Pipe size and flow rate

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Trying to understand how water flows through varying sizes of pipe.

If you have water flowing (left to right) through 20m of 15mm pipe:

--> water
==================================


And you have 10m of 22mm and then 10m of 15mm pipe

--> water
|||||||||||||||||||||||||||||||=================


It's quite clear to me now (having read up!) that the latter gives you more volume of water and more flow rate.

But I'm unclear on whether the following will also gives the same flow rate (same length of 15mm and 22mm pipe, just different order):

1m of 15mm, 10m of 22mm and 9m of 15mm:

--> water
==|||||||||||||||||||||||||||||||===============


I believe it would, as the overall resistance in the pipework is the same. But Im not certain.
 
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Context to this question is I'm considering upgrading my pipework to 28mm. However, the megaflo inlet, pressure reducing valve and water softener are all 22mm or 3/4", hence the majority of pipework will be after or in between these restrictions.

I noticed the Megaflo Eco Plus is 1"/28mm inlets and uses a 3.5 bar Pressure Reducing Valve. And they quote 176 litres/min on their website(!). Not sure if this was available circa 2012, but wish I'd known about it if it was.
 
as the overall resistance in the pipework is the same. But Im not certain.

Every change of pipe diameter causes turbulance which reduces flow rate.

Hence

==|||||||||||||||||||||||||||||||===============

will have slightly more resistance to flow than

|||||||||||||||||||||||||||||||=================
 
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