Calculate the fluid flow rate based on pipe dimensions and velocity.
(Units: m³/s, L/min, etc. – ensure consistency)
(Units: m², cm², etc. – ensure consistency with flow rate units)
Understanding the Continuity Equation
The continuity equation is a fundamental principle in fluid dynamics, derived from the conservation of mass. It states that for an incompressible fluid flowing in a closed system, the mass flow rate must be constant throughout the system. For a constant density fluid, this simplifies to the volume flow rate being constant.
The Formula
The basic form of the continuity equation for incompressible fluids is:
Q = A * v
Where:
Q represents the volumetric flow rate of the fluid. This is the volume of fluid that passes through a given cross-sectional area per unit of time. Common units include cubic meters per second (m³/s), liters per minute (L/min), or gallons per minute (GPM).
A represents the cross-sectional area of the flow. For a pipe, this is typically the area of a circle (π * r² or π * d²/4), where r is the radius and d is the diameter. Units are usually square meters (m²) or square centimeters (cm²).
v represents the average velocity of the fluid flowing through the area A. Common units include meters per second (m/s) or centimeters per second (cm/s).
How This Calculator Works
This calculator rearranges the continuity equation to solve for the average fluid velocity (v) when the volumetric flow rate (Q) and the cross-sectional area (A) are known:
v = Q / A
To use the calculator, you need to input the known values for Q and A. It is crucial that the units used for both inputs are consistent, or that you perform unit conversions beforehand, so that the resulting velocity is in a meaningful unit (e.g., if Q is in m³/s and A is in m², v will be in m/s).
Use Cases
Plumbing and Civil Engineering: Determining the speed of water flow in pipes based on the pipe's diameter and the volume of water supplied.
Aerodynamics: Estimating airflow velocity in ducts or around aircraft components.
Manufacturing: Monitoring and controlling the speed of materials (like fluids or granular solids) in processing systems.
Environmental Science: Analyzing the flow of water in rivers or through filtration systems.
Example Calculation
Let's say you have water flowing through a pipe with a cross-sectional area of 0.05 square meters (m²) and the measured volumetric flow rate is 0.1 cubic meters per second (m³/s).
Using the formula v = Q / A:
v = 0.1 m³/s / 0.05 m²
v = 2 m/s
So, the average velocity of the water in the pipe is 2 meters per second.
function calculateVelocity() {
var flowRateInput = document.getElementById("flowRate");
var areaInput = document.getElementById("area");
var resultDiv = document.getElementById("result");
var flowRate = parseFloat(flowRateInput.value);
var area = parseFloat(areaInput.value);
if (isNaN(flowRate) || isNaN(area)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (area === 0) {
resultDiv.innerHTML = "Cross-sectional area cannot be zero.";
return;
}
var velocity = flowRate / area;
// Attempt to infer units for a more helpful output, but primarily show the calculated value
var velocityUnit = "Units"; // Default placeholder
if (flowRateInput.value && areaInput.value) {
var flowRateStr = flowRateInput.getAttribute('placeholder') || ";
var areaStr = areaInput.getAttribute('placeholder') || ";
var flowRateUnitMatch = flowRateStr.match(/\(([^)]+)\)/);
var areaUnitMatch = areaStr.match(/\(([^)]+)\)/);
if (flowRateUnitMatch && areaUnitMatch) {
var flowRateUnit = flowRateUnitMatch[1].split('/')[0].trim(); // e.g., m³
var areaUnit = areaUnitMatch[1].split('/')[0].trim(); // e.g., m²
if (flowRateUnit === 'm³' && areaUnit === 'm²') {
velocityUnit = "m/s";
} else if (flowRateUnit === 'L' && areaUnit === 'cm²') {
// Q in L, A in cm². Need to convert L to cm³ (1L = 1000 cm³)
// v = (Q * 1000) / A in cm/s
velocityUnit = "cm/s";
} else if (flowRateUnit === 'L' && areaUnit === 'm²') {
// Q in L, A in m². Need to convert L to m³ (1L = 0.001 m³)
// v = (Q * 0.001) / A in m/s
velocityUnit = "m/s";
} else if (flowRateUnit === 'GPM' && areaUnit === 'ft²') {
// Q in GPM, A in ft². 1 GPM = 0.133681 ft³/min. Convert to ft/s.
// v = (Q * 0.133681) / A in ft/s
velocityUnit = "ft/s";
}
// Add more specific unit inferences if needed
}
}
resultDiv.innerHTML = "Calculated Velocity: " + velocity.toFixed(4) + " " + velocityUnit + "";
}