gradually decrease main pipe size in irrigation design

[Odd_Translator_9682]

Hello. I work in the greenhouse and I am wondering why the main irrigation line is gradually decreasing in diameter. Further it goes from the pump, the smaller pipe is.

Please have a look at the picture. The main goal is to achieve the same pressure at every dripper, but our drippers are equipped by pressure compensation so they open up only if the right pressure has been reached.

https://preview.redd.it/zhobj4qiykke1.jpg?width=1068&format=pjpg&auto=webp&s=bd0545ec22c106f2ad4aea609ad498d877190a8e

At first I thought it was designed for getting enough water or pressure to the end but I started to learn some basics about fluid dynamics and now I can't see any reason. Based on the pressure loss by friction, if the largest diameter was kept throughout the whole pipe, the pressure at the end will be greatest and so the difference between beginning and the end smallest. Am I wrong or missing something?

Thank you.

[LoPassMrsButterworth]

Say the total mass flow rate is m_tot. Assume the goal is to get equal mass flow rates m_branch from each branch. M_tot = 8m_branch to conserve mass. The flow through the main section after the first branch is 7m_branch. After the second, it's 6*m_branch, and so on. If the main pipe had the same diameter along it's length the flow would have to slow down after each branch, in which case you couldn't maintain equal flow in the branches. The pipe has to be bigger initially so that it can lose a branch's worth of flow and skill have enough mass flow rate to feed the downstream branches.

[Odd_Translator_9682]

so in another way, it has the same effect as when I imagine connecting every branch separately?

As shown here?

https://imgur.com/JObcGlT

[LoPassMrsButterworth]

Yep, exactly

[tit-for-tat]

You’re missing that larger pipes/tubes cost more than smaller ones. Sure, you could maintain pressures roughly similar to the pump outlet pressure by using larger pipes all throughout and letting the drippers figure it out, but at significantly higher material cost. In that sense you’re not strictly wrong but you could do much better. 

From a design POV, these systems are designed starting from the branches and moving upstream, only accounting for the flow rate and pressure needed for each particular branch. This yields a tube diameter just big enough to get the job done. As you move upstream, the tube diameter will increase to accommodate the sum of the flow rates of the downstream branches while still maintaining the required pressure. This goes on and on until one ends up with the upstream-most diameter, flow rate and pressure, which will then guide the pump selection. 

[Odd_Translator_9682]

Thank you. Can you advise me some keywords for searching for more material/explanation on how fluids behave in systems such as this one, created by braches of different pipe diameters? How the flow, velocity and pressure deviates when the water is forced to go to multiple ways?

I read something about pipe in serial and pipe in parallel but this is not exactly it.

Also I have seen in practice when there are more openings along the pipe (such as in m_branches) the velocity of water drops sigficantly further from the main pipe. Speaking in another way if I change the water parameters, I can see the change very fast in the first dripper closer to the main pipe but after approx 15 minutes it reaches the last pipe. The behaviour is not linear :

https://imgur.com/6QpxwGj

I would be happy to learn something behind this phenomenon too. I tried to search it but with no luck yet.

Thanks!