Cubic Feet / Sec (CFS)
Gallons / Min (GPM)
Million Gallons / Day (MGD)
Cubic Meters / Sec (CMS)
Liters / Sec (LPS)
Calculated Flow Rate (Q):0.00CFS
Formula: Q = C * Ha^n
Status: Free-Flow Condition Assumed
function calculateParshallFlow() {
var size = document.getElementById("flumeSize").value;
var head = parseFloat(document.getElementById("headValue").value);
var headUnit = document.getElementById("headUnit").value;
var outputUnit = document.getElementById("outputUnit").value;
if (isNaN(head) || head <= 0) {
alert("Please enter a valid positive value for Measured Head (Ha).");
return;
}
// Convert Head to Feet for standard formula calculation
var headInFeet = head;
if (headUnit === "in") headInFeet = head / 12;
else if (headUnit === "m") headInFeet = head * 3.28084;
else if (headUnit === "cm") headInFeet = head / 30.48;
// Constants based on Throat Width (Standard English Units)
var C = 4.0;
var n = 1.522;
var sizeLabel = "1 foot";
// Lookup Table for Constants (W in feet)
var config = {
"0.0833": { c: 0.338, n: 1.55, label: "1 inch" },
"0.1667": { c: 0.676, n: 1.55, label: "2 inch" },
"0.25": { c: 0.992, n: 1.547, label: "3 inch" },
"0.5": { c: 2.06, n: 1.58, label: "6 inch" },
"0.75": { c: 3.07, n: 1.53, label: "9 inch" },
"1.0": { c: 4.0, n: 1.522, label: "1 foot" },
"1.5": { c: 6.0, n: 1.538, label: "1.5 feet" },
"2.0": { c: 8.0, n: 1.550, label: "2 feet" },
"3.0": { c: 12.0, n: 1.566, label: "3 feet" },
"4.0": { c: 16.0, n: 1.578, label: "4 feet" },
"5.0": { c: 20.0, n: 1.587, label: "5 feet" },
"6.0": { c: 24.0, n: 1.595, label: "6 feet" },
"8.0": { c: 32.0, n: 1.607, label: "8 feet" },
"10.0": { c: 40.0, n: 1.617, label: "10 feet" }
};
if (config[size]) {
C = config[size].c;
n = config[size].n;
sizeLabel = config[size].label;
}
// Calculate Flow (Q) in Cubic Feet per Second (CFS)
var qCFS = C * Math.pow(headInFeet, n);
var finalResult = qCFS;
var unitLabel = "CFS";
// Convert Q to requested output unit
if (outputUnit === "gpm") {
finalResult = qCFS * 448.831;
unitLabel = "GPM";
} else if (outputUnit === "mgd") {
finalResult = qCFS * 0.646317;
unitLabel = "MGD";
} else if (outputUnit === "cms") {
finalResult = qCFS / 35.3147;
unitLabel = "CMS";
} else if (outputUnit === "lps") {
finalResult = (qCFS / 35.3147) * 1000;
unitLabel = "LPS";
}
// Display Results
document.getElementById("flowResult").innerText = finalResult.toLocaleString(undefined, {minimumFractionDigits: 3, maximumFractionDigits: 3});
document.getElementById("unitResult").innerText = unitLabel;
document.getElementById("formulaUsed").innerText = "Formula used for " + sizeLabel + " flume: Q = " + C + " * Ha^" + n;
document.getElementById("resultArea").style.display = "block";
}
Understanding Parshall Flume Flow Measurement
The Parshall flume is a specialized fixed-structure hydraulic device used to measure the flow rate of surface water, wastewater, and industrial discharge in open channels. Developed by Ralph L. Parshall in the 1920s, it is one of the most widely used flumes globally due to its ability to operate with minimal head loss and its "self-cleaning" design.
The Calculation Formula
Under free-flow conditions, the discharge through a Parshall flume is calculated using the power law equation:
Q = C * (Ha)^n
Q: The flow rate (Discharge).
C: The free-flow coefficient (specific to the throat width W).
Ha: The measured head at the primary point of measurement.
n: The exponent based on the throat width.
Where to Measure Head (Ha)
To get an accurate reading, you must measure the water level (Head) at the correct location. For a Parshall flume, the measurement point Ha is located in the converging section, specifically at a distance of 2/3 of the length of the converging wall upstream from the beginning of the throat.
Free Flow vs. Submerged Flow
This calculator assumes Free-Flow conditions. Free flow occurs when the downstream water level does not significantly impede the flow through the flume. If the downstream level rises (Submergence), a correction factor must be applied. For a 1-foot flume, submergence is usually critical when the ratio of the downstream head (Hb) to the upstream head (Ha) exceeds 0.70 (70%).
Example Calculation
If you have a 6-inch flume (C=2.06, n=1.58) and you measure a head Ha of 0.5 feet: