One must be very careful when interpreting valve behavior on the field or designing a new installation. Indeed, the characteristics presented above are ideal and not the actual one. Once in the circuit, the characteristic will actually vary depending on the pressure drop through the valve compared to the total pressure drop of the line.
This actually shows that there is only 2 basic types of valve : linear or exponential, with each type that can evolve to one of the standard characteristics when the valve is mounted in series of the circuit - be careful the characteristics is different if the valve is mounted in parallel
A linear valve is in the field, once installed on the line, almost
never linear. It will be linear only if the totality of the pressure
drop of the line is created by the valve which is not practically
often true. It must however be noted that, when the valve represent
only few percent of the total pressure drop, the characteristic will
actually be the one of a quick opening valve.
Figure 1 : Change of characteristics of a linear valve as a function of alpha = pressure drop through the valve / total pressure drop in the pipe network considered, at maximum flow.
For the limit condition alpha = 1, which can be considered as the valve alone, we find the linear charactertistic presented above. If one wants to keep a linear characteritics once the valve is in series in a pipe with other element, the pressure drop represented by the valve will have to be at least 2/3 of the total pressure drop, which may not be practical. As mentionned, the practice will be more to have a valve representing around 1/3 of the total pressure drop, which means that its behavior will not be ideal.
An exponential valve will show a behavior of equal percentage only
if it creates the majority of the pressure drop in the line. If it
creates few pressure drop, the characteristics will flatten and
approach a linear characteristics.
Figure 2 : Change of characteristics of an exponential valve - or equal percentage - as a function of alpha = pressure drop through the valve / total pressure drop in the pipe network considered, at maximum flow.
For the limit condition alpha = 1, which can be considered as the valve alone, we find the exponential charactertistic presented above.
You can access the Excel files having been used to generate the graphs here : Link