I bring this up occasionally to either:

  A.  Dispell a popular myth

  or   B.  Eliminate a big misunderstanding on my own part.

  I'll accept either outcome but so far no one has addressed the issue. Based on everything I (think I ) know about pumps:

  Assumeing a constant pump speed, when the thermostat closes and head pressure goes up,  power required to drive the waterpump does NOT go up.  It actually goes DOWN.  Reason:  There is less mass being accelerated (energy) at lower flow rates.  In the extream example  (zero flow) the same water in the pump housing is being spun around at a constant velocity which requires no energy.  Of course there are losses in the pump so the energy consumed is not zero.

  This argument applies ONLY to centrifugal pumps (of which automotive waterpumps are an example) and not positive displacement types (like oil pumps).

  OK, somebody shoot this argument down and educate me.