QS Energy Inc (QSEP)

[Myrka]

Where Delta p is the pressure drop from one end of a pipe section to another, mu is dynamic viscosity, L is length of the pipe, Q is volumetric flow, and r is the radius of the pipe. The total Delta P is the sum of Delta P's for each section; if you lower mu for a section then the Delta P for that section is redcuced, and the total Delta P for the full system is reduced.

This is where I disagree. The law of conservation of mass applies to this closed system and the pressure drop used to compute the power required to pump the fluid through this length of pipe has to be derived from the system as a whole. The Delta P's for each section should be replaced by Delta P for the system.

Look at the equation: V = velocity in pipe = Q (flow rate through pipe) / A (pipe cross section area)
In a closed system (pipeline) the A is constant and the Q on entry is equal to the Q on exit (conservation of mass), therefore the velocity in the pipe is unchanged.