The bottom portion of the pneumatic valve has an orifice that separates the upstream and downstream flows. A tapered plug, capable of blocking the orifice in varying proportion, is attached to a stem that is connected to a diaphragm in the top portion of the valve. A spring restricts the movement of the stem. When air pressure above the diaphragm forces the stem to move downwards, the plug starts reducing the aperture of the orifice and eventually blocks the orifice at high air pressure. As a result the flow of fluid through the orifice is gradually decreased from “FULL FLOW” to “NO FLOW” condition. As the air pressure at the top of the diaphragm is released, the plug moves back to its original position resulting in full flow of fluid. This is called “FAIL OPEN” valve (Fig. VII.9(a)) because when the control signal fails to provide enough air pressure, the valve remains in fully open condition. Similarly the “FAIL CLOSED” valve is shown in Fig VII.9(b) where the shape of the plug is opposite.

The dynamics of a typical pneumatic valve is usually second order in nature. The position of stem (or plug) determines the size of the aperture of the orifice that consequently determines the fluid flow rate. The position of the stem is determined by balancing all the forces acting on it. These forces are:

•  Force exerted by the compressed air at the top of the diaphragm

•  Force exerted by the spring

•  Force exerted due to friction between stem and the valve packing

Hence,

(VII.1)

Where, pressure exerted by the compressed air, area of the diaphragm, displacement of stem, Hooke's constant of the spring, coefficient of friction between stem and the packing, mass of stem and its attachments.
Rearranging the eq. (VII.1), we obtain

(VII.2)