Pressure to Flow Rate Calculator

Pressure to Flow Rate Calculator

Calculation Results:

Volumetric Flow Rate: L/min

Volumetric Flow Rate: m³/h

Velocity at Orifice: m/s

function calculateFlow() { var P = parseFloat(document.getElementById('pressureDiff').value); var d = parseFloat(document.getElementById('orificeDiameter').value); var Cd = parseFloat(document.getElementById('dischargeCoeff').value); var rho = parseFloat(document.getElementById('fluidDensity').value); if (isNaN(P) || isNaN(d) || isNaN(Cd) || isNaN(rho) || P <= 0 || d <= 0 || rho <= 0) { alert("Please enter valid positive numeric values."); return; } // Convert Bar to Pascals (1 Bar = 100,000 Pa) var deltaP = P * 100000; // Convert diameter mm to meters var diameterM = d / 1000; // Calculate Area (A = pi * r^2) var area = Math.PI * Math.pow((diameterM / 2), 2); // Bernoulli based Orifice Equation: Q = Cd * A * sqrt( (2 * deltaP) / rho ) var flowRateM3S = Cd * area * Math.sqrt((2 * deltaP) / rho); // Convert m3/s to L/min (1 m3/s = 60,000 L/min) var flowLPM = flowRateM3S * 60000; // Convert m3/s to m3/h (1 m3/s = 3600 m3/h) var flowM3H = flowRateM3S * 3600; // Velocity V = Q / A var vel = flowRateM3S / area; document.getElementById('flowRateLPM').innerText = flowLPM.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('flowRateM3H').innerText = flowM3H.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4}); document.getElementById('velocity').innerText = vel.toFixed(2); document.getElementById('resultArea').style.display = 'block'; }

Calculating the flow rate based on a pressure differential is a fundamental task in fluid mechanics, civil engineering, and industrial piping design. Whether you are sizing a nozzle, estimating leakage, or designing a hydraulic system, understanding how pressure translates into volume displacement is crucial.

The Physics Behind the Calculation

The relationship between pressure and flow is governed by the Bernoulli Principle. When a fluid passes through a restriction (like an orifice or a nozzle), its potential energy (pressure) is converted into kinetic energy (velocity). As the pressure difference across the restriction increases, the velocity—and consequently the flow rate—increases proportionally to the square root of that pressure change.

The Orifice Flow Formula

The standard formula used in this calculator is:

Q = Cd × A × √(2 × ΔP / ρ)

• Q: Volumetric Flow Rate (m³/s)
• Cd: Discharge Coefficient (accounts for energy losses and turbulence)
• A: Cross-sectional area of the opening (m²)
• ΔP: Pressure difference across the opening (Pascals)
• ρ (rho): Density of the fluid (kg/m³)

Key Factors Influencing Flow

1. Discharge Coefficient (Cd)

In a perfect theoretical world, Cd would be 1.0. However, due to friction and the "Vena Contracta" effect (where the fluid stream narrows after passing through the hole), real-world values are lower. For a sharp-edged orifice, 0.62 is a standard engineering estimate. For well-rounded nozzles, this value may rise to 0.98.

2. Fluid Density

The weight of the fluid affects how much energy is required to move it. Water has a density of approximately 1000 kg/m³. If you are calculating the flow for oils or gases, the density will be different, which significantly impacts the resulting flow rate.

3. Pressure Differential

It is important to note that flow is driven by the difference in pressure between two points, not the absolute pressure. For example, if the internal pipe pressure is 5 Bar and it is venting to the atmosphere (0 Bar gauge), the differential is 5 Bar.

Practical Example Calculation

Imagine a water tank (density 1000 kg/m³) with a 10mm hole at the bottom. If the water level creates a pressure of 0.5 Bar at the hole, what is the flow rate?

1. Pressure: 0.5 Bar = 50,000 Pa
2. Area: 10mm diameter = 0.0000785 m²
3. Coefficient: We assume 0.62 for a standard hole.
4. Calculation: Q = 0.62 × 0.0000785 × √(2 × 50,000 / 1000)
5. Result: Approximately 29.2 Liters per minute.

Frequently Asked Questions

Does doubling the pressure double the flow?
No. Because the flow rate is proportional to the square root of the pressure, you would need to quadruple (4x) the pressure to double the flow rate.

How does temperature affect this?
Temperature changes the density and viscosity of the fluid. For most liquids, the density change is minimal at standard ranges, but for gases, temperature is a critical factor in flow calculations.

What is the typical Cd for a pipe?
For standard pipes and fittings, engineers often use Cv (Flow Coefficient) or Kv values provided by manufacturers, which simplify these complex physics into a single constant.