Pressure Vessel Flow Rate Calculation

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Pressure Vessel Flow Rate Calculator

Pressure Vessel Flow Rate Calculator

Diameter of the leak or outlet.
Internal pressure minus external pressure.
Water = 1.0, Oil ≈ 0.8-0.9
Sharp edge ≈ 0.61, Smooth nozzle ≈ 0.98
Volumetric Flow (GPM)
0.00
Gallons Per Minute
Metric Flow (L/min)
0.00
Liters Per Minute
Fluid Velocity
0.00
Feet per Second (ft/s)

Based on the standard orifice equation for incompressible fluids.

Understanding Pressure Vessel Flow Rate Calculations

Calculating the flow rate of fluid escaping from a pressure vessel is a critical task in process engineering, safety analysis, and hydraulic system design. Whether sizing a safety relief valve, estimating the time to drain a tank, or analyzing a leak scenario, understanding the relationship between pressure, orifice size, and fluid properties is essential.

The Governing Formula

This calculator utilizes the standard Orifice Equation derived from Bernoulli's principle for incompressible fluids (liquids). The flow rate ($Q$) is determined by the pressure differential across the opening and the geometry of the orifice. The simplified formula for US Customary units is:

Q = 29.84 × Cd × d² × √(ΔP / SG)

Where:

  • Q: Flow rate in Gallons Per Minute (GPM).
  • Cd: Discharge Coefficient (dimensionless factor representing flow efficiency).
  • d: Diameter of the orifice in inches.
  • ΔP: Pressure differential (Internal Pressure – External Pressure) in psi.
  • SG: Specific Gravity of the fluid (Water = 1.0).

Key Input Parameters

1. Orifice Diameter

This is the diameter of the hole, nozzle, or pipe break through which the fluid is escaping. The flow rate is proportional to the square of the diameter, meaning that doubling the hole size increases the flow rate by a factor of four.

2. Pressure Differential (ΔP)

This is the driving force of the flow. For a vessel venting to the atmosphere, this is equal to the gauge pressure inside the vessel. Higher pressure results in higher exit velocity and greater volumetric flow.

3. Discharge Coefficient ($C_d$)

Real-world flow is never perfect due to turbulence and contraction of the fluid stream (vena contracta). The $C_d$ accounts for these losses.

  • 0.61: Standard sharp-edged orifice (most conservative for leaks).
  • 0.80 – 0.85: Short tube or thick plate orifice.
  • 0.95 – 0.98: Smooth, rounded nozzle or venturi.

4. Specific Gravity (SG)

SG compares the density of the fluid to the density of water. Heavier fluids (higher SG) flow more slowly than lighter fluids under the same pressure conditions due to inertia.

Applications in Industry

Safety Relief Sizing: Engineers must calculate the maximum possible flow rate during an overpressure event to ensure relief valves can vent fluid fast enough to prevent vessel rupture.

Leak Analysis: In environmental risk assessments, estimating the volume of hazardous fluid released from a crack or punctured pipe is vital for containment planning.

function calculateFlowRate() { // 1. Get DOM elements var diameterInput = document.getElementById("orificeDiameter"); var pressureInput = document.getElementById("pressureDiff"); var sgInput = document.getElementById("specificGravity"); var cdInput = document.getElementById("dischargeCoeff"); var resultGPM = document.getElementById("resultGPM"); var resultLPM = document.getElementById("resultLPM"); var resultVelocity = document.getElementById("resultVelocity"); var resultsArea = document.getElementById("resultsArea"); // 2. Parse Inputs var d = parseFloat(diameterInput.value); var P = parseFloat(pressureInput.value); var sg = parseFloat(sgInput.value); var Cd = parseFloat(cdInput.value); // 3. Validation if (isNaN(d) || isNaN(P) || isNaN(sg) || isNaN(Cd)) { alert("Please enter valid numbers in all fields."); return; } if (d <= 0 || sg <= 0 || Cd <= 0) { alert("Diameter, SG, and Cd must be positive numbers."); return; } if (P 0) { velocityFtS = flowCFS / areaSqFt; } // 5. Display Results resultGPM.innerText = flowGPM.toLocaleString('en-US', { minimumFractionDigits: 2, maximumFractionDigits: 2 }); resultLPM.innerText = flowLPM.toLocaleString('en-US', { minimumFractionDigits: 2, maximumFractionDigits: 2 }); resultVelocity.innerText = velocityFtS.toLocaleString('en-US', { minimumFractionDigits: 2, maximumFractionDigits: 2 }); // Show results area resultsArea.style.display = "block"; }

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