Manning's Pipe Flow Calculator

Calculate water flow rate and velocity in circular pipes using the Manning Equation.

Pipe Diameter (mm)

Manning's n (Roughness)

Pipe Slope (m/m)

Calculation Results (Full Pipe)

Flow Rate (Q):

0.00 m³/s

Flow Velocity (V):

0.00 m/s

Flow Rate (Liters):

0.00 L/s

Hydraulic Radius (Rh):

0.00 m

Understanding the Manning Pipe Flow Formula

The Manning formula is an empirical equation that applies to uniform flow in open channels and pipes. It is a fundamental tool for civil and hydraulic engineers when designing gravity-fed sewer systems, storm drains, and irrigation pipes. While the formula is originally for open channels, it is used for pipes by assuming they are running "full" or "partially full" under gravity, rather than under pressure.

The Manning Equation Formula

V = (1 / n) * Rh^(2/3) * S^(1/2)

Where:

V: Average velocity (m/s).
n: Manning's roughness coefficient (unitless).
Rh: Hydraulic radius (m), which is the cross-sectional area divided by the wetted perimeter.
S: Slope of the pipe (m/m).

Typical Manning's Roughness Coefficients (n)

Material	Typical "n" Value
PVC / Plastic	0.009 – 0.011
Ductile Iron (Cement lined)	0.011 – 0.013
Concrete (Smooth)	0.012 – 0.014
Corrugated Metal Pipe	0.022 – 0.025

Example Calculation

Imagine a concrete storm pipe with a diameter of 600mm (0.6m) and a slope of 0.5% (0.005 m/m). We use a roughness coefficient (n) of 0.013.

Area (A): π * (0.3)² = 0.2827 m²
Hydraulic Radius (Rh): For a full pipe, Rh = Diameter / 4 = 0.6 / 4 = 0.15m
Velocity (V): (1 / 0.013) * (0.15)^(2/3) * (0.005)^(1/2) ≈ 1.53 m/s
Flow Rate (Q): A * V = 0.2827 * 1.53 ≈ 0.433 m³/s

Importance of Slope and Diameter

The Manning formula highlights that the flow capacity increases significantly with the pipe's diameter and slope. However, engineers must balance flow rate with "scouring velocity." If the velocity is too low, solids will settle (siltation); if it's too high, it may damage the pipe material (erosion). Ideally, sewer pipes are designed to maintain a velocity of at least 0.6 to 0.9 m/s to remain self-cleansing.

function calculateManningFlow() { var diameterMm = parseFloat(document.getElementById('pipeDiameter').value); var n = parseFloat(document.getElementById('manningN').value); var slope = parseFloat(document.getElementById('pipeSlope').value); if (isNaN(diameterMm) || isNaN(n) || isNaN(slope) || diameterMm <= 0 || n <= 0 || slope <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Convert Diameter to meters var D = diameterMm / 1000; // Cross-sectional Area A = (PI * D^2) / 4 var A = (Math.PI * Math.pow(D, 2)) / 4; // Wetted Perimeter P = PI * D var P = Math.PI * D; // Hydraulic Radius Rh = A / P = D / 4 (for full pipe) var Rh = D / 4; // Velocity V = (1/n) * Rh^(2/3) * S^(1/2) var V = (1 / n) * Math.pow(Rh, (2 / 3)) * Math.pow(slope, 0.5); // Flow Rate Q = A * V var Q = A * V; // Liters per second var Lps = Q * 1000; // Display Results document.getElementById('resFlowRate').innerText = Q.toFixed(4) + " m³/s"; document.getElementById('resVelocity').innerText = V.toFixed(3) + " m/s"; document.getElementById('resLiters').innerText = Lps.toFixed(2) + " L/s"; document.getElementById('resHydRadius').innerText = Rh.toFixed(4) + " m"; document.getElementById('resultsArea').style.display = "block"; }

Mannings Pipe Flow Calculator