Frictional Loss Vs Viscosity

At high Reynolds Number, the flow is such that the velocity gradient produces turbulence near the boundary. The bulk of the flow is largely lacking in turbulence. As the velocity increases further, the velocity gradient near the walls steepens and the cross-section of the bulk flow widens, so the Friction Factor, which relates the pressure drop to the velocity goes down.

In the water-air comparison, viscosity is in the divisor of the Reynolds Number, so lowering the viscosity increases the Reynolds Number.

In laminar flow in pipes, the density term in the Reynolds Number is cancelled-out by the density term elsewhere in the Darcy-Weisbach equation, so viscosity rules, and pressure drop will increase with viscosity to the power of 1.0. Increasing the Reynolds Number into turbulent flow increases the pressure drop in accordance with the equation you have stated; this time, viscosity leads to the power of 0.75 .

Not bad for a polooceman, eh?