Figure 4 shows an inverted pilot-operated valve designed for large flows. Both the pilot and main poppets are exposed to system pressure. Spring force keeps the pilot poppet on the seat. When system pressure rises, the pilot poppet lifts and exposes the main poppet’s actuator A3 to p1 at the set point. In the main section, stem diameter d3 is much less than seat diameter d4. Such a design increases the seating force in parallel with rising system pressure. Therefore, the seat sealing force remains high until the pilot valve causes the main poppet to lift.

When the pilot opens and fluid flows into the main actuator region, exposing it to system pressure, the actuator area exceeds the main seat area. In addition, the net force against the spring lifts the main poppet. The pilot closes upon restoration of set pressure force balance, which then closes the main section (a small orifice aids the closing motion by bleeding the spring zone, which also acts as a damping chamber).

When the pilot opens and allows flows, it fills the zone under the main actuator and lifts the main poppet. After the lift is complete, the fluid leg between the pilot seat and the actuator becomes a dead leg. The pressure throughout this zone now sits at p1. Therefore, internal components of the pilot see system pressure. The pilot’s force balance, caused by the ratio of areas A1/A2, now changes from the preflow conditions to affect the closing pressure. Here, the pilot closing pressure is lower than its opening pressure.

The force balances at the pilot on opening are: F1o + p1o A1 = p1o A2;

On closing they are: F1c = p1c A2.

Because spring force in the pilot remains nearly constant: F1o = F1c

Also, the closing pressure existing in the pilot is: p1c = p1o (A2 A1)/A2 = p1o [1 ‒ (d1/d2)2].

The blowdown strongly relates to the squares of the poppet dimensions, as in the previous example.

A brief history on relief valves

The relief valve was reported to have been used (or perhaps invented by) James Watt to prevent boiler explosions in his early pressure-driven steam engines used for driving locomotives. The original valves were placed close to the engineer’s cabin where the fireman would shovel coal to feed the fire. Early engines had no sophisticated feedback systems to regulate boiler pressure except the relief valve. When the boiler pressure would reach (or exceed) the valve’s set pressure (say 50 psi), it would open and blow off.

Typically, early valves consisted of a conical seated poppet vertically closing the relief port. The closing force was provided by a weight or leaf spring (see figure). Due to blowdown, the head of steam would drop considerably (say 20 psi) and the engine would lose force or torque at the load. The solution was to shovel more coal and rebuild the steam head. This meant extra work for the fireman, so to avoid having to perform more work, he might use ropes to tie down the relief valve’s poppet to prevent it from moving. The result was a boiler explosion.

To prevent intervention from the fireman, the relief valve was moved away from the cabin area — far from his reach. Later locomotives placed the valve near the front of the vehicle. The cabin area typically at the rear of the locomotive was now well away from dangerous hands.

Bob Archer is a consulting mechanical engineer in Woodbury, N. Y. For more information, contact him at