Manning Flow Calculator

Manning Flow Calculator

Metric (m, m/s, m³/s) Imperial (ft, ft/s, ft³/s)

Understanding the Manning Formula

The Manning formula is an empirical equation used to estimate the velocity of liquids flowing in open channels. Engineers and hydrologists use this calculation to design sewers, drainage systems, and irrigation canals. Unlike pipe flow under pressure, open channel flow is driven by gravity and the slope of the channel bed.

The Calculation Logic

The Manning Flow Calculator uses the following equations:

• Hydraulic Radius (Rh): Rh = A / P
• Velocity (v) Metric: v = (1 / n) * Rh^(2/3) * S^(1/2)
• Velocity (v) Imperial: v = (1.486 / n) * Rh^(2/3) * S^(1/2)
• Discharge (Q): Q = A * v

Key Variables Explained

• Manning's n: This represents the roughness of the channel. A smooth PVC pipe might have an n-value of 0.009, while a rocky natural stream could exceed 0.040.
• Slope (S): The vertical drop divided by the horizontal length of the channel.
• Cross-Sectional Area (A): The area of the water at a specific depth, perpendicular to the flow.
• Wetted Perimeter (P): The length of the channel surface in contact with the water.

Manning's n-Value Reference Table

Material	Typical n-Value
Smooth Plastic (PVC)	0.009 – 0.011
Finished Concrete	0.012 – 0.014
Cast Iron	0.013 – 0.015
Corrugated Metal	0.021 – 0.025
Earth Canal (Clean)	0.018 – 0.025
Natural Stream (Sluggish)	0.040 – 0.050

Example Calculation

Imagine a rectangular concrete channel with the following characteristics:

• Width: 2 meters
• Water Depth: 0.5 meters
• Slope: 0.01 (1%)
• Roughness (n): 0.013

Step 1: Calculate Area (A) = 2m * 0.5m = 1.0 m².

Step 2: Calculate Wetted Perimeter (P) = 0.5m + 2m + 0.5m = 3.0 m.

Step 3: Calculate Hydraulic Radius (Rh) = 1.0 / 3.0 = 0.333 m.

Step 4: Calculate Velocity (v) = (1 / 0.013) * (0.333)^(2/3) * (0.01)^0.5 = 3.69 m/s.

Step 5: Calculate Discharge (Q) = 1.0 m² * 3.69 m/s = 3.69 m³/s.

function updateLabels() { var unit = document.getElementById('unitSystem').value; var areaLabel = document.getElementById('areaLabel'); var perimeterLabel = document.getElementById('perimeterLabel'); if (unit === 'metric') { areaLabel.innerText = "Cross-Sectional Area (A) [m²]"; perimeterLabel.innerText = "Wetted Perimeter (P) [m]"; } else { areaLabel.innerText = "Cross-Sectional Area (A) [ft²]"; perimeterLabel.innerText = "Wetted Perimeter (P) [ft]"; } } function calculateManningFlow() { var unit = document.getElementById('unitSystem').value; var n = parseFloat(document.getElementById('manningN').value); var s = parseFloat(document.getElementById('slope').value); var a = parseFloat(document.getElementById('area').value); var p = parseFloat(document.getElementById('perimeter').value); var resultsDiv = document.getElementById('results'); var resRh = document.getElementById('resRh'); var resV = document.getElementById('resV'); var resQ = document.getElementById('resQ'); // Validation if (isNaN(n) || isNaN(s) || isNaN(a) || isNaN(p) || n <= 0 || s <= 0 || a <= 0 || p <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // k constant var k = (unit === 'metric') ? 1.0 : 1.486; // Hydraulic Radius var rh = a / p; // Velocity // v = (k/n) * Rh^(2/3) * S^(1/2) var velocity = (k / n) * Math.pow(rh, (2/3)) * Math.pow(s, 0.5); // Discharge var discharge = a * velocity; // Display Units var unitV = (unit === 'metric') ? ' m/s' : ' ft/s'; var unitQ = (unit === 'metric') ? ' m³/s' : ' ft³/s'; var unitRh = (unit === 'metric') ? ' m' : ' ft'; // Set Results resRh.innerHTML = rh.toFixed(4) + unitRh; resV.innerHTML = velocity.toFixed(3) + unitV; resQ.innerHTML = discharge.toFixed(3) + unitQ; resultsDiv.style.display = 'block'; }