I guess I am having a hard time seeing what that manometer is doing.
I assume that as fluid moves in at 1 it causes a displacement of the manometer fluid by some distance h.
Now, are we assuming that the pressure is uniform throughout the diameter of the pipe? I think we are, otherwise, I do not see how the manometer reading would be a reflection of the pipe pressure.
So, that being said, the pressure increase on the left side of the manometer is p1 and the pressure decrease on the right side of the manometer is p2.
So, if the pressure in the pipe=p1=the pressure at some depth h into the manometer and the same for p2, then we have:
[itex]p_1=\rho_mgh[/itex] and [tex]p_2=\rho_1gh[/itex]