The equations derived below are based on the following principles. The equations below are for two pipes but can be extended to n pipes.

For pipes in series:

Qr = Q1 = Q2

where Q = flow, r refers to the resulting pipe, and 1 and 2 refer to the pipes being removed.

hr = h1 + h2

For pipes in parallel:

Qr = Q1 + Q2

and

hr = h1 = h2

As long as the units are consistent, then any appropriate units can be used. For example, if the diameters are in feet, then the resulting diameter will be in feet.