Flow Rate Calculator Pressure Differential

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Flow Rate Calculator (Pressure Differential)

Calculate fluid flow rate based on differential pressure across a valve or restriction.

Input Parameters

PSI
PSI
Cv
Often found on valve spec sheets.
Water = 1.0, Oil ≈ 0.8-0.9

Calculation Results

Pressure Differential (ΔP)
0 PSI
Calculated Flow Rate (Q)
0 GPM

Formula Used: Q = Cv × √(ΔP / SG)

function calculateFlowRate() { // Get Input Values var p1 = parseFloat(document.getElementById('p1_input').value); var p2 = parseFloat(document.getElementById('p2_input').value); var cv = parseFloat(document.getElementById('cv_input').value); var sg = parseFloat(document.getElementById('sg_input').value); var errorMsg = document.getElementById('error_msg'); var resultsArea = document.getElementById('results_area'); // Reset Error errorMsg.style.display = 'none'; resultsArea.style.display = 'none'; // Validation if (isNaN(p1) || isNaN(p2) || isNaN(cv) || isNaN(sg)) { errorMsg.innerText = "Please fill in all fields with valid numbers."; errorMsg.style.display = 'block'; return; } if (sg = p1) { errorMsg.innerText = "Inlet Pressure (P1) must be higher than Outlet Pressure (P2) for forward flow."; errorMsg.style.display = 'block'; return; } if (cv < 0) { errorMsg.innerText = "Flow Coefficient (Cv) cannot be negative."; errorMsg.style.display = 'block'; return; } // Calculation Logic // Formula: Q = Cv * sqrt(dP / SG) var dp = p1 – p2; // Differential Pressure in PSI var rootTerm = Math.sqrt(dp / sg); var flowRate = cv * rootTerm; // Flow Rate in GPM // Output Display document.getElementById('result_dp').innerText = dp.toFixed(2) + " PSI"; document.getElementById('result_flow').innerText = flowRate.toFixed(2) + " GPM"; resultsArea.style.display = 'block'; }

Understanding Flow Rate and Pressure Differential

In fluid dynamics and industrial engineering, calculating the flow rate based on pressure differential is a fundamental task. When a fluid passes through a restriction—such as a control valve, orifice plate, or nozzle—the pressure drops. This drop in pressure, known as the Pressure Differential (ΔP), is directly related to the rate at which the fluid is flowing.

This calculator utilizes the standard valve sizing equation commonly used in HVAC, chemical processing, and water systems to determine the volumetric flow rate (measured in Gallons Per Minute, or GPM) given specific system parameters.

The Physics Behind the Calculation

The relationship between flow rate and pressure drop is derived from Bernoulli's principle. For turbulent flow through a fixed geometry (like a valve), the flow rate is proportional to the square root of the pressure differential.

The Formula:
Q = Cv × √(ΔP / SG)
  • Q: Volumetric Flow Rate (GPM – US Gallons per Minute).
  • Cv: Flow Coefficient. This is an empirical value usually provided by valve manufacturers. It represents the number of gallons of water per minute that will flow through a restriction with a 1 PSI pressure drop at 60°F.
  • ΔP (Delta P): The pressure differential (P₁ – P₂) measured in PSI.
  • SG: Specific Gravity of the fluid. Water has an SG of 1.0. Fluids heavier than water have an SG > 1.0, and lighter fluids (like many oils) have an SG < 1.0.

How to Find Your Input Values

1. Inlet and Outlet Pressures (P₁ & P₂)

These values are obtained via pressure gauges installed upstream (inlet) and downstream (outlet) of the valve or restriction. The Inlet Pressure must always be higher than the Outlet Pressure for flow to occur in the forward direction. The difference between these two is your ΔP.

2. Flow Coefficient (Cv)

The Cv value is specific to the device causing the pressure drop.

  • Valves: Check the manufacturer's technical datasheet or the tag on the valve body. A fully open ball valve will have a significantly higher Cv than a globe valve of the same size.
  • Orifice Plates: The Cv is calculated based on the ratio of the orifice diameter to the pipe diameter (Beta ratio).

3. Specific Gravity (SG)

This measures the density of the fluid relative to water.

  • 💧 Water (at 60°F): SG = 1.0
  • 🛢️ Gasoline: SG ≈ 0.74
  • 🍯 Heavy Oil: SG ≈ 0.90
  • 🧂 Brine/Seawater: SG ≈ 1.03

Practical Example

Imagine you have a control valve in a cooling water system.

  • The pressure gauge before the valve reads 60 PSI.
  • The pressure gauge after the valve reads 50 PSI.
  • The valve manufacturer states the Cv is 25.
  • The fluid is Water (SG = 1).

First, calculate the differential pressure: 60 – 50 = 10 PSI.
Next, apply the formula: Q = 25 × √(10 / 1) = 25 × 3.16.
Result: The flow rate is approximately 79 GPM.

Why is Pressure Differential Important?

Monitoring pressure differential is critical for system health. A sudden increase in ΔP (where P₂ drops significantly compared to P₁) often indicates a blockage or a clogged filter. Conversely, a decrease in ΔP might indicate a blown seal or pump failure. Using this calculator helps engineers verify if the system is performing within its design specifications.

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