# Control valve Q&A

#### Q: When calculating the required control valve Cv for an application, one of the required inputs is the vapor pressure of the liquid. I have seen tables of vapor pressure vs temperature for water but not for any of the other liquids that I encounter. Can you suggest a method for calculating the vapor pressure of a liquid?

A: The requirement for liquid vapor pressure when sizing a control valve for liquid flow is because the flow of a liquid through a control valve as the pressure drop increases, behaves as shown in Figure 1. At first, when the pressure drop across the valve is low, the flow increases in a linear manner in proportion to the square root or the pressure differential across the valve (green line in Figure 1.) At some point, as the pressure across the valve increases, the pressure at the restriction where throttling takes place drops to the vapor pressure of the liquid, and the liquid begins vaporizing. When that happens, further increasing the pressure drop across the valve causes more of the liquid to vaporize, but the flow does not increase, and we say, “flow is choked” (red line in Figure 1.) The IEC/ISA valve sizing equation standards refer to the pressure drop across the valve at the point where the flow chokes as: ∆Pchoked. Prior to the current IEC/ISA versions of the standards, no name was given to the point at which flow became choked, so valve manufacturers coined their own names for that point. Some of these former names are shown in the figure.

As you mention, there are tables of water vapor pressure vs temperature. Using the vapor pressure of water for water-based chemicals will nearly always give conservative values of the “choked pressure drop” when sizing control valves. There are several equations in the literature for calculating the vapor pressure of water. One very accurate one is the Buck equation:

Where T is in degrees C, and P is in kPa. The calculation can be done by hand or programmed into a programmable calculator or into an Excel sheet.
For many other chemicals, published vapor pressure data is scarce.
There are several calculation methods for liquid vapor pressure, but most are too complex for hand calculations, and require the input of chemical properties that are not always readily available. The simplest calculation method is the Antoine equation: The only problem is finding comprehensive tables of Antoine constants. Any set of Antoine constants (Constant A, B and C) is only valid for a limited range of temperatures, and many of the tables of constants I have seen only include constants for one temperature range. Some tables, which only include one set of constants, do not tell you what the valid temperature range is, which can lead
to unreliable calculation results. The best database that I have found that is available at no charge (at least at present) is the
NIST (National Institute of Standards and Technology) Chemistry WebBook, which can be found at: https://webbook.nist.gov/chemistry/ The Antoine constants given in the WebBook are for temperature in kelvins and return a vapor pressure in bar. You can carry out the calculations by hand, or you can construct an Excel® worksheet to make the calculations.
As an alternative, you can use the Excel
sheet I have made, which lists step-by-step instructions for finding the Antoine constants in the NIST Chemistry DataBook. It converts your temperature, which you most likely know in degrees F or C, to kelvins which are required by the NIST Antoine formula, and it displays the calculated vapor pressure in bar and psia. You can download the Excel sheet at no charge at: www.control-valve-application-tools.com 