[abi111]

This question just popped in my head but i couldn't reconcile the contradiction. Assuming water ( incompressible assumption) flow (developed flow) through a horizontal pipe with a constant diameter, by some head gradient driving force (neglecting head losses) between the pipes edges. looking at 2 arbitrary cross sections along the pipe and applying bernoulli's principle i can conclude that non of the energy components change (pressure,velocity,gravitational potential). but i also been taught that fluid flows from high to lower head, but those two arbitrary cross-section appear to have the same head...or i got something wrong?

Thanks for the help!

[FMDenaro]

a simple 1D model equation for your case:

du/dx= 0 (continuity)

u*du/dx + (1/rho)*dp/dx = 0 (momentum)

therefore u=constant is a solution that satisfies the dp/dx=0 constraint.

In a real flow pipe, the condition dp/dx<0 is conseguent to the balance with viscous forces.

[abi111]

I still didnt quite get it. By just looking at these two cross sections, if the pressure gradient is 0 aand its horizontal what is the flow driving force ?

[FMDenaro]

Originally Posted by abi111

I still didnt quite get it. By just looking at these two cross sections, if the pressure gradient is 0 aand its horizontal what is the flow driving force ?

if you assume no energy dissipation (inviscid flow) the equations simply say that if a flow already has a constant velocity (and constant kinetic energy), the energy is conserved and the flow moves indefinitely without pressure gradient.