The control valve is where the plant's intentions become steam flow — and the most routinely mis-sized component in Indian steam systems, because it is so often bought by pipe size. This lesson is the working selection method: capacity by Kv, the critical-drop check, the characteristic choice, and the actuator — finished with a real selection for the practice plant's jacketed vessel.
Kv: capacity, honestly stated
A valve's Kv is its flow coefficient — the capacity of the open valve at a stated travel (Kvs fully open). For dry saturated steam the working formulas, with pressures in bar absolute and flow in kg/h, are:
Sub-critical (P₂ > 0.58 P₁): ṁ ≈ 12 · Kv ·
√(ΔP · P₂)
Critical (P₂ ≤ 0.58 P₁): ṁ ≈ 6 · Kv · P₁
The second line is the famous one. Drop the downstream pressure below about 58% of the upstream and the steam reaches sonic velocity in the valve throat — choked flow (the glossary term the thermocompressor lesson also leans on). Past that point, lowering P₂ further changes nothing: capacity depends on P₁ alone. This is why a valve venting to atmosphere from 10.5 kg/cm²g cannot be "helped" by a bigger downstream pipe, and why deep-cut PRVs roar (lesson C3) — the throat is running at the speed of sound.
The worked selection
The practice plant's jacketed vessel (lesson A10): peak duty 760 kg/h. Supply after the PRS: 3.5 kg/cm²g = 4.45 bar a. Full-load jacket pressure: 3.0 bar a (133 °C — still 43 °C of driving ΔT over the 90 °C product end-point).
1. Critical check: 0.58 × 4.45 = 2.58 bar a. P₂ = 3.0 > 2.58 —
sub-critical; use the first formula.
2. Kv required: Kv = 760 ÷ (12 × √(1.45 × 3.0)) = 760 ÷ 25.0 ≈
30.
3. Select: next standard body, Kvs 40 — running at ~76% of capacity at
peak, which is healthy (a valve sized to run at 95% has no reserve; one at 30% controls
on the bottom of its travel).
4. Sanity-check the turndown: holding load ~70 kg/h needs Kv ≈ 2.8 —
7% of Kvs. A 14:1 working range is real work: it demands an equal-percentage
characteristic and a good positioner, and it is the argument for not adding "just in
case" margin — at Kvs 63 the same holding load sits at 4% of travel, where no valve
controls well. Note the DN: a Kvs-40 globe valve is typically DN40/50 — smaller than
the line. Correct looks small (lesson C3's rule, again).
Characteristic and actuator
Characteristic — how Kv grows with travel. Equal percentage (each increment of travel multiplies flow by the same factor) is the default for temperature control: it is gentle at small openings, and its rising gain neatly offsets the falling process gain as a heater approaches temperature. Linear trim suits pressure control and duties holding near one flow. Actuator — overwhelmingly the pneumatic diaphragm, with a positioner (which turns the controller's signal into an enforced valve position, defeating friction and pressure forces) now standard rather than optional. Choose the failure action deliberately: heating duties fail closed (air failure stops the heat — safe), while some duties (a boiler feed valve) must fail open. Say it on the datasheet; it is the one specification nobody can infer later.
- Size from duty, never from pipe: Kv from the formulas, next Kvs up, and expect a body one or two DN below the line.
- A hunting temperature loop on a valve that runs below ~10% travel is oversized trim, not bad tuning. Check the running Kv before touching the controller.
- Always run the critical check — a valve that has gone choked at low load behaves differently than its sub-critical sizing predicts.
- Record fail action, Kvs, characteristic and positioner on the equipment card; these four facts save every future troubleshooting visit an hour.
- Sub-critical: ṁ ≈ 12·Kv·√(ΔP·P₂). Choked (P₂ ≤ 0.58 P₁): ṁ ≈ 6·Kv·P₁ — downstream stops mattering.
- Select the next Kvs above requirement; healthy valves peak at 70–85% capacity.
- Equal percentage for temperature, linear for pressure; positioner always.
- The practice plant's 760 kg/h duty: Kv 30 → Kvs 40 → DN40/50 body in a DN80 line. Correct looks small.
- Fail action is a decision, not a default — write it down.
The equal-percentage characteristic was not derived — it was carved. Early valve-makers filed and tested plug profiles until temperature loops stopped hunting, and only later did control theory explain why the survivors all shared the same exponential shape: their rising gain cancels a heat exchanger's falling one, leaving the loop with roughly constant gain across the load range. It stands among engineering's happiest accidents — a control-theory theorem discovered by patient men with files, decades before anyone could write it down.