Determining parallel flow off header
Determining parallel flow off header
(OP)
I have a header of 8" line pressurized up to 70 psig with water. The end of the header is capped.
Branching off of the header are a 5" line, 3" line, and 1" line. They are all the same length of 72' and dumping to atmospheric pressure. What I am trying to determine is the flow rate in each line.
I realize that more flow will come out of the 5", then 3", and the smallest flow coming from the 1". The problem I am having is determining the flow rate in each pipe.
Is there an equation to determine this?
Branching off of the header are a 5" line, 3" line, and 1" line. They are all the same length of 72' and dumping to atmospheric pressure. What I am trying to determine is the flow rate in each line.
I realize that more flow will come out of the 5", then 3", and the smallest flow coming from the 1". The problem I am having is determining the flow rate in each pipe.
Is there an equation to determine this?





RE: Determining parallel flow off header
5" - 3400 GPM
3" - 920 GPM
1" - 55 GPM
This is assuming constant 70 psig pressure in the header.
RE: Determining parallel flow off header
RE: Determining parallel flow off header
Also how would I account for the pressure drop across each pipe penetration if the header is in fact a 8" line fed from a pump upstream?
RE: Determining parallel flow off header
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"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Determining parallel flow off header
So the pressure in the header, assuming a pipe, would have a lower pressure after the first 5" penetration than before it? And so on for the other 2 penetrations?
RE: Determining parallel flow off header
A more uniform pressure drop along the whole header might be obtained by placing the inlet near the middle of the header's length and arranging the smallest outlets closer to the header's inlet with larger outlets closest to the end caps.
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Determining parallel flow off header
Good luck,
Latexman
RE: Determining parallel flow off header
One thing that was really counterintuitive was when I saw a demonstration of a manifold that was not capped at the end and allowed to flow through to a open pot. Each of the 5 pipes off the manifold had closed valves. As the valves were opened, the static pressure in the manifold across each pipe went UP not DOWN. They attributed this to a reduction in velocity as the flow dropped out the first pipe, then the second, and so on.
Check it out here. The demonstration starts about 7 minutes into the video.
http://
RE: Determining parallel flow off header
Good luck,
Latexman
RE: Determining parallel flow off header
If inlet pressure is held constant and equal and outlet pressures are held constant and equal, its equivalent to attaching all the inlets together and then attaching all the outlets together, and the 3 pipe flows can be found by the "equivalent pipe" method, 1 among others.
If you want to not consider the header for a minute and approximate a solution,
You have a pressure loss in each pipe of 70 psi, or 161 feet, if its water. You can make any combination of pipes of any diameter you want (all with length 72 feet) that have a head loss of 161 feet, and the flow in each pipe will be the flow that gives you 161 feet of loss. The only other condition is that the flow into the inlet joint of all pipes must be the sum of the individual pipe flows, which will also be equal to the sum of all outflows from each individual pipe at the outlet joint.
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Determining parallel flow off header
Your calculated flows seem to be inline. You can assume the header to be a big tank if the take-offs are close to each other, then you only need to account for the equivalent length of the tees. If the take-offs are far apart, then you will need to calculate the pressure at each take-off at points B, C & D. The pressure at A is 70 psi. See diagram below (assuming the diagram compiled correctly), as follows:
Since you don't know the pressures at B, C & D, you will need to do a trial and error solution. The flow rates you calculated were based on 70 psi and can be used for your first approximation.
5" - 3400 GPM
3" - 920 GPM
1" - 55 GPM
You will need to calculate the pressure at B using the flow in the 8" line from A to B of Q=(3400 GPM+920 GPM+55 GPM).
You will calculate the pressure at C using the flow in the 8" line from B to C of Q=(920 GPM+55 GPM).
And you will calculate the pressure at D using the flow in the 8" line from C to D of Q=(55 GPM).
Once you obtain the pressures at B, C & D you will need to re-calculate the 5", 3", and 1" flow rates. Iterate this process until the change in pressure at points B, C & D is trivial.
A 8" B 8" C 8" D
══════════════════╦════════════════════╦════════════════╦╡
║ ║ ║
║ ║ ║
║ ║ ║
5" 3" 1"
RE: Determining parallel flow off header
**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies) http://virtualpipeline.spaces.live.com/
RE: Determining parallel flow off header
RE: Determining parallel flow off header
Good luck,
Latexman
RE: Determining parallel flow off header
RE: Determining parallel flow off header
You need to do a frictional flow calculation taking into account the 8" pipe lengths A to B, B to C and C to D. Your pressures should not increase in the direction of flow. The pressure at A is 70 psi the pressure at B will be less due to frictional loss. The pressure at C will be less than the pressure at B, etc.
Try using a pipe flow calculator such as the one on this website: http://kirkmansoftware.com/ or similar.
RE: Determining parallel flow off header
In a short diverging header, momentum effects rule and the pressure increases. In a long diverging header, frictional effects rule and the pressure decreases.
See and read the parts on Figure 3 at:
http://web.mit.edu/hml/ncfmf/06PFFA.pdf
Good luck,
Latexman
RE: Determining parallel flow off header
Both friction and momentum should be accounted for.
Good luck,
Latexman
RE: Determining parallel flow off header
Thank you for the article. It looks good. I printed it out and am looking forward to reading it.
I do recall a little about the De Laval nozzle from my college days. As I recall, for M<1, as the fluid enters the convergent section of the nozzle the fluid pressure reduces from the initial P1 to the throat pressure PT while the fluid speed increases. As the fluid enters the divergent section of the nozzle the fluid pressure increases from PT to P2 while the fluid velocity decreases. At no time is P2 ever greater than P1 as you seem to imply; this would violate the first law of thermodynamics.
Looking at dfa1979's worksheet, he is clearly confused by this because he has the fluid pressure increasing as the fluid flows through the drainage distribution system. It bears repeating; this is a violation of the first law of thermodynamics. You cannot have the system pressure higher than the source pressure without introducing some shaft work.
I agree with you that nozzle effects can be very important in fluidic circuits. However, in distribution system design it is a very small effect and in 30 years of design I have never had occasion to account for nozzle effects other than the use of K factors. The pressures throughout a distribution are always lower than the source pressure because of fluid friction.