อัปเดต 2026-09-07

Restriction Orifice Sizing

ISO 5167-2 / Crane TP-410

Sizes a fixed sharp-edged restriction orifice (or a multi-stage cascade) to dissipate a required permanent pressure drop at a target liquid or gas flow — the inverse-design twin of a metering orifice. Covers liquid (Bernoulli), and gas both sub-critical (ISO 5167-2 expansibility ε) and choked/critical (Crane isentropic mass flux).

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Manual mode uses a fixed Cd = 0.61 closed form; auto mode bisects on the bore ratio β because the Reader-Harris/Gallagher discharge coefficient depends on the Reynolds number, which depends on the (yet unknown) bore. Gas flow picks critical vs sub-critical branch by comparing the actual pressure ratio to the Crane critical ratio.

สมการ

Liquid RO sizing (Bernoulli)

q = C_{d} E A \frac{2 Δ ϖ}{ρ}

Δϖ = permanent (unrecovered) pressure drop the RO must dissipate, Pa; E = 1/√(1−β⁴) velocity-of-approach; Cd ≈ 0.61 manual or RHG-iterated (ISO 5167-2 §5.3.2, 'orifice-corner').

Gas choked (critical) mass flux — Crane TP-410 §1-10

G^{*} = C_{d} k ρ_{1} p_{1} (\frac{2}{k + 1})^{\frac{k + 1}{2 ( k - 1 )}}, A = \frac{m ˙}{G ^{*}}

Fires when the pressure ratio r = p2/p1 ≤ r_crit = (2/(k+1))^(k/(k-1)); RHG Cd is metering-only so the choked branch forces the manual Cd = 0.61.

Cavitation index σ

σ = \frac{p _{1} - p _{v}}{Δ ϖ}

σ ≥ 1.5 'ok', 1.0–1.5 'incipient', 0.5–1.0 'damage', < 0.5 'choked' — mirrors the control-valve σ convention for a sharp-edged plate.

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