Understanding the Differential Pressure to Flow Rate Calculation
In fluid dynamics and industrial process control, the relationship between differential pressure ($\Delta P$) and volumetric flow rate ($Q$) is one of the most fundamental concepts. This calculator utilizes the standard valve sizing equation derived from Bernoulli's principle to estimate the flow rate of a liquid passing through a restriction, such as a control valve or an orifice plate.
Accurately calculating flow rate from differential pressure is critical for sizing pumps, selecting control valves, balancing HVAC systems, and monitoring industrial pipelines.
The Flow Rate Formula
For non-compressible fluids (liquids) like water, the flow rate is proportional to the square root of the differential pressure. The standard industry formula used in this calculator is:
Q = Cv × √(ΔP / SG)
Where:
Q = Volumetric Flow Rate (GPM – Gallons Per Minute)
Cv = Valve Flow Coefficient
ΔP = Differential Pressure (psi)
SG = Specific Gravity of the fluid (Water at 60°F = 1.0)
Definitions of Input Parameters
Flow Coefficient (Cv)
The flow coefficient ($C_v$) is a relative measure of the efficiency of a valve or flow element. It represents the number of US gallons of water at 60°F that will flow through a valve per minute with a pressure drop of 1 psi. A higher $C_v$ indicates a larger valve or less resistance to flow.
Differential Pressure ($\Delta P$)
This is the difference in pressure between the inlet (upstream) and the outlet (downstream) of the flow restriction. It is typically measured in pounds per square inch (psi). An increase in differential pressure results in an increase in flow rate, following a square root relationship. To double the flow, you need four times the pressure.
Specific Gravity (SG)
Specific gravity is the ratio of the density of the fluid to the density of a reference fluid (usually water).
Water: SG = 1.0
Oil/Gasoline: SG < 1.0 (Lighter than water)
Brine/Heavy Liquids: SG > 1.0 (Heavier than water)
Example Calculation
Imagine you have a control valve with a flow coefficient ($C_v$) of 15. You measure a pressure drop ($\Delta P$) of 9 psi across the valve. The fluid is water ($SG = 1.0$).
Using the formula:
$Q = 15 \times \sqrt{9 / 1}$
$Q = 15 \times 3$
$Q = 45 \text{ GPM}$
Why is this calculation important?
System Troubleshooting: If a system is not achieving the desired cooling or heating, technicians measure the pressure drop across balancing valves. By converting this pressure drop to flow rate, they can determine if the equipment is receiving the correct amount of fluid.
Component Sizing: Engineers use this relationship to ensure that pumps are powerful enough to overcome the pressure losses ($Delta P$) required to deliver the necessary flow rate ($Q$) through the system components.
function calculateDPFlow() {
// Get input values
var cvVal = document.getElementById('flow_cv').value;
var dpVal = document.getElementById('diff_pressure').value;
var sgVal = document.getElementById('specific_gravity').value;
// Clean inputs (convert to float)
var cv = parseFloat(cvVal);
var dp = parseFloat(dpVal);
var sg = parseFloat(sgVal);
// Validation
if (isNaN(cv) || isNaN(dp) || isNaN(sg)) {
alert("Please enter valid numbers for all fields.");
return;
}
if (cv < 0 || dp < 0) {
alert("Flow Coefficient and Differential Pressure must be positive numbers.");
return;
}
if (sg <= 0) {
alert("Specific Gravity must be greater than zero.");
return;
}
// Calculation Logic: Q = Cv * sqrt(dP / SG)
var sqrtTerm = Math.sqrt(dp / sg);
var flowRate = cv * sqrtTerm;
// Display Result
var resultContainer = document.getElementById('result_container');
var resultText = document.getElementById('flow_result');
resultText.innerHTML = flowRate.toFixed(2) + " GPM";
resultContainer.style.display = "block";
}