Stream-line, A path tangent to flow at all of its points.
Streak-line, The path containing all of the particles that have passed through a certain location.
Path-line, The path along which a particular fluid particle has passed.
Steady Flow, Flow velocity and direction do not change with respect to time at a given location. For steady flow stream-lines, streak-lines, and path-lines are all identical.
Bernoulli’s pressure is related to the conservation of energy as applied to a particle passing through a streamline. When expressed as below, it states that the energy of a particle is conserved as it passes along a streamline. In particular, it relates a pressure times volume term (I’m imagining this as potential for work to be done if the particle were to be imploded by the ambient pressure), the kinetic energy, and the gravitational potential energy. In this expression, each term has units of energy.
$$ \frac{mp}\rho+\frac 12mv^2+mgz=U_{pV}+U_{kinetic}+U_{gravitationa\>potential}=c $$
The typical form expresses a quantity that is conserved along streamlines. To apply this simplified expression, the assumptions of steady, inviscid, and incompressible flow across a streamline must be applied. It has terms as follows.
(1) Static Pressure (actual thermodynamic pressure) (2) Dynamic Pressure (3) Hydrostatic Pressure
$$ p+\frac 12\rho v^2+\gamma z=c $$
This final form gives a very physical interpretation to each term. (1) the pressure head, the height of liquid required to produce $p$ (2) the velocity head, the vertical distance the fluid must fall to reach velocity $v$ from rest (3) the elevation head, relating to the potential energy of the particle, all summing to (4) the total head. In this form, each term has units of energy per weight, of units length.
$$ \frac p\gamma+\frac{v^2}{2g}+z=c $$