body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 1200px;
margin: 0 auto;
padding: 20px;
background-color: #f4f7f6;
}
.calculator-container {
background: #ffffff;
padding: 30px;
border-radius: 12px;
box-shadow: 0 4px 15px rgba(0,0,0,0.1);
margin-bottom: 40px;
border-top: 5px solid #0056b3;
}
.calculator-title {
font-size: 24px;
font-weight: 700;
color: #2c3e50;
margin-bottom: 25px;
text-align: center;
}
.input-group {
margin-bottom: 20px;
display: flex;
flex-direction: column;
}
.input-group label {
font-weight: 600;
margin-bottom: 8px;
color: #4a5568;
}
.input-group input {
padding: 12px;
border: 1px solid #cbd5e0;
border-radius: 6px;
font-size: 16px;
transition: border-color 0.2s;
}
.input-group input:focus {
border-color: #0056b3;
outline: none;
box-shadow: 0 0 0 3px rgba(0, 86, 179, 0.1);
}
.grid-2 {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
.calculate-btn {
background-color: #0056b3;
color: white;
border: none;
padding: 15px 30px;
font-size: 18px;
font-weight: bold;
border-radius: 6px;
cursor: pointer;
width: 100%;
margin-top: 10px;
transition: background-color 0.2s;
}
.calculate-btn:hover {
background-color: #004494;
}
.results-area {
margin-top: 30px;
background-color: #f8fafc;
border-radius: 8px;
padding: 20px;
display: none;
border: 1px solid #e2e8f0;
}
.result-item {
display: flex;
justify-content: space-between;
align-items: center;
padding: 12px 0;
border-bottom: 1px solid #e2e8f0;
}
.result-item:last-child {
border-bottom: none;
}
.result-label {
font-weight: 600;
color: #64748b;
}
.result-value {
font-size: 20px;
font-weight: 700;
color: #0056b3;
}
.article-content {
background: white;
padding: 30px;
border-radius: 12px;
box-shadow: 0 2px 10px rgba(0,0,0,0.05);
}
h2 {
color: #2c3e50;
margin-top: 30px;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
h3 {
color: #34495e;
margin-top: 25px;
}
.formula-box {
background: #eef2f7;
padding: 20px;
border-left: 4px solid #0056b3;
font-family: monospace;
font-size: 1.1em;
margin: 20px 0;
}
p {
margin-bottom: 15px;
}
ul {
margin-bottom: 20px;
}
@media (max-width: 768px) {
.grid-2 {
grid-template-columns: 1fr;
}
}
Understanding the Centrifugal Pump Flow Rate Formula
Calculating the flow rate of a centrifugal pump is a fundamental task in fluid mechanics and engineering. Unlike positive displacement pumps where flow is strictly a function of speed and displacement per revolution, a centrifugal pump's flow rate depends heavily on the system head (pressure), the power applied, and the efficiency of the impeller design.
This calculator determines the theoretical flow rate based on the available hydraulic power, which is derived from the shaft power of the motor and the pump's efficiency.
The Flow Rate Calculation Formula
The relationship between Flow Rate ($Q$), Total Dynamic Head ($H$), Power ($P$), and Efficiency ($\eta$) is governed by the following physics equation:
P = (ρ × g × Q × H) / η
Where:
- P = Shaft Power (Watts)
- ρ (rho) = Fluid Density (kg/m³)
- g = Acceleration due to gravity (approx. 9.81 m/s²)
- Q = Flow Rate (m³/s)
- H = Total Dynamic Head (meters)
- η (eta) = Pump Efficiency (decimal, e.g., 0.75)
To solve for Flow Rate (Q), we rearrange the formula:
Q = (P × η) / (ρ × g × H)
Key Input Parameters Explained
1. Motor/Shaft Power (kW)
This is the power delivered by the motor to the pump shaft. It is important to distinguish between the electrical power consumed by the motor and the mechanical power delivered to the shaft. For this formula, we use the mechanical power rating. Note that 1 kW = 1000 Watts.
2. Total Dynamic Head (m)
Head is a measure of the energy content of the fluid. In practical terms, Total Dynamic Head (TDH) represents the vertical height the pump must lift the fluid, plus the friction losses in the pipework. If the head increases (e.g., closing a valve or pumping higher), the flow rate of a centrifugal pump will naturally decrease.
3. Fluid Density (kg/m³)
The mass of the fluid per unit volume. Standard water at room temperature is approximately 997 kg/m³. Heavier fluids (like brine) require more power to pump at the same flow rate and head, while lighter fluids (like gasoline) require less.
4. Pump Efficiency (%)
No pump converts 100% of input power into hydraulic energy. Losses occur due to friction, internal recirculation, and mechanical drag. Standard centrifugal pumps typically operate between 50% and 85% efficiency at their Best Efficiency Point (BEP).
Affinity Laws and Flow Rate
It is also worth noting that if you already have a known flow rate and want to adjust the speed (RPM) of the pump, you can use the Pump Affinity Laws:
- Flow is proportional to Speed: $Q_2 / Q_1 = N_2 / N_1$
- Head is proportional to Speed squared: $H_2 / H_1 = (N_2 / N_1)^2$
- Power is proportional to Speed cubed: $P_2 / P_1 = (N_2 / N_1)^3$
This means a small increase in pump speed yields a proportional increase in flow rate, but requires a significant increase in power.
function calculateFlowRate() {
// 1. Get Input Values
var powerKW = document.getElementById("shaftPower").value;
var headMeters = document.getElementById("totalHead").value;
var density = document.getElementById("fluidDensity").value;
var efficiencyPercent = document.getElementById("pumpEfficiency").value;
var resultsArea = document.getElementById("resultsArea");
// 2. Validation
if (!powerKW || !headMeters || !density || !efficiencyPercent) {
alert("Please fill in all fields to calculate the flow rate.");
return;
}
var powerVal = parseFloat(powerKW);
var headVal = parseFloat(headMeters);
var densityVal = parseFloat(density);
var effVal = parseFloat(efficiencyPercent);
if (powerVal <= 0 || headVal <= 0 || densityVal <= 0 || effVal 100) {
alert("Efficiency cannot exceed 100%.");
return;
}
// 3. Calculation Logic
// Constants
var gravity = 9.81; // m/s^2
// Convert Power from kW to Watts
var powerWatts = powerVal * 1000;
// Convert Efficiency to decimal
var effDecimal = effVal / 100;
// Formula: Q (m3/s) = (Power_Watts * Efficiency) / (Density * Gravity * Head)
// P_hydraulic = rho * g * Q * H
// P_shaft = P_hydraulic / eff
// P_shaft = (rho * g * Q * H) / eff
// Q = (P_shaft * eff) / (rho * g * H)
var denominator = densityVal * gravity * headVal;
var numerator = powerWatts * effDecimal;
// Result in Cubic Meters per Second
var flowM3PerSec = numerator / denominator;
// 4. Unit Conversions
// m3/h = m3/s * 3600
var flowM3PerHour = flowM3PerSec * 3600;
// L/s = m3/s * 1000
var flowLitersPerSec = flowM3PerSec * 1000;
// L/min = L/s * 60
var flowLitersPerMin = flowLitersPerSec * 60;
// GPM (US Gallons per min) = L/min / 3.78541
var flowGPM = flowLitersPerMin / 3.78541;
// 5. Display Results
document.getElementById("resultM3H").innerText = flowM3PerHour.toFixed(2) + " m³/h";
document.getElementById("resultLPM").innerText = flowLitersPerMin.toFixed(1) + " L/min";
document.getElementById("resultLPS").innerText = flowLitersPerSec.toFixed(2) + " L/s";
document.getElementById("resultGPM").innerText = flowGPM.toFixed(1) + " GPM";
// Show results container
resultsArea.style.display = "block";
}