Several approximate valve capacity factors (Cd) for di erent control valve types are shown here36, assuming full-area (not reduced-port) trim, a wide-open position, and diameter measured in inches:

To calculate the approximate Cv for any valve, all we need to do is square that valve’s pipe diameter (in inches) and multiply by the valve type’s relative flow capacity (Cd):

Cv ≈ d2Cd

Based on the figures in this table, for example, we may predict that a segmented ball valve with a pipe size of 3 inches will have a flow capacity (Cv ) of approximately 225, or that a single-port cage-guided globe valve with an 8 inch pipe size will have a Cv of approximately 960.

As you can see from a comparison of Cd values, a no-o set butterfly valve has nearly 4 times the flow capacity of a single-ported contoured-plug globe valve of the same pipe size (Cd = 40 versus Cd = 11). This makes butterfly valves advantageous in applications where large flow capacities must be achieved at minimal cost, such as in air handling (HVAC) systems for commercial buildings and combustion air controls for large industrial burners.

At first glance this may seem to make larger Cd valve types the superior choice for control valve applications, yielding the greatest Cv values for the smallest pipe sizes. However, there are other factors to consider such as ease of maintenance, noise and cavitation abatement, characterization, and valve seat leakage. For these reasons some of the lowest-Cd valve types (e.g. globe valves) remain popular choices for industrial control applications even though they require larger pipe sizes to achieve the same amount of flow compared to other valve types (e.g. ball valves).

27.13Control valve characterization

Control valves are supposed to deliver reliable, repeatable control of process fluid flow rate over a wide range of operating conditions. As we will soon see, this is something of a challenge, as the rate of fluid flow through a control valve depends on more than just the position of its stem. This section discusses the problem of control valve behavior in real process applications, and explores the concept of characterization as a solution to the problem.

36Source for Cd factors: Chapter 4.17: Valve Sizing of B´ela Lipt´ak’s Instrument Engineers’ Handbook, Process Control (Volume II), Third Edition, page 590.

27.13.1Inherent versus installed characteristics

When control valves are tested in a laboratory setting, they are connected to a piping system providing a nearly constant pressure di erence between upstream and downstream (P1 − P2 = constant). With a fluid of constant density and a constant pressure drop across the valve, flow rate becomes directly proportional to the valve’s flow coe cient (Cv ). This is clear from an examination of the basic valve capacity equation, if we replace the pressure and specific gravity terms with a single constant k:

s

Q = Cv

P1 − P2

Gf

(If pressures and specific gravity are constant . . .)

Q = kCv

As discussed in an earlier section of this chapter (see section 27.12.1), the amount of “resistance” o ered by a restriction of any kind to a turbulent fluid depends on the cross-sectional area of that restriction and also the proportion of fluid kinetic energy dissipated in turbulence. If a control valve is designed such that the combined e ect of these two parameters vary linearly with stem motion, the Cv of the valve will likewise be proportional to stem position. That is to say, the Cv of a “linear” control valve will be approximately half its maximum rating with the stem position at 50%; approximately one-quarter its maximum rating with the stem position at 25%; and so on.

If such a valve is placed in a laboratory flow test piping system with constant di erential pressure and constant fluid density, the relationship of flow rate to stem position will be linear. With constant pressure drop, the flow rate through any valve is directly proportional to that valve’s Cv , and with a “linear” valve design the Cv (and therefore the flow rate as well) must be directly proportional to stem position:

Stem position (%)

27.13.2Control valve performance with constant pressure

First, let us imagine a control valve installed at the base of a dam, releasing water from the reservoir. Given a constant height of water in the reservoir, the upstream (hydrostatic) pressure at the valve will likewise be constant. Let’s assume this constant upstream pressure will be 20 PSI (corresponding to approximately 46 feet of water column above the valve inlet). With the valve discharging into the air, downstream pressure will essentially be zero. This set of upstream and downstream conditions guarantees a constant pressure drop of 20 PSI across our control valve at all times, for all flow conditions:

Downstream