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 ?
About the author
Jon F . Monsen , PhD , PE , is a control valve technology specialist with more than 45 years of experience in the control valve industry . He has lectured nationally and internationally on the subjects of control valve application and sizing . Jon currently hosts a website , www . Control-Valve-Application- Tools . com where he freely shares articles , training and professional development materials , and Excel worksheets that might be of interest to those who use or specify control valves . He can be reached at cvapptools @ gmail . com .
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 : ∆P choked
. 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 :
T ´
T
P Buck
= 0.61121 ´ e
( 18.678 -
234.5 257.14 + T
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
(
FLOW , Q
Q ∝ ∆P
Non-Choked Flow
Figure 1 . Liquid flow vs . pressure drop in a control valve the input of chemical properties that are not always readily available . The simplest calculation method is the Antoine equation :
log 10
( P ) = A -
B C + T
∆P choked
Q Constant
Former terms for choked pressure drop :
∆P T
= Terminal Pressure Drop
∆P ( Allowable )
∆P ( Max )
∆P ( Crit .) or ( Critical )
Choked Flow
∆P
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
14 Valve World April 2023 www . valve-world . net