Is it an open or closed channel?? 2

[carletes]

Hello,

I have the following problem I don't know how to handle. I have a closed circular pipe with a known inlet flow at atmospheric pressure that discharges at a lower level, at atmospheric pressure as well, by means only of gravuty force. Is it considered as an open or closed channel? If I calculate Bernouilli Equation at the inlet and at the discharge I get (as both are at atmospheric pressure but different heigths) that flow velocity at the discharge must be bigger, so the flow area must be smaller. That is to say, the flow doesn't fill the pipe along the way so the pressure must be atmospheric inside the pipe. Am I right? What are the correct formulas and theory to calculate pressure and velocity in each point?
Thank you very much for your help.

 

[waterexpert]

Try this link

http://www.lmnoeng.com/circular.htm

 

[25362]

My question is whether you used the extended Bernuoilli equation.

The extended Bernouilli equation includes a friction loss element between entrance and pipe outlet we must not neglect. Although there are also losses at pipe entrance these are normally considered negligible in gravitational flow.

The friction due to flow would have the effect of retarding the outlet velocity by dividing the static presure difference delta H by (1 + f L/D). Thus,

V^2/2g = delta H / (1 + f L/D).

f is the Fanning friction factor obtained from Re numbers and pipe rugosities, assumed to be constant along the pipe. There are plenty of graphs on this subject. g = 9.8 m/s^2.

Let's make an exercise for water flowing in a pipe:

Assume L/D = 1000, f = 0.01, delta H = 3 m.

V = sqrt {2 x 9.8 [3 / (1 + 0.01 x 1000)]} = 2.3 m/s

Compare this velocity with V =sq rt [(2 x 9.8) x 3] = 7.7 m/s when neglecting friction.

The same calculation can be done for any point along the pipe using the proper L/D.

Of course, when using much lower flow rates the pipe would be partly empty (open channel) as actually happens in sewage and drainage. Calculations of these conditions are difficult. Hydraulic engineers may be of help.

 

[carletes]

Thank you very much 25362 for your help. I hadn't taken into account that friction, but the question I have now is the following. As you say, the velocity along the pipe is changing according to the formula you have given to me, so, the flow area must change as well (because the volume flow must be constant). Doesn't it mean that the pipe is partly empty?
Moreover, what about pressure? Is it atmospheric in the whole pipe??

Thank you again.

 

[BobPE]

carletes:

Whether or not it the pipe is in gravity flow for the entire length is something you have got to tell us. You may have two flow regeims in the pipe, gravity and pressure. You must look at the profile of the pipe. If it was designed as a gravity main then there will be known slopes and from that information you can determine whether or not the flow you measure going into the pipe will convert to pressure flow since flow is conserved. If the pipe was designed as a pressure pipe, then again, you will be able to determine what sections are gravity and what are pressure flow from the profile drawings of the main.

Yes the flow must reference atmospheric pressure somehow inside the pipe for it to be considered gravity flow.

The formulas for gravity and pressure flow can be found in any fluids book.

BobPE

 

[waterexpert]

I would have thought the Manning equation more appropriate. The link I gave above is for a free plug in the numbers calculator based on the Manning Equation.

 

[carletes]

Thanks BobPe for your help. If I have correctly understood your explanation, when I have a pipe with a certain slope and diamteter and the volume flow I want to discharge is known as well, I have to try with the Manning Equation (valid for gravity flows), for example, to discover whether such flow can be discharged only by means of gravity with. If that flow is too big then it will be a flow under pressure.
Now, I suppose that in those parts of the pipe where the flow is by gravity the pressue will be atmospherical, but in the rest of them? What happens if the pipe has got parts with minor slope and other with bigger and the gravity flow is not possibble in all of them? What is the pressure in the different sections? How can I calculate it? If, perhaps, answering all these questions is tedious for you, could you recommend me a link or book to study this matter?

Thank you again and regards.

 

[BobPE]

carletes:

Nothing is too tedious when you enjoy what you do!!!

In those parts of your pipe that go to pressure flow, the water will back up in the pipe until sufficient head is reached to maintain the flow observed in the gravity sections. I would use the Hazen-Williams formula to estimate the pressure flow using a C value of 100 just to get an estimate. The head that is needed will give you the elevation of water in the pipe and from this you can tell how far the water backs up in the pipe. Now during transition from gravity to pressure flow in the pipe, strange things happen. Look at your gravity pipe hydraulic elements curves and you will note that somewhere around 90 percent full in a gravity pipe you reach the maximum flow obtainable in the pipe, its at this time that you will start to go into pressure flow and you may have trapped air in the pipe that will increase headloss so using an estimate will get you close enough to the understanding.

Using hazen-williams will allow you to generate the hydraulic gradient through the pressure sections which when coupled with elevational information, will give you the pressures you are looking for at various points in the pipe.

Good luck...

BobPE

 

[saxon]

carletes, The basic formulas for hydraulic design/calculating velocity and flow in closed gravity systems are based on the Manning Equations, the most commonly used equations are as follows:

v=(1.486/n)*r^2/3*s^1/2
q=(1.486/n)*a*r^2/3*s^1/2

Where:
v= flow vel. (fps)
q= flow vol. (cfs)
n= coeff. of roughness for pipe material
a= cross sect. area of flow in pipe (ft^2)
r= hydraulic radius "wetted cross sect. area of pipe" (ft)
r=a*length of wetted perimeter
s= slope of energy gradient, equal to the slope of invert and hydraulic surface (ft)

Check the "Handbook of Hydraulics", by McGraw Hill or contact the National Clay Pipe Institute and ask for a copy of the "Clay Pipe Engineering Manual" between these two sources it will allow you to design any type of gravity system, either open channel or closed.

Hope this helps.
saxon

 

[carletes]

Thanks again BobPe and Saxon for your help. I think this time I have understood it (my English is not that good and I'm afraid of not having caught it properly): if in a gravitional flow I have a section between point 1 and point 2, where the slope is not enough to discharge by gravity the flow that enters in point 1, then a pressure flow happens. To make this pressure flow possibble, in the point 1 an increase in pressure happens (is it something like a vortex?? I don't see clearly )by menas of a flow back, that acts like a pumping. This flow back goes up in the pipe making that pressure in point 1 is enough to overcome the required head loss (Hazen-Williams formula)in section 1-2 and make the flow arrive to the following gravitional section flow in point 2 with atmospheric pressure (I suppose, but I/m not sure). To calculate pressure along this section 1-2 is enough calculating Bernouilli equation in the different points of the section, taking into account the head loss by friction and the presure reached in point 1.
If I am right, is it possibble that in a point between point 1 and 2 there is a pressure below atmospherical (because as the velocity in the whole section is the same and the point 2 will be at atmospherical pressure, there may be points above point 2 with certain vacuum pressure, I suppose).
And finally, according to Manning equation, if I increase the slope of the pipe a lot (until placing it almost vertical), the velocity would increase a lot as well and I would be able to discharge any flow by gravity. Is it correct? Or is there a critical slope apart from which the discharged flow doesn't increase?

I know they are lots of questions, but if you could answer me it would be a big, big help.

Best Regards,

Carletes

 

[BobPE]

If you are in gravity flow regeim, your thoughts on verticle pipe would hold. If you are in pressure flow, verticle pipe will not influence flow.

As for vacuum, the head in front of your transition to pressure flow will be atmoshpheric plus water head. and should end up as atmospheric pressure on the discharge side. If your pipe travels above the hydraulic gradient, then it is possible to have vacuum conditions in the pipe.

Sounds like you are making progress....

Take care

BobPE

 

[carletes]

Sorry BobPe, but what do you mean with "your thoughts on verticle pipe would hold", I don't understand it. Do you want to mean that Manning equation is valid for vertical pipes as well with no restrictions? That is to say, a vertical pipe, as the slopwe is infinite, can discharge any flow just by gravity?

Finally, how is it possibble that at the beginning of the section with pressure flow the pressure increase? Is it like or vortex or similar? I suppose is not simple to explain, so if you recommend me a link or book..

Thank you for the sixth o seventh time in 2 days.

 

[BobPE]

carletes:

The transition from gravity to pressure happens when your design pipe (assumed grafity flow) cannot handle the flow anymore due to some problem like surchaging. That section that can not handle the flow goes into pressure flow. Since flow that entered the pipe must exit the pipe because of the law of conservation of mass, the energy needed to make the flow go through the pipe as pressure flow is head. The necessary head builds up at the transition from gravity to pressure and equalizes when the flow eguals the flow in the gravity section. There are a lot of engineering principals involved here, so refering you to one book will most likely not help. If it is a big problem for you I would suggest getting an engineer to help you with this.

Take care

BobPE

 

[carletes]

Thanks for everything BobPe. I think I have it all more or less clear (except the question about whether I can use the Manning equation to determine the maximum gravity flow in an almost vertical pipe. I think you have said nothing about it)

Take care

Note: Alhough it sounds incredible, I am an enginner, but a young and inexperienced one.

 

[25362]

to Carletes, as BobPE says,

There are various strange behaviours on clean sewer (open channel) pipes. For example:

1. Velocities:

* Liquid velocities increase with depth but the maximum value is attained at about 80% of the diameter !

* The velocity of a pipe running full equals that when running half full! This means that for every diameter coverage between 50% and full there are two possible velocities, except at the maximum at 80%.

2. Flow rates

* Liquid flow rates at 80% diameter depth equal those of a full pipe.

* The maximum liquid flow rate is attained at about 93% diameter coverage. This means that at any diameter depth, between 80% and full, there are two possible flow rates, except at the maximum (93% diameter).

 

[25362]

When reading an hydraulic engineering excerpt I came to learn that for sewer piping running full the Manning formula becomes:

Q = 0.4632/n (D^2/3) (S^0.5)

Q flow rate in cf/s
n roughness coefficient
D diameter of pipe, feet
S hydraulic gradient ft head loss/feet length

The same article says sewers have a minimum diameter of 8" and should be laid on a grade sufficient to produce a velocity of 2 fps when running full to prevent the deposition of suspended solids.

 

[kenvlach]

Are you flowing rinsewater in your pipe?

In the metal finishing industry, rinse water is re-used as much as possible via gravity flow between tanks.
One difficulty is entrained air due to the use of air agitation. Hence, one puts the inlet near the top (also reduces backflow chances)and runs the pipe part full, allowing most of the air to escape. At the other tank, the flow is directed to the bottom with an elbow and a short pipe (everything is PVC, by the way). Several holes are drilled in the top of the elbow for air venting.
If you piping has a high point where air can trap, you can either drill holes directly into the pipe, or better, tee-in a short riser.

I have used several of the equations mentioned above, and it seems to me that the inlet factor becomes more and more important the closer you are to the surface, and maybe dominates right at the surface.

In case your flow turns out to be inadequate and you are unable to change tank elevations: Use an air lift, like one of those bubbler things used in aquariums. The less dense water+air mixture will rise higher inside a tube, then you can drain off the water with the pipe.

 

[stanier]

Go to this site and download Flowpro2. It will help in the design of sections under gravity. The software is free and easy to use.

The thing you need to consider is the hydraulic radius for partially full pipes. This will explain why a partially full pipe has greater flow than a full pipe. Set up a spreadsheet to calculate the hydraulic radius form empty to full and you can plot the hydraulic radius against depth.

flow.

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