How to find Best Efficiency Point for pumps in series?

[theone]

Homework Statement

I read here http://www.engineeringtoolbox.com/pump-system-curves-d_635.html
that this is where the system curve and the pump performance curve intersect.

But if the situation involves pumps in series, what will the system curve be a plot of? Is it flow rate and the total pump head?

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Homework Statement

I read here http://www.engineeringtoolbox.com/pump-system-curves-d_635.html
that this is where the system curve and the pump performance curve intersect.

But if the situation involves pumps in series, what will the system curve be a plot of? Is it flow rate and the total pump head?

Homework Equations

The Attempt at a Solution

The system curve is derived from totaling up all of the friction losses in the piping and fittings for different flow rates. It's going to be the same regardless of how many pumps there are. The pump curve is superimposed on the system curve to determine the operating point for the piping system.

If you know the performance of an individual pump, performance for multiple pumps in parallel or in series can be determined according to this article:

http://www.engineeringtoolbox.com/pumps-parallel-serial-d_636.html

 

[theone]

The system curve is derived from totaling up all of the friction losses in the piping and fittings for different flow rates. It's going to be the same regardless of how many pumps there are. The pump curve is superimposed on the system curve to determine the operating point for the piping system.

If you know the performance of an individual pump, performance for multiple pumps in parallel or in series can be determined according to this article:

http://www.engineeringtoolbox.com/pumps-parallel-serial-d_636.html

thanks. Also, is there a way for me to estimate the pump run out Qmax and the maximum efficiency.The function I have for the pump curve requires these values