If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli’s equation may be written
H = p/ρ + z + q2/2g = P/ρ + h,
(8)
where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.
In particular, for a jet issuing into the atmosphere, where p = P,
q2/2g = h − z,
(9)
or the velocity of the jet is due to the head k − z of the still free surface above the orifice; this is Torricelli’s theorem (1643), the foundation of the science of hydrodynamics.
27. Uniplanar Motion.—In the uniplanar motion of a homogeneous liquid the equation of continuity reduces to
| du | + | dv | = 0, |
| dx | dy |