In Bernoulli equation, the only term which corresponds to what one usually calls "pressure" is $p$, the other are still pressures dimensionally but their meaning is linked to kinetic and potential energy per unit volume. Nevertheless I get confused especially for the term $\rho g h$. Can it be seen as a pressure due to weight, similarly to Stevin law, but for hydrodynamics?
My guess would be a clear no because Stevin law in only valid in hydrostatics, but consider, for istance this example, where a liquid (say water) is flowing in the venturi meter.
To read the manometer and calculate pressure difference I have to take into account not only the height $h$, but also the difference $z_2-z_1$ between the two points in the tube.
But, since in the manometer the consideration are about hydrostatics that means to consider a further pressure difference given by $\rho g (z_2-z_1)$, which reminds Stevin law for the height difference $z_2-z_1$. But Stevin law is valid iff the fluid is static, which is not here.
So does a fluid in motion have the same "effect" in terms of pressure caused by weight, than a situation where the fluid is static?
The question is also: is there a pressure difference between point $1$ in the center of the tube and a point on the same section but very close to the tube boundary? (Does the weight of the fluid between $1$ and the boundary create a pressure difference between these two points?)