piezometric head

Hello together,

my professor just failed me in an oral exam. It was shwn a graph of a piezometric headline that increased. I said that its because of an increase of the diameter of the tube. He said afterwards:

Piezometric head can only increase as a result of energy being added to the system (e.g. a pump); but it is never a sustained increase, but a vertical line. A change in diameter changes the slope... but it is always a negative slope (going down) as there will always be losses. The situation shown in the figure is impossible.
My question now is: Is that really true what he says? If the diameter increase, the hydraulic headline could also increase or not even if there are losses?
Exactly like in this picture: http://www.gs-harper.com/images/hydraulics/energy2.gif

Thank you very much for your help.