Please enter valid positive numbers for all fields.
Flow Rate (Discharge Q):0 L/s
Flow Rate (Hourly):0 m³/h
Flow Velocity (V):0 m/s
Hydraulic Radius (R):0 m
Understanding Sewage Discharge Rate Calculation
Calculating the sewage discharge rate is a critical component of hydraulic engineering and wastewater management system design. By determining the flow rate through pipes and channels, engineers can ensure that sewer systems have adequate capacity to handle peak loads without causing back-ups or environmental hazards.
How This Calculator Works
This tool utilizes Manning's Equation, the standard empirical formula used in hydraulic engineering for open channel flow. Even though sewer pipes are closed conduits, they typically operate under "gravity flow" conditions (partially full), which acts like an open channel.
The calculation considers the physical properties of the pipe and the fluid level to determine the Discharge ($Q$) and Velocity ($V$).
The internal diameter of the sewer pipe. Standard municipal sewer mains often range from 150mm (6 inches) to over 1000mm. The larger the diameter, the higher the potential capacity.
2. Pipe Slope (Gradient)
The slope is the vertical drop of the pipe per unit of horizontal distance, typically expressed as a percentage. Slope creates the gravitational force that moves the sewage.
Example: A 1% slope means the pipe drops 1 meter for every 100 meters of length.
3. Filling Percentage
Sewers are rarely designed to run 100% full to prevent pressurization and allow for air movement.
Dry Weather Flow: Often calculated at low filling percentages.
Design Capacity: Typically calculated at 50% to 75% filling.
4. Manning's Roughness Coefficient (n)
This value represents the friction inside the pipe. Smoother materials allow for faster flow.
PVC (Plastic): n ≈ 0.009 (Very smooth, high flow)
Concrete: n ≈ 0.013 (Standard roughness)
Corrugated Metal: n ≈ 0.024 (High friction, slower flow)
Why Velocity Matters
In sewage design, achieving a "self-cleansing velocity" is crucial. If the flow is too slow (typically under 0.6 m/s or 2 ft/s), solids may settle and clog the pipe. If the flow is too fast (over 3.0 m/s), it may cause abrasion and damage the pipe material over time.
function calculateSewageDischarge() {
// 1. Get Input Elements
var diameterInput = document.getElementById('pipe_diameter');
var slopeInput = document.getElementById('pipe_slope');
var fillInput = document.getElementById('fill_percentage');
var materialInput = document.getElementById('pipe_material');
var resultBox = document.getElementById('results');
var errorBox = document.getElementById('error-message');
// 2. Parse Values
var D_mm = parseFloat(diameterInput.value); // Diameter in mm
var slope_percent = parseFloat(slopeInput.value); // Slope in %
var fill_percent = parseFloat(fillInput.value); // Filling in %
var n = parseFloat(materialInput.value); // Manning's n
// 3. Validation
if (isNaN(D_mm) || D_mm <= 0 ||
isNaN(slope_percent) || slope_percent <= 0 ||
isNaN(fill_percent) || fill_percent 100 ||
isNaN(n)) {
errorBox.style.display = 'block';
resultBox.style.display = 'none';
return;
}
errorBox.style.display = 'none';
resultBox.style.display = 'block';
// 4. Conversion to SI Units for Calculation
var D = D_mm / 1000; // Convert mm to meters
var S = slope_percent / 100; // Convert percentage to decimal
var r = D / 2; // Radius of pipe
// 5. Geometric Calculations based on Filling Percentage
// Depth of flow (h)
var h = D * (fill_percent / 100);
var theta; // Central angle in radians
var A; // Wetted Area
var P; // Wetted Perimeter
// Handle full pipe case separately to avoid math errors with acos
if (fill_percent >= 100) {
theta = 2 * Math.PI;
A = Math.PI * Math.pow(r, 2);
P = Math.PI * D;
} else {
// Theta formula: 2 * acos(1 – 2 * (h/D))
// The term inside acos represents (r-h)/r which simplifies to 1 – 2(h/D)
theta = 2 * Math.acos(1 – (2 * h / D));
// Area segment formula: (r^2 / 2) * (theta – sin(theta))
A = (Math.pow(r, 2) / 2) * (theta – Math.sin(theta));
// Perimeter arc formula: r * theta
P = r * theta;
}
// Hydraulic Radius (R)
var R = A / P;
// 6. Manning's Equation Calculation
// Q = (1/n) * A * R^(2/3) * S^(1/2)
var Q_m3s = (1 / n) * A * Math.pow(R, 2/3) * Math.pow(S, 1/2);
// Velocity V = Q / A
var V = Q_m3s / A;
// 7. Unit Conversions for Output
var Q_ls = Q_m3s * 1000; // Liters per second
var Q_m3h = Q_m3s * 3600; // Cubic meters per hour
// 8. Display Results
document.getElementById('res_q_ls').innerHTML = Q_ls.toFixed(2) + ' L/s';
document.getElementById('res_q_m3h').innerHTML = Q_m3h.toFixed(2) + ' m³/h';
document.getElementById('res_v').innerHTML = V.toFixed(2) + ' m/s';
document.getElementById('res_r').innerHTML = R.toFixed(4) + ' m';
}