[Tom Hill]

I think your formulation is correct. I misplaced the left square bracket. Sorry 'bout that.

I like your suggestion for using goal seek in Excel. However, if one has multiple pipes within the same hydraulic system within the same spreadsheet, then the manual keystrokes involved in performing many goalseek operations can become tedious.

I sometimes have need of performing this same calculation on "gunbarrel" crude oil pipelines, in which the temperature, and hence the fluid viscosity, is changing continuously down the length of the pipeline. In this case, the pipeline is broken into many contiguous segments for pressure drop calculations. I find that the iterative approach, although more messy numerically, is actually quicker than using multiple goalseek operations.