation is the slope of the Hydraulic grade line (HGL). For gravity flow, S is the same as the (uniform sized) pipe invert slope.
"In other words, the headwater elevation minus discharge elevation, divided by length."

For the case you describe, you also need to take in to account any entrance and exit losses using the Bernoulli Eq. ( which is simply a special case of the Law of Comservation of Energy. )

good luck

 

[bimr]

Mannings equation is more convenient in open channel calculations. Note the correction in the mannings equation for the hydraulic radius for full pipe.

r = A/P = Hydraulic radius (feet) – Note: for pipes full or near full, r = 4/Depth

http://www.ctre.iastate.edu/pubs/stormwater/documents/2M-4StormSewerSizing.pdf

 

[Hoagie]

be careful. just because you have headwater doesn't mean that the pipe will go pressure...actually, its rare to see a 'pure' pressure situation for a short length of pipe. you will need to check to see if it is and inlet or outlet control situation based on both headwater and tailwater conditions. for a primer, check out the second paragraph of this....

http://www.fhwa.dot.gov/engineering/hydraulics/pubs/06138/chapt2.cfm

 

[jartgo]

I concur with Hoagie. You are on the right track as others pointed out, in that the slope term in Manning's is the HGL (not the slope of the pipe). You deserve kudos just for knowing that alone! Many people don't understand that concept.

However, it has been my experience that it's a rare occasion that an open system will be controlled by the surcharge pressure (since the pressure from a few feet of water is relatively small), it will likely be controlled by inlet or outlet conditions.

You've apparently eliminated outlet control as a possibility, but when you say "no tailwater with free outflow, no culvert condition" you've only eliminated one possible culvert condition, that is, outlet control. It is very likely that it's operating under inlet control. That is, the pipe could flow a heck of a lot more water, if you could get it in the pipe fast enough.

As RWF pointed out, Bernoulli is the most extensive way to analyze the condition. A quick check would be to use the simple orifice equation and measure head from the surcharge elevation to the center of the pipe.