Calculate Mass Flow Rate from Pressure

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Mass Flow Rate Calculator (Ideal Gas)

function calculateMassFlowRate() { var p1 = parseFloat(document.getElementById("inletPressure").value); var t1 = parseFloat(document.getElementById("inletTemperature").value); var d = parseFloat(document.getElementById("orificeDiameter").value); var cd = parseFloat(document.getElementById("dischargeCoefficient").value); var r = parseFloat(document.getElementById("gasConstant").value); var resultElement = document.getElementById("result"); if (isNaN(p1) || isNaN(t1) || isNaN(d) || isNaN(cd) || isNaN(r) || p1 <= 0 || t1 <= 0 || d <= 0 || cd 1 || r p_critical) { // Subsonic flow (using isentropic nozzle flow equation) // This is a simplification. A more rigorous calculation would involve iteration. // For this calculator, we assume choked flow if upstream pressure is high enough. // If not choked, the formula below is for choked conditions, which might overestimate. // For simplicity and typical calculator use cases, we proceed with the choked flow assumption if p1 is sufficient. } massFlowRate = cd * area * p1 * c_star_prime / Math.sqrt(t1); resultElement.innerHTML = "Calculated Mass Flow Rate: " + massFlowRate.toFixed(4) + " kg/s"; }

Understanding Mass Flow Rate Calculation from Pressure

Mass flow rate is a crucial parameter in many engineering applications, particularly in fluid dynamics and thermodynamics. It quantifies the amount of mass of a substance that passes through a given surface per unit of time. When dealing with gases, and particularly when gases flow through an orifice or a nozzle, the pressure difference is a primary driver for this flow.

The calculator above estimates the mass flow rate of an ideal gas through an orifice based on inlet conditions and orifice geometry. The calculation employs principles derived from compressible fluid dynamics, specifically related to nozzle flow.

Key Concepts and Formulas:

  • Inlet Pressure (P1): The absolute pressure of the gas upstream of the orifice. Higher pressure generally leads to higher mass flow rate.
  • Inlet Temperature (T1): The absolute temperature of the gas upstream of the orifice. Higher temperature generally leads to lower mass flow rate for a given pressure (as density decreases).
  • Orifice Diameter (d): The diameter of the opening through which the gas flows. A larger diameter allows for a greater flow rate.
  • Discharge Coefficient (Cd): A dimensionless empirical factor that accounts for the inefficiencies in flow through the orifice due to friction and vena contracta. It's typically between 0.6 and 0.9.
  • Specific Gas Constant (R): A thermodynamic property of the gas, defined as the universal gas constant divided by the molar mass of the gas. For air, it's approximately 287.05 J/(kg·K).
  • Specific Heat Ratio (γ): The ratio of specific heat at constant pressure to specific heat at constant volume. For diatomic gases like air, it's approximately 1.4.

The formula used is a simplified version of the isentropic nozzle flow equation for choked or near-choked conditions:

ṁ = Cd * A * P1 * sqrt(γ / (R * T1)) * (2 / (γ + 1))^((γ + 1) / (2 * (γ - 1)))

Where:

  • ṁ is the mass flow rate (kg/s)
  • A is the area of the orifice (m²)
  • P1 is the inlet pressure (Pa)
  • T1 is the inlet temperature (K)
  • Cd is the discharge coefficient
  • R is the specific gas constant (J/kg·K)
  • γ is the specific heat ratio

Choked Flow: This calculation often assumes choked flow, which occurs when the pressure at the narrowest point (throat) of the flow reaches a critical pressure, and the velocity is sonic. The critical pressure ratio determines when this happens. If the downstream pressure is sufficiently low, the flow will be choked, and the mass flow rate is maximized for the given upstream conditions. This calculator uses a common formulation that is accurate for choked flow and a reasonable approximation for high-pressure ratios.

Example Calculation:

Let's assume we have air flowing through an orifice.

  • Inlet Pressure: 200,000 Pa (approx. 2 atm)
  • Inlet Temperature: 300 K (approx. 27°C)
  • Orifice Diameter: 0.02 m (2 cm)
  • Discharge Coefficient: 0.8
  • Specific Gas Constant for air: 287.05 J/kg·K

Using these values in the calculator will yield the estimated mass flow rate in kg/s.

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