The transfer function between stem position and the actuating pressure is

(VII.3)

which is indeed a second order dynamics. However, the movement of stem is always aided by proper lubrication which eventually reduces its coefficient of friction. Moreover, mass of the stem and its attachments are very small compared to the Hooke's constant ( and ) . Hence the dynamics of pneumatic valve can be neglected and movement of stem can be regarded as instantaneous in response to change of air pressure.

(VII.4)

Flow rate of non-flashing liquid is given by

(VII.5)

Where, flow rate of liquid, pressure drop across the upstream and downstream side of the valve, density of liquid, flow coefficient that depends on valve size, flow characteristic curve of the valve which is a function of the stem position .

The shape of the flow characteristic curve depends on the shape of plug of the valve. There are five major types of flow characteristics used for designing the valve:

•  Linear,

•  Square root,

•  Equal percentage,

•  Hyperbolic,

•  Quick opening,