Gas Flow Rate Calculation Through Orifice

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Gas Flow Rate Calculator (Orifice Plate)

Calculation Results:

Mass Flow Rate: kg/h

Standard Volume Flow (15°C, 1 atm): Sm³/h

Beta Ratio (β):

Expansibility Factor (ε):

function calculateGasFlow() { // Get inputs var d_mm = parseFloat(document.getElementById("orf_d_mm").value); var D_mm = parseFloat(document.getElementById("pipe_D_mm").value); var P1_barg = parseFloat(document.getElementById("p1_bar_g").value); var dP_mbar = parseFloat(document.getElementById("dp_mbar").value); var T_c = parseFloat(document.getElementById("temp_c").value); var SG = parseFloat(document.getElementById("sg_gas").value); var k = parseFloat(document.getElementById("k_isen").value); // Validation if (isNaN(d_mm) || isNaN(D_mm) || isNaN(P1_barg) || isNaN(dP_mbar) || isNaN(T_c) || isNaN(SG) || isNaN(k) || d_mm <= 0 || D_mm <= 0 || dP_mbar <= 0 || SG <= 0 || k 1."); return; } if (d_mm >= D_mm) { alert("Orifice bore diameter (d) must be smaller than pipe internal diameter (D)."); return; } // Constants var C_discharge = 0.61; // Assumed discharge coefficient for estimation var R_universal = 8314; // J/(kmol K) var MW_air = 28.964; // kg/kmol var Std_T_K = 288.15; // 15°C in Kelvin var Std_P_Pa = 101325; // 1 atm in Pa // Unit Conversions for Calculation (SI Units: meters, Pa, Kelvin, kg) var d_m = d_mm / 1000; var D_m = D_mm / 1000; var P1_abs_Pa = (P1_barg * 100000) + Std_P_Pa; var dP_Pa = dP_mbar * 100; var T_K = T_c + 273.15; // Intermediate Calculations var beta = d_m / D_m; var beta4 = Math.pow(beta, 4); var Area_d = (Math.PI / 4) * Math.pow(d_m, 2); var VelApproach_Ev = 1 / Math.sqrt(1 – beta4); // Gas Properties var MW_gas = SG * MW_air; var R_specific = R_universal / MW_gas; // J/(kg K) var rho1 = P1_abs_Pa / (R_specific * T_K); // Upstream density (kg/m³) // Expansibility Factor (ε) approximation (AGA-3 / simplified ISO form) var pressureRatioTerm = dP_Pa / (P1_abs_Pa * k); var epsilon = 1 – (0.41 + 0.35 * beta4) * pressureRatioTerm; // Main Flow Calculation (Mass Flow rate qm in kg/s) // formula: qm = C * Ev * ε * Ad * sqrt(2 * dP * rho1) var qm_kgs = C_discharge * VelApproach_Ev * epsilon * Area_d * Math.sqrt(2 * dP_Pa * rho1); // Convert to output units var qm_kgh = qm_kgs * 3600; // Calculate Standard Volumetric Flow (Sm³/h at 15°C, 1.01325 bar(a)) var rho_std = Std_P_Pa / (R_specific * Std_T_K); var Q_std_m3s = qm_kgs / rho_std; var Q_std_m3h = Q_std_m3s * 3600; // Display Results document.getElementById("massFlowOutput").textContent = qm_kgh.toFixed(2); document.getElementById("volFlowOutput").textContent = Q_std_m3h.toFixed(2); document.getElementById("betaRatioOutput").textContent = beta.toFixed(4); document.getElementById("expansibilityOutput").textContent = epsilon.toFixed(4); document.getElementById("flowResult").style.display = "block"; }

Understanding Gas Flow Measurement with Orifice Plates

The orifice plate is one of the most common and well-understood devices for measuring the flow rate of gases in pipelines. It operates on the principles of differential pressure measurement, utilizing Bernoulli's principle which relates the pressure and velocity of a fluid.

How the Calculation Works

An orifice plate is a thin plate with a specific hole (the bore) placed in a pipe. As gas flows through this restriction, its velocity increases, causing a corresponding decrease in pressure. This pressure drop, measured immediately before (upstream) and after (downstream) the plate, is directly proportional to the square of the flow rate.

The calculator above uses a simplified version of standard industrial equations (derived from ISO 5167 and AGA Report No. 3 principles) to estimate the mass and volumetric flow rates. Key factors in the calculation include:

  • Diameter Ratio (β): The ratio of the orifice bore diameter to the internal pipe diameter.
  • Discharge Coefficient (C): An empirical factor that accounts for the profile of the flow and frictional losses. This calculator uses a representative value of 0.61.
  • Expansibility Factor (ε): Because gas is compressible, its density changes as pressure drops across the orifice. This factor corrects for that density change based on the pressure ratio and the gas's isentropic exponent.

Important Input Parameters

To obtain an accurate estimate, ensure your inputs are precise:

  • Pressures: Upstream pressure must be gauge pressure (what a standard gauge reads). Differential pressure is usually very small compared to static pressure and is measured in millibars (mbar) or inches of water column.
  • Specific Gravity (SG): The ratio of the gas density to air density at standard conditions. Air is 1.0. Natural gas is typically around 0.6 to 0.7.
  • Isentropic Exponent (k): Also known as the ratio of specific heats (Cp/Cv). For diatomic gases like air, it is approximately 1.4. For hydrocarbon gases, it is often lower (e.g., 1.3 for natural gas).

Example Calculation

Let's calculate the flow rate for a natural gas line using typical parameters entered into the calculator:

  • Orifice Diameter: 50 mm
  • Pipe Diameter: 100 mm
  • Upstream Pressure: 10 bar g
  • Differential Pressure: 250 mbar
  • Temperature: 20 °C
  • Specific Gravity: 0.6 (typical for natural gas)
  • Isentropic Exponent (k): 1.3

Based on these inputs, the calculator determines the gas density at operating conditions and the necessary correction factors (like expansibility due to the pressure drop). The estimated results would be approximately 2767 kg/h mass flow, translating to roughly 3765 Sm³/h (standard cubic meters per hour at 15°C and 1 atm).

Note: This calculator provides an engineering estimate based on simplified standard equations. For custody transfer or critical applications, rigorous calculations iterating for Reynolds number and exact coefficients according to ISO 5167 standards should be performed.

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