How to Calculate Flow Rate with Pressure and Diameter

Flow Rate Calculator (Pressure & Diameter)

Calculate the volumetric flow rate of liquid through an orifice or pipe based on differential pressure.

Results:

Flow Rate (Liters/min): –

Flow Rate (m³/hour): –

Fluid Velocity (m/s): –

function calculateLiquidFlow() { var d = parseFloat(document.getElementById('flowDiameter').value); var pBar = parseFloat(document.getElementById('flowPressure').value); var rho = parseFloat(document.getElementById('flowDensity').value); var cd = parseFloat(document.getElementById('flowCd').value); if (isNaN(d) || isNaN(pBar) || isNaN(rho) || isNaN(cd) || d <= 0 || rho <= 0) { alert('Please enter valid positive numbers.'); return; } // 1. Convert Diameter (mm) to Area (m^2) var radiusM = (d / 1000) / 2; var area = Math.PI * Math.pow(radiusM, 2); // 2. Convert Pressure (bar) to Pascals (N/m^2) var pPascal = pBar * 100000; // 3. Bernoulli's principle for velocity (v = sqrt(2*dP/rho)) var velocity = Math.sqrt((2 * pPascal) / rho); // 4. Calculate Flow Rate (Q = Cd * A * v) var qM3s = cd * area * velocity; // 5. Convert m^3/s to other units var qLmin = qM3s * 60 * 1000; var qM3h = qM3s * 3600; document.getElementById('resLmin').innerText = qLmin.toFixed(2) + " L/min"; document.getElementById('resM3h').innerText = qM3h.toFixed(3) + " m³/h"; document.getElementById('resVel').innerText = (velocity * cd).toFixed(2) + " m/s"; document.getElementById('flowResult').style.display = 'block'; }

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Understanding Flow Rate from Pressure and Diameter

Calculating the flow rate of a liquid based on the internal pressure and the diameter of the opening is a fundamental concept in fluid mechanics, specifically governed by Bernoulli's principle. This calculation is essential for engineers, plumbers, and hobbyists working with irrigation, industrial piping, or nozzle selection.

The Mathematical Formula

The relationship is derived from the continuity equation and Bernoulli's equation. For practical applications, we use the following modified version:

Q = C_d × A × √(2ΔP / ρ)

• Q: Volumetric flow rate.
• C_d: Discharge coefficient (accounts for turbulence and orifice shape).
• A: Cross-sectional area of the pipe (πr²).
• ΔP: Pressure difference (Pascals).
• ρ (rho): Fluid density (e.g., 1000 kg/m³ for water).

Key Factors Explained

Pipe Diameter: The area increases exponentially with the diameter. Even a small increase in diameter can lead to a significant jump in flow capacity.

Pressure: Pressure provides the energy required to move the fluid. In this calculator, we use differential pressure, which is the difference between the pressure inside the pipe and the atmospheric pressure (or the pressure at the exit).

Discharge Coefficient (Cd): No real-world system is 100% efficient. Friction and the "Vena Contracta" effect (where the fluid stream narrows as it exits) reduce the actual flow. A value of 0.62 is common for sharp-edged orifices, while values closer to 0.98 are used for well-rounded nozzles.

Calculation Example

Suppose you have a 50mm pipe discharging water into the air at a pressure of 3 bar.

1. Convert Units: 50mm = 0.05m diameter. 3 bar = 300,000 Pascals.
2. Calculate Area: Area = π × (0.025)² = 0.00196 m².
3. Calculate Velocity: v = √(2 × 300,000 / 1000) = 24.49 m/s.
4. Apply Coefficient: If Cd is 0.62, the effective flow is 0.62 × 0.00196 × 24.49 ≈ 0.0297 m³/s.
5. Final Result: This converts to roughly 1,784 Liters per minute.