In essence a valve simply functions as a restriction in a flow line, with flow areas A1 and A2 and pressure differential p1 – p2, as shown in Below Figure.
The below mentioned flow equation describe the flow rate of a fluid through a valve. The form of this equation used by valve suppliers is:
where C is the valve flow coefficient, q the flow rate of the liquid through the valve, Δp = p1 – p2 the pressure difference across the valve and G the specific gravity (relative density) of the fluid.
For historical reasons, the flow rate q, in above Equation, is measured in gallons per minute (gpm) and the pressure difference Δp, in pounds per square inch (psi). Valve coefficient, C is fundamentally determined by the effective flow areas A1 and A2 of the valve.
The value of C will therefore change from zero (when the valve is fully closed) to a maximum value (when the valve is fully opened).
Assume that a valve is opened a certain amount x (with x denoting the fractional valve opening or valve travel between 0 and 1 ( 0% to 100%)).
The flow rate q, of the liquid (we will assume water with G = 1 ), flowing through the valve, is now allowed to increase until the pressure Δp across the valve, reaches a maximum of say 4 psi (assumption).
We may conceivably expect the results depicted in Below Figure, shown for x = 0 (valve fully closed), x = 0.25 (valve one quarter open), x = 0.5 (valve half open), x = 0.75 (valve three quarters open) and x = 1 (valve fully open).
The special value of C that corresponds to the valve fully open, is called the characteristic flow coefficient of the valve and denoted by CV.
The characteristic flow coefficient CV, is an extremely important parameter of a specific valve, and is used extensively when choosing the correct valve for a certain application.
For the valve characteristics in Above Figure, for example, CV = 40.
The way q varies when the pressure is kept constant (normally the rated pressure drop across the valve for maximum flow) and the way C changes as the valve opening x changes, may be available for a particular valve, provided by the manufacturer in tabulated format.
For example, the graph of q (with Δp = 4 psi) as a function of x and the graph of C as a function of x, are shown in Below Figures (a) and (b) respectively, for the flow characteristics of our hypothetical valve, depicted in above Figure.
The different values of C obtained as the valve travels through its full range (or stroke as it is also called) from closed to open, is generally expressed in the following format, by valve manufacturers:
C = CV×f(x) …Equation 1
where f(x) is called the inherent valve characteristic of a particular valve. For example, from the graph of C, in Above Figure (b), we could express C as:
C = 40x
and we conclude therefore from Equation 1, that CV = 40 and f(x) = x.
The function f(x) varies from 0 (valve closed with x equal to 0) to 1 (valve fully open with x equal to 1). The inherent valve characteristic f(x), is intimately linked to the flow rate q through a valve, as we can see if we replace C with CVf(x) (as per Equation 1), to rewrite the valve Equation in the form:
It is indeed clear from above Equation that if we keep Δp constant (for a given liquid, G is constant as well), q and f(x) will have exactly the same shape.
A valve for which f(x) = x, is called a linear valve because the flow rate will change linearly with valve opening x. Depending however on the valve design, f(x) may also reflect quick opening or equal percentage (slow opening) characteristics, as shown in Below Figure.
The flow behaviour of a valve is dictated by the manner in which the flow areas A1 and A2 changes with valve position and therefore by the style and design of the valve trimming and in particular the design of the valve seat and closure member (plug).
The quick opening flow characteristic provides for maximum change in flow rate at low valve travels with a nearly linear relationship. Additional increases in valve travel gives sharply reduced changes in flow rate.
The linear flow characteristic curve allows the flow 