Liquid Critical Pressure Ratio Factor Ff

Tags: Pressure Valve Sizing

Liquid critical pressure ratio factor, abbreviated as \(F_f\), a dimensionless number, is the ratio between pressure in vena contracta and the pressure at the maximum effective choke pressure drop across the valve.  Or you could say it describe the behavior of a liquid when it is expanded from a high pressure state to a lower pressure, specifically when approaching its critical point.   The critical point is a thermodynamic state at which the liquid and vapor phases of a substance become indistinguishable.

The critical point at which the liquid and vapor phases are indistinguishable

• \(F_f\) < 1  -  It indicates that the initial pressure is significantly below the critical pressure of the liquid.  In this case, the liquid will typically behave as a subcritical fluid and will undergo a normal phase change (vaporization) as it expands to the lower pressure.  There won't be any significant influence from the critical point.
• \(F_f\)≈ 1  -  It suggests that the initial pressure is near the critical pressure of the liquid.  As the liquid expands, it approaches the critical point, and its properties become more affected by critical phenomena, such as enhanced compressibility, diverging densities, and changes in specific heat capacity.  The behavior becomes transitional between subcritical and supercritical.
• \(F_f\) > 1  -  It indicates that the initial pressure is above the critical pressure of the liquid.  In this case, the liquid will behave as a supercritical fluid as it expands, and its properties will be significantly influenced by the proximity to the critical point.  Supercritical fluids often exhibit unique properties, such as high compressibility, low viscosity, and enhanced solubility.

The \(F_f\) is particularly relevant in the study of phase transitions and the behavior of fluids near their critical points.  It helps determine whether a fluid will undergo a typical phase change or exhibit critical behavior as it is expanded or subjected to changes in pressure

 

Liquid Critical Pressure Ratio Factor \(F_f\) Formula
\(\large{ F_f = \frac{ p_i }{ p_c }   }\)     (Liquid Critical Pressure Ratio Factor \(F_f\)) \(\large{ p_i = F_f \; p_c    }\) \(\large{ p_c = \frac{ p_i }{ F_f }   }\)
Symbol	English	Metric
\(\large{ F_f }\) = Liquid Critical Pressure Ratio Factor \(F_f\)	\(\large{dimensionless}\)
\(\large{ p_i }\) = the initial pressure of the liquid (usually in a high-pressure state)	\(\large{ \frac{lbf}{in^2} }\)	\(\large{ Pa }\)
\(\large{ p_c }\) = the pressure at the critical point of the liquid	\(\large{ \frac{lbf}{in^2} }\)	\(\large{ Pa }\)