Typically 0.60 – 0.65 for sharp-edged orifices, close to 1.0 for smooth nozzles.
Calculation Results
Cross-Sectional Area:0 m²
Flow Velocity (Approx):0 m/s
Mass Flow Rate (kg/s):0 kg/s
Mass Flow Rate (kg/hr):0 kg/h
function calculateFlowRate() {
// 1. Get DOM elements
var inputP = document.getElementById("pressureDrop");
var inputRho = document.getElementById("fluidDensity");
var inputD = document.getElementById("orificeDiameter");
var inputCd = document.getElementById("dischargeCoeff");
var errorDiv = document.getElementById("errorDisplay");
var resultDiv = document.getElementById("resultDisplay");
var resArea = document.getElementById("resArea");
var resVelocity = document.getElementById("resVelocity");
var resFlowSec = document.getElementById("resFlowSec");
var resFlowHour = document.getElementById("resFlowHour");
// 2. Parse values
var deltaP = parseFloat(inputP.value);
var density = parseFloat(inputRho.value);
var diamMM = parseFloat(inputD.value);
var cd = parseFloat(inputCd.value);
// 3. Reset display
errorDiv.style.display = "none";
resultDiv.style.display = "none";
errorDiv.innerHTML = "";
// 4. Validate Inputs
if (isNaN(deltaP) || isNaN(density) || isNaN(diamMM) || isNaN(cd)) {
errorDiv.innerHTML = "Please enter valid numbers for all fields.";
errorDiv.style.display = "block";
return;
}
if (deltaP < 0 || density <= 0 || diamMM <= 0 || cd approx v = Cd * sqrt(2*dP/rho)
// Or strictly derived: v = MassFlow / (Density * Area)
// Note: This velocity represents the velocity at the vena contracta or constriction
var velocity = massFlowRate / (density * area);
// Convert to kg/hr
var massFlowHour = massFlowRate * 3600;
// 6. Display Results
resArea.innerHTML = area.toExponential(4) + " m²";
resVelocity.innerHTML = velocity.toFixed(2) + " m/s";
resFlowSec.innerHTML = massFlowRate.toFixed(4) + " kg/s";
resFlowHour.innerHTML = massFlowHour.toFixed(2) + " kg/h";
resultDiv.style.display = "block";
}
How to Calculate Mass Flow Rate from Pressure Drop
In fluid dynamics and engineering, determining the mass flow rate based on a known pressure drop is a critical task. Whether you are designing HVAC systems, managing chemical pipelines, or analyzing automotive fuel injectors, understanding the relationship between differential pressure and flow is essential.
This calculator utilizes the fundamental principles of Bernoulli's equation and discharge coefficients to estimate the mass flow rate through an orifice or restriction.
The Physics Behind the Calculation
The relationship between flow rate and pressure drop is non-linear. Specifically, the flow rate is proportional to the square root of the pressure drop. This means that to double the flow rate, you typically need four times the pressure drop.
The Formula
For incompressible fluids (liquids) or gases with low pressure drops, the mass flow rate ($\dot{m}$) can be calculated using the following equation:
ṁ = Cd × A × √(2 × ρ × ΔP)
Where:
ṁ (m_dot): Mass Flow Rate (kg/s)
Cd: Discharge Coefficient (dimensionless, usually 0.60–0.98)
A: Cross-sectional Area of the orifice or pipe ($m^2$)
ρ (rho): Fluid Density ($kg/m^3$)
ΔP (Delta P): Pressure Drop across the restriction (Pascals)
Understanding the Variables
1. Pressure Drop (ΔP)
This is the difference in pressure between the upstream side and the downstream side of the restriction. In our calculator, this input requires Pascals (Pa). If you have measurements in PSI or Bar, they must be converted first (1 PSI ≈ 6894.76 Pa).
2. Fluid Density (ρ)
Density significantly impacts mass flow. A denser fluid (like water) requires a higher pressure drop to achieve the same velocity as a lighter fluid (like air), but it carries more mass per unit of volume. Common values include:
Water: ~997 kg/m³
Air (at sea level): ~1.225 kg/m³
Hydraulic Oil: ~870 kg/m³
3. Discharge Coefficient (Cd)
Theoretical equations assume ideal flow with no friction or turbulence losses. In reality, flow is restricted by the geometry of the opening. The Discharge Coefficient ($C_d$) corrects for these losses.
Sharp-edged orifice: 0.60 – 0.62
Venturi tube: 0.95 – 0.98
Short tube: 0.75 – 0.85
Practical Example
Let's say you have a water pipe with a 50mm orifice plate. The pressure drop across the plate is measured at 5,000 Pa. The density of water is 997 kg/m³, and we assume a standard discharge coefficient of 0.61.
Using the calculator above:
Convert diameter: 50mm = 0.05m. Area $A \approx 0.001963 m^2$.
This result helps engineers size pumps and ensure pipes are not over-pressurized for the required flow rate.
Limitations
This simplified calculation assumes the fluid is incompressible (density remains constant). For gases where the pressure drop is significant relative to the absolute pressure, compressibility factors must be considered, and more complex equations (like the expansion factor equation) are required.