A Venturi meter is a device used for measuring the rate of flow of a fluid flowing through a pipe. It works on the principle of Bernoulli's equation. When a fluid passes through a constricted section (the throat) of a pipe, its velocity increases and its pressure decreases. By measuring the pressure difference between the inlet and the throat, we can accurately calculate the discharge or flow rate.
The Flow Rate Formula
The actual flow rate (Q) in a Venturi meter is calculated using the following formula:
Q = Cd * [(A1 * A2) / sqrt(A1² – A2²)] * sqrt(2 * g * h)
Q: Actual flow rate (m³/s)
Cd: Coefficient of discharge (typically 0.95 to 0.99)
A1: Area of the inlet (m²)
A2: Area of the throat (m²)
g: Acceleration due to gravity (9.81 m/s²)
h: Difference in pressure head (m)
Step-by-Step Calculation Example
Suppose you have a pipe with an inlet diameter of 200 mm and a throat diameter of 100 mm. The differential manometer shows a head difference of 2 meters of water. Assume Cd = 0.98.
Convert Diameters to Meters: D1 = 0.2m, D2 = 0.1m.
Convert to Liters: 0.0497 * 1000 = 49.7 Liters/second.
Key Factors Affecting Accuracy
Several factors can influence the precision of your Venturi meter readings:
Surface Roughness: Internal friction can lower the Coefficient of Discharge.
Installation: Venturi meters require a certain length of straight pipe before and after the device to ensure laminar flow.
Fluid Viscosity: Highly viscous fluids may deviate from standard Bernoulli behavior, requiring a specific Reynolds number correction.
function calculateVenturiFlow() {
var d1_mm = document.getElementById("inlet_d").value;
var d2_mm = document.getElementById("throat_d").value;
var h = document.getElementById("head_diff").value;
var cd = document.getElementById("coeff_d").value;
var g = 9.81;
if (d1_mm && d2_mm && h && cd) {
var d1 = parseFloat(d1_mm) / 1000;
var d2 = parseFloat(d2_mm) / 1000;
var head = parseFloat(h);
var coeff = parseFloat(cd);
if (d2 >= d1) {
alert("Throat diameter must be smaller than inlet diameter.");
return;
}
// Areas
var a1 = (Math.PI * Math.pow(d1, 2)) / 4;
var a2 = (Math.PI * Math.pow(d2, 2)) / 4;
// Math logic
var numerator = a1 * a2;
var denominator = Math.sqrt(Math.pow(a1, 2) – Math.pow(a2, 2));
var velocityPart = Math.sqrt(2 * g * head);
var theoryQ = (numerator / denominator) * velocityPart;
var actualQ = coeff * theoryQ;
var litersQ = actualQ * 1000;
document.getElementById("theory-q").innerText = theoryQ.toFixed(5);
document.getElementById("actual-q").innerText = actualQ.toFixed(5);
document.getElementById("liters-q").innerText = litersQ.toFixed(2);
document.getElementById("venturi-results").style.display = "block";
} else {
alert("Please fill in all fields with valid numbers.");
}
}