Restriction Orifice Calculator
Bore size or flow rate for a restriction orifice in liquid, gas, or steam service per ISO 5167 and Crane TP-410, with a choked-flow check.
When to use this calculator
Use when deliberately restricting flow — limiting a bypass or a recycle, protecting downstream equipment from over-pressure, or dropping pressure on a continuous vent or purge. It runs in both directions: size the bore for a required flow and pressure drop, or find the flow that an existing bore will pass. In compressible service it checks whether the orifice is choked, which changes the governing equation and means downstream pressure no longer affects the flow.
Required inputs
- Mode — size the bore, or rate an existing bore
- Service — liquid, gas, or steam
- Upstream and downstream pressure, temperature, and fluid properties
- Required mass flow or the known bore diameter, and the discharge coefficient Cd
Expected outputs
- Bore diameter d and the beta ratio
- Mass flow passed, and the flow regime
- Expansion factor Y for compressible service
- Choked or subcritical status with the critical pressure ratio
Formula overview
SI: ṁ in kg/s, A in m², ρ in kg/m³, pressures absolute in Pa, d in mm on output. β is the bore-to-pipe diameter ratio; Cd is typically 0.6 to 0.65 for a square-edged plate.
Liquid — incompressible:
ṁ = Cd · A · √(2·ρ·ΔP), A = π·d²/4
Gas and steam — subcritical:
ṁ = Cd · Y · A · √(2·ρ₁·ΔP)
Y = 1 − (0.351 + 0.256β⁴ + 0.93β⁸)(1 − (P₂/P₁)^(1/k))
Gas and steam — choked:
ṁ = Cd · A · √( k·ρ₁·P₁ · (2/(k+1))^((k+1)/(k−1)) )Worked example
Liquid sizing: pass 10 kg/s of water across 3 bar,
ρ = 998 kg/m³, Cd = 0.62
A = ṁ / (Cd · √(2ρΔP))
= 10 / (0.62 × √(2 × 998 × 300 000))
= 10 / (0.62 × 24 470) = 6.59 × 10⁻⁴ m²
d = √(4A/π) = 29.0 mm
On a 4" line (ID 102.3 mm) that is β = 0.28 — a heavy restriction, so
check for cavitation as well as flow.Common mistakes
- Treating a restriction orifice as a measuring orifice. A metering plate to ISO 5167 is built to tight tolerances at a modest beta so its coefficient is predictable; a restriction plate is a pressure-breaking device, and its Cd carries more uncertainty.
- Ignoring cavitation in liquid service. A large drop across a single plate can flash the liquid at the vena contracta, producing noise, vibration, and rapid erosion. Where the drop is severe, a multi-stage plate or several plates in series is the right answer.
- Using downstream pressure once the orifice is choked. Beyond the critical pressure ratio the flow is fixed by upstream conditions, and lowering P2 further does nothing — sizing on the full ΔP overstates capacity.
FAQ
Learn
Related articles
Pipe Sizing Calculation คืออะไร
ทำความเข้าใจหลักการเลือกขนาดท่อจาก flow rate และ velocity พร้อมสมการพื้นฐานที่วิศวกรใช้จริง
Pressure Drop Calculation
คู่มือคำนวณการสูญเสียความดันในระบบท่อ (Pressure Drop) ด้วย Darcy–Weisbach Equation, Reynolds Number, Friction Factor และ Minor Losses พร้อมตัวอย่างคำนวณจริงสำหรับวิศวกร
วิธีคำนวณ Hydrotest Pressure
หลักการคำนวณความดันทดสอบ hydrostatic ตาม ASME B31.3 สำหรับงาน commissioning