[Fluids] Does pressure loss drive velocity drop in a pipe ?

Let's talk about real - incompressible - fluids.

Let take an horizzontal, section constant, pipe so that static pressures (\rho g h) are equals (h1 = h2).

At each extremity atmospheric pressure is the same P0.

Let injects water at the volumetric flow rate of 2500 L/h in the pipe inlet .

I expect a pressure loss proportional to the square of the velocity and proportional to the length of the pipe .

Since the only pressure existing here is the kinetic one (\rho v*v / 2) I expect a diminution of that kinetic pressure and then the diminution of the average velocity at the outlet.

Physically I imagine the average velocity decreasing under the effect of pipe walls friction.

In other words the conservation of the volumetric flow rate (and mass flow rate) cannot be applied in real fluids .

Is this reasoning correct or not at all ?

submitted by /u/kiodos
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