Jedax:
All I have tried to do is to help you out in what I consider to be a rather simple and direct application. If you feel I am using my 48 years of engineering experience to overwhelm you, I can only assure you that I have no intent on that. While I refuse to apologize for my age and my experience, I can only add that all that you have been asking is answered, repeated, and calculated in an Excel workbook that we have posted for free downloading within the Student Forum on this Website. You will find it at the very beginning of the Student Forum. If you download and read through this workbook, you will find many similar – if not identical problems resolved. You will also find detailed listings of the commercial Pipe Tables, with all the important pipe details carefully listed for your use. Additionally, you will also find a copy of all the "official" Hydraulic Institute water tables that give you the velocity and pressure drop for water in commercial piping. The answer to your problem(s) is directly found in this table.
As I've stated, I have been in the "real world" of designing for 48 years, so I can identify easily with your problem. You now propose to remove the 1x1-1/4" expander in the pump suction line (which I think is foolish, but anyway I'll go along ….). This scenario now becomes what I've added to the Excel spreadsheet as "Schematic & Calculations(2) worksheet. You should now refer to the revised workbook attached to this thread. The answers to your specific new questions are:
1) "Can you tell me the output of Q3 …."
This, again, is easy. Q3 remains the same as before (0.94 L/s) since it still is the sum of Q1 (0.47 L/s) and Q2 (also 0.47 L/s)
2) "and V3?"
Since you have now removed the expander, I can only presume that the diameter of the pump suction line is now also 1", schedule 40 commercial pipe. That being the case, the velocity of the water entering the pump suction is now DOUBLED (5.53 ft/s) – since the flow rate has doubled within the same pipe I.D. (1.049"). As I've stated, all this fluid flow information is explained and detailed in my free Crane Calculations workbook.
I hope this helps you out.
Now that one helps a lot. I appreciate your help Art and others also who shared their knowledge and experience.