rate to be directly proportional to the valve travel (Δq/Δx equals a constant) or in terms of the inherent valve characteristic, f(x) = x.
An equal percentage valve starts initially with a slow increase in flow rate with valve position which dramatically increases as the valve opens more.
The term equal percentage for a slow opening characteristic curve may at first be confused with the description of a linear characteristic curve.
However, for an equal percentage valve, Δq/Δx at any stage, is proportional to the flow rate q at that moment. This is in contrast with a linear characteristic for which Δq/Δx is constant.
That Δq/Δx is proportional to q, may be rephrased as Δq/q is proportional to Δx. This means the percentage change Δq with respect to the current flow rate q (that is (Δq/q)×100), is equal at every valve travel position x for the same change in valve travel Δx, hence the term ‘equal percentage’.
The inherent valve characteristic for an equal percentage valve is exponential in nature and is normally given by valve manufacturers in the form
where R is a constant for the valve.
The exponential behaviour of an equal percentage valve is explored further in Below Example
An equal percentage valve delivers 8 gpm of water when the valve is 50% open (x=0.5). When the valve is 60% open (x=0.6), the flow rate increases to 16 gpm. Estimate the flow rate through the valve when it is 70% open (x=0.7).
Assume that the pressure drop across the valve remains constant.
When the valve opens from 50% to 60%, the flow rate changes from 8 gpm to 16 gpm. This means that Δq is 8 gpm. when Δx is 0.1 and q = 8.
Therefore Δq/q = 8/8 = 1 and the percentage change is 100% (Δq/q×100) at x = 0,5.
For an equal percentage valve, the percentage change in flow rate when the valve opens from 50% to 60%, (Δx = 0.1) must be equal to the percentage change in flow rate when the valve opens from 60% to 70% (the same Δx of 0.1).
Therefore Δq/q at x = 0.6 must also be 1 (or 100%) for Δx = 0,1. But q is 16 gpm. when the valve is 60% open and we conclude that Δq should be 16 gpm. when the valve opening changes from 60% to 70%.
The flow rate through the valve is therefore approximately 32 gpm. at 70% valve opening.
Installed flow characteristic
When valves are installed with pumps, piping and fittings, and other process equipment, the pressure drop across the valve will vary as the valve travel changes.
When the actual flow in a system is plotted against valve opening, the curve is called the installed flow characteristic and it will differ from the inherent valve characteristic which assumed constant pressure drop across the valve.
When in service, a linear valve will in general resemble a quick opening valve while an equal percentage valve will in general resemble a linear valve.
Typical application of quick opening, linear and equal percentage valves
i) Quick opening valve
- Frequent on-off service.
- Used for systems where ‘instant’ large flow is needed (safety or cooling water systems).
ii) Linear valve
- Liquid level and flow control loops.
- Used in systems where the pressure drop across the valve is expected to remain fairly constant.
iii) Equal percentage valve (most commonly used valve)
- Temperature and pressure control loops.
- Used in systems where large changes in pressure drop across the valve are expected.