Head loss - Parallel pipes

[dianad]

Hi,

This question was already debated too much times in thsi forum, but i still doesn't understand one thing that questions all that i've learned until now.

In series pipes, everyone knows that to determine the head loss we have to sum all the head losses of each consumer.
But in parallel flow, i've red every kind of possibilities to solve this problem.

I've red a lot that if we have for example 5 consumer that have the same pressure loss (for example solar collectors), the total head loss is equal to the head loss of 1 collector. But in other books i red that to determine the pressure loss in parallel flow, we have to make some kind of simillarity to electronics. So in this case some books refer:

1/Rtotal = 1/R1 + 1/R2 + 1/r3 + ...

So, how do we solve this simple problem that many books solve them differently.

I've attached an image to show an example.

Thanks!

 

[prex]

Surprisingly no one above stated the simple rule that:
- if the flows in parallel are through equal paths
and
- the head loss though the inlet and the outlet collectors is negligible with respect to the head loss in the branches,
then the flow rates in each branch will be the same.
Please note dianad that the second condition above is unlikely to be true, especially if the dynamic head in the collectors is non negligible.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[BigInch]

Actually I thought I did, although not using your exact words.

"When in parallel, flows proportion through all components, such that the head loss between any common points are equal"

Tells me that, if head loss is equal, flows are equal and that doesn't require that flow losses be negligable anywhere.

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com

 

[prex]

Sorry for using an uncommon meaning of the word collector in my post above: this should be replaced with header.
BigInch, the sketch from dianad has 6 (supposedly) equal branches and two headers. For the flow through each branch to be the same, what I require is that the loss+dynamic head in the headers is negligible with respect to the loss in the branches.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[BigInch]

OK. That's usually the case.

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com