Flow in 4" cast iron pipe 2

[PEDARRIN2]

I am trying to calculate the force on a fitting in an 4" interior horizontal storm pipe (cast iron no hub with no hub bands)

But first I need to determine what the actual flow is.

assumptions/knowns:

piping is full (single phase, no air bubbles)
d = 3.94 in
L = 20 ft (10 vertical and 10 horizontal)
Single 90 degree elbow which I was using K = 30 f(t) which the f(t) is 0.17 per Crane. This gives me an L/D = 26. I know I am mixing methods/equations, but there is no data I know of relating the friction factor of a cast iron 90 to equivalent length L/D - so I use Crane's K factor section.
friction factor: 0.041 based on iteration of Colebrook formula
Velocity at top = 0
Pressure at both top and bottom are 14.7 psia (open to atmosphere)

So using Bernoulli's with the h(l) factor included, I get

10 = [V(2)^2]/2g + (1+fL/D)*[V(2)^2]/2g

From this, I get a final velocity of 17.6 ft/s which equates to a gpm of 668.8

Given that my math/assumptions are correct - I do not know if this is realistic.

Comparing to what I would get if I used Manning (knowing there is no static head), I get 87 gpm for a fully flowing pipe at 1/8" slope.

Now I know I am not accounting for slope in the first calculation (which would only add 1.25" to the z factor), but does adding 10 feet of static really increase the flow by approximately 8 times?

Any help would be appreciated.

 

[cvg]

again, you are ignoring friction and other head losses.

you will have a significant entrance loss and that loss is based on velocity squared. the fluid in the tank (which has no downward velocity) must accelerate, converge on the inlet structure, turn 90 degrees and go downward through the grates. that will take considerable amount of head. Your attached ASPE paper gives you some flow rates through 4 inch roof drains, note that they are way below 700 gpm. There is a limit to how deep you can pond water on the roof, so there will be significantly less flow allowed into your drain that what you are assuming.

then two 90 degree elbows - these will introduce more head loss.

Your "flat" section will likely not flow full as it is discharging to atmosphere and you have not indicated any sort of tailwater condition which would cause it to flow full. so you must calculate using open channel flow.

you cannot just assume a flow of 700 or 600, you need to estimate a flow based on your hydraulic constraints, calculate the losses and then iterate.

 

[bimr]

Here is an example of a controlled flow roof drain. This will slow the flow entering the storm drain.

The alternative is uncontrolled flow, which will generate 10 -15 ft/ sec of velocity in the drain pipe.

 

[PEDARRIN2]

bimr,

I would love to be able to specify a controlled flow roof drain system, or even a siphonic roof drain system. The problem with the controlled flow is the designed ponding that will occur. The structural engineer has to design for larger roof loads. The roofing design has to be increased to deal with the increased water pressure and weight of the water. Not going to happen to "merely" control the flow of the water from the roof. If the project wants to control the flow of water, it is typically done by the civil engineer.

Siphonic drains tend to lend themselves to very large, flat roofs, like for a warehouse, which I don't see too many. They also seem to depend on every drain being flooded so the entire roof is a reservoir. Again, the structure and roofing designs are enhanced.

I am still getting confused by my perception of the responses. cvg indicates I could not have a full pipe, which I understand to be because I would have air in the pipe and the loss due to friction would not allow me to have full flow.

But bimr indicates I could have 10-15 ft/sec in the pipe. Per storm water pipe sizing charts, from ASPE Data Book 4, which use Mannings Formula, a 4" pipe at 1/8" per foot slope, the "full pipe discharge capacity" is 87 gpm and 2.22 ft/s. If my velocity is 10-15 ft/s, how could I not be full and pressurized - so Mannings would no longer apply and I would need to use a modified Bernoulli (with a Darcy friction factor)?

I fully acknowledge my understanding of the Manning is less than my understanding of Bernoulli and that I would rather deal with Bernoulli, because I can include static head and, with the friction factor, I can account for loss due to the roughness of the pipe better than a simple "n" in the denominator.

I realize I might not have full flow, but I guess I would like to know why I don't have full flow from the experts (you).

Remember, my original intent is to determine the forces on a fitting to see if the restraints being used are sufficient for a more intense storm event. I understand how to calculate this with full flow. I really have no idea how to do it for partial flow. But that might be fodder for another post.

Again, thanks for sharpening my skills and knowledge base and for putting up with my thick skull.

 

[bimr]

No ponding will occur because there should be an emergency overflow. Talk to the person who is designing the roof structure.

10-15 ft/sec is the terminal velocity in an open drain like a toilet stack. If the roof is not ponded, there is no way that you can have full pipe flow. A toilet stack does not flow full.

The concept of a siphonic drain is to utilize full flow so that a smaller drain pipe can be used.

 

[PEDARRIN2]

bimr,

There would likely be some ponding at the primary drain of a non controlled flow and non siphonic system because the overflow drain has a standpipe in it or is located up the roof slope enough to be at a slightly higher elevation, usually 2"-4" above roof level. Now 2" is not much, but there have been instances when there is a large storm event where there is no blockage of the primary roof drain, but there is flow out of both systems, indicating the likelihood of ponding.

I understand 10-15 ft/s is the terminal velocity of a partially full stack, but I am assuming (maybe incorrectly) that the stack is full so I do not have to deal with the hydraulic jump that will occur when the flow turns horizontally. There is some thought that it is the pressure fluctuations that occur with this hydraulic jump that causes the fitting couplings to fail. In a sanitary system, you cannot connect to the stack within 10 pipe diameters of tall stacks just for this reason. There are also vents throughout the system to help relieve this air flow. But there is no similar prohibition for connections that close to a storm downspout or vents. Maybe there should be.

So a 4" stack, which is typically designed for at most 1/3 full (due to the maximum number of fixtures allowed to be connected to it by code) to maintain self venting and not induce more than 1" w.c. (+/-), per ASPE Data Book 1, Capacity of Stacks, indicates 180 gpm of flow. Even if it is assumed the stack is only 1/4 full, it would still have 112 gpm. This is more than the 87 gpm for a 4" horizontal pipe, flowing full.

So, if these numbers are correct, what is coming down the stack exceeds what the horizontal pipe can flow (using Manning). So, the horizontal pipe would start to fill, pushing the air out and eventually there would be a build up of water in the near upstream vertical portion of the first elbow. Eventually, no air from the stack will be getting past this slug of water and the horizontal pipe will not have any more air in it and eventually be fully filled with water. Then, as long as there continues to be enough excess flow in the stack, the entire short section (10' in my assumption) of the horizontal pipe will fill and be pressurized and be calculated by Bernoulli, not Manning.

Now, I realize there are likely those who will say, "No it won't", but I do not understand why.

 

[bimr]

Which gets to one of the reasons for installing the siphon system because it eliminates the messy hydraulics with two phase flow.

If you have enough rain, the stack may be eventually filled. But the bottom line is that the total energy can not be more than 10 feet of water.

If you are worried about the water backing up into the riser, consider increasing the horizontal pipe to 6-Inch.