Sizing a Restriction Orifice (RO) or evaluating flow across a given orifice plate is a daily task in process engineering. Whether you are checking pump minimum flow lines (liquids) or making a preliminary estimate for gas restriction cases, understanding flow limits—especially choked flow—is critical.

This browser-based estimator provides preliminary mass-flow and upstream actual volumetric-flow estimates across an orifice for compressible gases and incompressible liquids.

🎛️ Restriction Orifice Flow Estimator

• Gas Mode: Calculates upstream density from P1, T1, MW, and Z. Uses subcritical/choked split.
• Liquid Mode: Uses incompressible orifice equation (no cavitation/flashing check).

Fluid Data

Instrument Data

🚨 Engineering Limitations & Disclaimer

Before using the estimates provided by this tool, please note the following critical boundaries:

  • Gas Density Calculation: For gases, the tool calculates upstream actual density from $P_1$, $T_1$, $MW$, and $Z$. Ensure $P_1$ is entered as absolute pressure, and $Z$ is evaluated at the specific inlet relieving condition.
  • Volumetric Flow: Reported volumetric flow is strictly based on upstream actual density. It should not be interpreted as standard/normal flow ($Sm^3/h$, $Nm^3/h$) or downstream actual flow.
  • Velocity of Approach ($E$): Applying the incompressible velocity-of-approach factor ($E$) to the compressible isentropic equations is a pragmatic approximation used in this estimator. It is not a rigorous application of standard compressible metering formulas.
  • Discharge Coefficient ($C_d$): The discharge coefficient is strictly a user-specified constant and is not dynamically correlated to the Reynolds number.
  • Scope of Use: This tool is intended for conceptual design and preliminary estimations only. It is not for final detailed design, custody transfer, or certified safety relief sizing.

📘 Technical Background & Equations

Unlike simple calculators that apply a generic expansibility factor to the incompressible equation, this estimator separates gas calculations into subcritical and choked regimes using a simplified ideal-gas-style isentropic approach.

1. Liquid Phase (Incompressible Flow)

For liquids, the density is assumed constant across the orifice. The mass flow rate ($q_m$) is calculated using the standard orifice equation:

$$q_m = C_d E A \sqrt{2 \rho_1 \Delta P}$$

Where:

  • $C_d$ = Discharge Coefficient (typically ~0.62)
  • $E$ = Velocity Approach Factor = $\frac{1}{\sqrt{1 - \beta^4}}$
  • $A$ = Orifice bore area ($m^2$)
  • $\rho_1$ = Upstream density ($kg/m^3$)
  • $\Delta P$ = Pressure drop ($P_1 - P_2$)

2. Gas Phase (Compressible Isentropic Flow)

When a gas passes through a restriction, it expands. This tool evaluates the critical pressure ratio ($r_c$) using the specific heat ratio ($k$):

$$r_c = \left(\frac{2}{k + 1}\right)^{\frac{k}{k - 1}}$$

Let $r$ be the actual pressure ratio ($P_2 / P_1$). The calculation diverges based on the flow regime:

A. Subcritical Flow ($r > r_c$): The flow is not limited by the speed of sound. The mass flow is calculated as:

$$q_m = C_d E A \sqrt{ 2 \rho_1 P_1 \left(\frac{k}{k-1}\right) \left[ r^{2/k} - r^{(k+1)/k} \right] }$$

B. Choked (Sonic) Flow ($r \le r_c$): When the flow reaches sonic conditions at the controlling section, the mass flow is evaluated using the critical-flow form. Further lowering the downstream pressure ($P_2$) will not increase the mass flow rate:

$$q_m = C_d E A \sqrt{ \rho_1 P_1 k \left(\frac{2}{k+1}\right)^{\frac{k+1}{k-1}} }$$

(The estimator will display a warning flag if choked conditions are reached, and the actual calculations will rely on the critical limit.)