Flow Rate Calculator (Velocity and Diameter)
This calculator helps you determine the volumetric flow rate of a fluid through a pipe or channel given its velocity and the cross-sectional diameter. The volumetric flow rate (Q) is the volume of fluid that passes through a given cross-sectional area per unit of time. It's a fundamental concept in fluid dynamics and is crucial for many engineering and scientific applications.
Understanding Flow Rate Calculation
The formula used to calculate volumetric flow rate (Q) from fluid velocity (v) and the cross-sectional area (A) is:
Q = v * A
Since we are given the diameter (d) of a circular pipe, we first need to calculate the cross-sectional area (A). The area of a circle is given by:
A = π * (r^2)
where 'r' is the radius of the pipe. The radius is half of the diameter (r = d/2).
Therefore, the area can be expressed in terms of diameter as:
A = π * (d/2)^2 = π * (d^2 / 4)
Substituting this back into the flow rate formula, we get:
Q = v * (π * d^2 / 4)
Where:
- Q is the volumetric flow rate (in cubic meters per second, m³/s).
- v is the average velocity of the fluid (in meters per second, m/s).
- d is the diameter of the pipe or channel (in meters, m).
- π (pi) is a mathematical constant, approximately 3.14159.
This calculator takes your input for velocity and diameter, calculates the area, and then computes the volumetric flow rate.
Example Calculation:
Let's say a fluid is flowing through a pipe with a diameter of 0.1 meters (10 cm) at an average velocity of 2.5 meters per second.
- Velocity (v) = 2.5 m/s
- Diameter (d) = 0.1 m
- Radius (r) = d / 2 = 0.1 m / 2 = 0.05 m
- Area (A) = π * r² = π * (0.05 m)² ≈ 3.14159 * 0.0025 m² ≈ 0.007854 m²
- Flow Rate (Q) = v * A = 2.5 m/s * 0.007854 m² ≈ 0.019635 m³/s
So, the volumetric flow rate in this example is approximately 0.0196 cubic meters per second.
function calculateFlowRate() {
var velocityInput = document.getElementById("velocity");
var diameterInput = document.getElementById("diameter");
var resultDiv = document.getElementById("result");
var velocity = parseFloat(velocityInput.value);
var diameter = parseFloat(diameterInput.value);
if (isNaN(velocity) || isNaN(diameter) || velocity < 0 || diameter <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for velocity and a positive number for diameter.";
return;
}
var pi = Math.PI;
var radius = diameter / 2;
var area = pi * Math.pow(radius, 2);
var flowRate = velocity * area;
resultDiv.innerHTML = "
Calculated Flow Rate: " + flowRate.toFixed(6) + " m³/s";
}
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