Antoine Equation 
The Antoine Equation is a vapor pressure equation and describes the relation between vapor pressure and temperature for pure water between 0°C and 373.946°C. [Wikipedia] For T in Kelvins and P in kPa:
273.150 < T ≤ 373.150: A = 16.5699, B = 3984.92, C = −39.724 Antoine(T) = exp(A − B / (T + C)) For temperatures above the critical temperature (373.946°C / 647.096K), where water is a superfluid, the increase in vapor pressure appears essentially linear† with the same slope (i.e. dP/dT ≈ 235.88 kPa/°C). This behavior appears consistent with the Ideal Gas Law and statements that supercritical water behaves like an ideal gas. Now if we define Tc = 647.096 K, we can write
P(T ≤ Tc) = Antoine(T)
Here I've plotted the vapor pressure of a fixed volume of water (in red) and the pressure of a fixed volume of air (in green) between 0°C and 373.946°C for comparision.
It was this graph that led me to ask the question “What if I replace all the air in a fluidyne with water and operate it above the critical temperature?” I decided to call such an engine a “hydrodyne” to avoid confusion with fluidynes.
For readers who have no experience of supercritical fluids, this video shows a fluid being heated through its critical point to become a superfluid, and then cooling to change back to a fluid. The video shows Xenon, but water would look exactly the same.
The formula for the difference in fluid levels within a Utube manometer is h = (Pa − Po) / (g · ρ), and when I used...
Pa = 21718 kPa applied pressure, ...I obtained h ≈ 2.2 km, as the head of a hydrodyne pump operating at Tc.
† Data from S. L. Rivkin and T. C. Akhundov plotted in “Steam Tables” by Keenan, Keys, Hill, and Moore. The authors cited “Teploenerg.”, No. 1, 5765 (1962), and No. 9, 6668 (1963).
