Head Loss through pipe system

[AlbertPotato]

What would be the head loss through this pipe system?

A 3" pipe branches off into 5 - 3/4" pipes all the same length and diameter. 3/4" Pipes discharge to the air.

Just taking into consideration flow through the pipes, is the head loss through the system equal to:

1) (HL in 3" Pipe) + (HL in 1 of the 3/4" Pipes)

or

2) (HL in 3" Pipe) + (HL in all of the 3/4" Pipes)

I'm pretty sure it's 1), but its been a long time....

 

[msquared48]

For Q1 = Q2, it would have to be #2, not #1, as you are talking about the head loss of the total piping system.

Mike McCann
MMC Engineering

 

[AlbertPotato]

Ok, perhaps I worded my question poorly. I'm trying to size a pump at the end of the 3" Pipe system above and I need to figure the Dynamic Head to develop a system curve.

I thought #1 was correct as the 3/4" pipes are in parallel and have the same HL across their length. The flow Q1 is divided into the 5 3/4" Pipes (Q1 = 5*Q2). So HL across the parallel system is equal to 1 of the 3/4" Pipes.

To develop this system curve, which is correct?

1) (HL in 3" Pipe) + (HL in 1 of the 3/4" Pipes)

or

2) (HL in 3" Pipe) + (HL in all of the 3/4" Pipes)

I appreciate your response and apologize if my question still is not clear.

 

[cvg]

closer to 1 than to 2
but neither is correct

to be accurate, there is additional headloss between each of the tee fittings such that the flow in the 5 3/4 inch pipes are not equal. there will be more flow in the first and less flow in each succeeding branch line.
in addition, I assume you mean friction loss only, not losses due to elevation change?

 

[AlbertPotato]

Thanks.

Yes I understand loss at each fitting and elevation head. Just not sure if I was suppose to add up the HL in all the pipes or assume they are in parallel.

 

[bimr]

Maybe this will help:

http://www.mcnallyinstitute.com/11-html/11-12.html

 

[BenJohnson]

The answer is #2.

Look at it this way. Pushing the liquid through each 3/4" pipe is going to need pressure to keep the water moving through all 5 pipes. To have the pressure you need, you must overcome the resistance (or drag) for each pipe. So you need to have enough head to push the liquid through all 5 pipes.

If you only have enough pressure from the pump to get water through one 3/4" pipe, water would not flow through the other 4 pipes - no pressure.

This is a simplistic illustration. in reality, water would just trickle through each 5 pipes at a very slow velocity because the are all sharing the pressure you provide for that single pipe.

This is an easy problem because all 5 pipes are the same diameter. To prove your solution #1 is wrong, what would you do if all 5 pipes were different diameter?

 

[Drew08]

The head at the outlet of all five branches are equal (atmospheric), the head at the upstream end of all five branches are also equal because they are all joined to the same 3" pipe. This is the case no matter the size of the branches, or even their lengths, or presence of bends and vales, even if one is a foot diameter and a mile long, and another a quarter inch diameter and a foot long. For a given applied driving head, size and length only determines flow distribution (head loss is always equal).

I think Ben Johnsons statement: “…you need enough head to push the liquid through all 5 pipes.” Would be more accurately stated, as “you need enough hydraulic horse power to push the liquid through all 5 pipes,” where hydraulic horse power is the ability for a pump to supply a greater flow rate at a given head.

If increasing pump power can be added to the system with additional branches being added, where the flow rate through each additional branch will remain the same, with the same driving head, then the total head loss through the system will also remain the same even after adding a hundred more branches.

The answer is number 1 without exception for bends, valves and other minor losses (though these things will cause flow in each pipe to not be equal and thus should be considered). It is hydraulic horse power that increase with added branches, not head loss.

 

[bimr]

The answer is #1 although I don't think that is what you are looking for.

If you want to guarantee equal flow through all five 3/4" pipes, you need to install some type of pressure device at the end of the 3/4" pipes so that the fluid resistance in the piping is inconsequential.