Gravity flow from circular pipe out of tank

[kwalton]

I am trying to determine the gravity flow out of an oil imterceptor tank. Water is flowing out of the tank through a 50mm diameter pipe and the pipe is about half full. Is there acalculation I can do along the lines of that for a v-notch wier to calculate the approximete rate of flow.

 

[Ussuri]

If it is just a circular pipe flowing part full it is relatively easy to calculate the flow. The flow is dependent on the profile, roughness and the gradient.

You can calculate pipeflow using mannings equation (as this is essentially open channel flow), there are published tables for flow rates and velocities (HR Wallingford Tables), you can determine full bore discharge using colebrook-white and modify the diameter using the Butler pinkerton shape correction factor to account for pipes part full. However, these are only valid if you do not have significant head behind the pipe and assume steady non-uniform flow.

As you have a tank with an inlet and an outlet it might be more complicated. If the tank is completely full all the flow that enters will ultimately leave, subject to the buffering capacity of the tank itself. It is also likely to flow in surges instead of a constant flow. You basically have a length small diameter pipe, widening to a very large length or pipe, narrowing back down to a small length of pipe. This is an non uniform flow situation. And if the flow entering is changing with respect to time it also becomes an unsteady flow situation.

As an approximatation, I would do a rough calc for a number of different top water levels, use that to calculate a hydraulic gradient across the tank and use that values as gradient (slope) then plug that into mannings equation.

 

[kwalton]

Thanks for that.

I have an open topped tank with pipe inlet at half bore and the outlet pipe is acting as an overflow so is flowing out under gravity at about half bore.

I have got Manning's formula but can you help me with the following:

Roughness - In a reference I have this can vary from 0.017 to 0.067, 0.17 being a smooth earth channel, but this is for channels dug in natural ground (I am a geotechnical engineer). I have found an internet link

http://www.pisces-aqua.co.uk/aquatext/calcs/channel.htm

-which says "typically 0.3". The outlet is a steel pipe welded to the side of the tank. What would you suggest for roughness?

Hydraulic Radius / Crosss sectional area - Is this the cross sectional area of the whole channel or just the area of the channel which is under water, i.e. corresponding to the wet perimeter.

Thanks

 

[bpattengale]

For a manning's N value I typically use 0.013 for Reinforced Concrete pipe(RCP) and 0.010 for PVC or HDPE pipe. I was unable to locate a consistant vaule for smooth steel pipe. However PVC pipe is considered to be extremely smooth pipe and RCP a rough pipe. Using an N value of 0.012 would be acceptable because steel pipe falls in between RCP and PCV as to how "rough" the pipe is. The cross sectional area is the area that the water is flowing through corresponding to the wet perimeter.

Mannings equation should provide a reasonable estimation of flow rate based on the depth of water in the pipe.

 

[JStephen]

Would a 5-gallon bucket and a stopwatch maybe give better results?

 

[Ussuri]

Tables I have suggest:

Clean, uncoated cast iron 0.013-0.015
Clean, coated cast iron 0.012-0.014
dirty, tuberculed cast iron 0.015-0.035

There is a theoretical formula for n found in Ven T Chow's book "Open Channel Hydraulics"

n={[(R/k)^0.167]*[1/(21.9log(12.2R/k)]}*{(R/k)k^0.167)

Where R is the Hydraulic Radius
and k is the roughness height

 

[cvg]

note that Mannings equation is for uniform flow in a pipe or channel. Bernoulli equation would be better. Manning's also will not account for entrance or exit losses, bend losses, losses due to flow through a partially open/closed valve, loss through reducer or any other minor losses. The actual flow will be less than the flow calculated by Manning's alone. Also, it seems that your hydraulic control is at the inlet and it should probably be analyzed as an orifice - not using Manning's equation. Look up the equation for orifice flow in your hydraulics book. I would suggest "Handbook of Hydraulics" by Brater and King as good reading to more fully understand hydraulics.

 

[hydrae]

Kwalton

Do you have a slope on the exit pipe? (sounds like yes)
if so, does the flow according to the Mannings equation greater or less than critical? (probably greater)
if greater, then the tank exit-pipe entrance is a critical point therefor the level in the tank will depend solely upon the critical equation and the downstream pipe will have no effect upon the tank level,
besides the critical losses, you should include the entrance loss which is dependant upon if the pipe is reentrant, square, or champered as it connects to the tank.

Hydrae

 

[bpattengale]

cvg, bernoulli's equations would provide a better value, however velocity needs to be known and to determine velocity you either need to know flow rate(unknown) and cross sectional area or measure it directly.

If you wanted to get really precise, assuming it is only a pipe without any other flow controls,I'd analze the pipe as a culvet. You'd have to look at whether it was inlet, outlet, or barrel control. Then you get into whether the inlets and outlets are submerged ect. ect. Not the easiest thing to do for someone not familiar with hydraulics.

Kwalton, If you gave a more detailed description of the system, everyone may be able to provide you with a better answer.