:root {
–primary-color: #0066cc;
–secondary-color: #f0f7ff;
–text-color: #333;
–border-color: #ddd;
}
body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: var(–text-color);
max-width: 1200px;
margin: 0 auto;
padding: 20px;
}
.calculator-wrapper {
background: #fff;
border: 1px solid var(–border-color);
border-radius: 8px;
box-shadow: 0 4px 6px rgba(0,0,0,0.1);
padding: 30px;
margin-bottom: 40px;
max-width: 600px;
margin-left: auto;
margin-right: auto;
}
.calc-header {
text-align: center;
margin-bottom: 25px;
border-bottom: 2px solid var(–primary-color);
padding-bottom: 10px;
}
.form-group {
margin-bottom: 20px;
}
.form-group label {
display: block;
font-weight: 600;
margin-bottom: 8px;
color: #444;
}
.form-control {
width: 100%;
padding: 12px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.form-row {
display: flex;
gap: 20px;
}
.col {
flex: 1;
}
.btn-calculate {
background-color: var(–primary-color);
color: white;
border: none;
padding: 15px 30px;
font-size: 18px;
font-weight: bold;
border-radius: 4px;
cursor: pointer;
width: 100%;
transition: background-color 0.3s;
}
.btn-calculate:hover {
background-color: #0052a3;
}
.results-area {
margin-top: 30px;
background-color: var(–secondary-color);
padding: 20px;
border-radius: 6px;
display: none;
}
.result-row {
display: flex;
justify-content: space-between;
align-items: center;
padding: 10px 0;
border-bottom: 1px solid #dee2e6;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
font-weight: 600;
}
.result-value {
font-size: 20px;
color: var(–primary-color);
font-weight: bold;
}
.article-content {
background: #fff;
padding: 30px;
border-radius: 8px;
border: 1px solid #eee;
}
h2, h3 {
color: var(–primary-color);
margin-top: 1.5em;
}
.info-box {
background: #eef;
padding: 15px;
border-left: 4px solid var(–primary-color);
margin: 20px 0;
}
@media (max-width: 600px) {
.form-row {
flex-direction: column;
gap: 0;
}
}
How to Calculate Power from Flow Rate
Understanding the relationship between flow rate and power is fundamental in fluid mechanics, engineering, and industrial applications. Whether you are sizing a pump to move water up a hill or calculating the potential energy generation of a hydroelectric turbine, the core physics remains the same. This guide explains how to convert flow rate into power output or requirement.
The Hydraulic Power Formula
Hydraulic power represents the energy per unit time effectively transferred to or from the fluid. The calculation depends heavily on the specific gravity of the fluid, the flow rate, and the pressure head (or height) involved.
General Physics Equation:
P = ρ × g × Q × H
Where:
- P = Power (Watts)
- ρ (rho) = Density of fluid (kg/m³)
- g = Gravity (9.81 m/s²)
- Q = Flow rate (m³/s)
- H = Head (meters)
1. Calculating in Metric Units (SI)
In the metric system, we typically calculate power in Kilowatts (kW). When using standard engineering units like Liters per Second (L/s) and Meters (m), the formula simplifies to:
Hydraulic Power (kW) = (Flow [L/s] × Head [m] × 9.81 × SG) / 1000
Where SG is Specific Gravity (Water = 1.0).
2. Calculating in Imperial Units (US)
In the US, flow is often measured in Gallons Per Minute (GPM) and head in Feet. The resulting power is expressed in Horsepower (HP).
Hydraulic Power (HP) = (Flow [GPM] × Head [ft] × SG) / 3960
The constant 3960 relates horsepower to gallons, minutes, and weight of water.
Hydraulic Power vs. Shaft Power
The calculation above gives you the "Water Horsepower" or "Hydraulic Power"—the theoretical power assuming 100% efficiency. However, no machine is perfect.
For Pumps (Power Required)
To find the size of the motor needed to drive a pump, you must divide the hydraulic power by the pump's efficiency. This gives you the Brake Horsepower (BHP).
Shaft Power = Hydraulic Power / Efficiency (decimal)
Example: If you need 10 kW of hydraulic power and your pump is 75% efficient (0.75), you need a motor capable of delivering 13.33 kW.
For Turbines (Power Generated)
If you are calculating power generated from a flow (like a micro-hydro setup), you multiply the hydraulic power by the efficiency of the turbine and generator.
Output Power = Hydraulic Power × Efficiency (decimal)
Key Variables Explained
- Flow Rate (Q): The volume of fluid moving through the system per unit of time.
- Total Dynamic Head (H): The total equivalent height that the fluid is to be pumped, taking into account vertical lift and friction losses in the pipe.
- Specific Gravity (SG): The ratio of the fluid's density to the density of water. Water is 1.0. Heavier fluids (like sludge) require more power to move.
- Efficiency (η): The ratio of useful work performed to total energy expended. Typical centrifugal pumps range from 50% to 85% efficiency.
Practical Example
Imagine you need to pump water (SG = 1.0) up to a tank located 30 meters high. You require a flow rate of 25 Liters per second. The pump has an estimated efficiency of 70%.
- Calculate Hydraulic Power: (25 L/s × 30 m × 9.81 × 1.0) / 1000 = 7.36 kW.
- Calculate Shaft Power: 7.36 kW / 0.70 = 10.51 kW.
You would need a motor rated for at least 11 kW to handle this load safely.
// Initial label setup
updateLabels();
function updateLabels() {
var system = document.getElementById('unitSystem').value;
var flowLabel = document.getElementById('flowLabel');
var headLabel = document.getElementById('headLabel');
if (system === 'metric') {
flowLabel.innerHTML = 'L/s';
headLabel.innerHTML = 'meters';
} else {
flowLabel.innerHTML = 'GPM';
headLabel.innerHTML = 'feet';
}
}
function calculateHydraulicPower() {
// Get Inputs
var system = document.getElementById('unitSystem').value;
var type = document.getElementById('machineType').value;
var flow = parseFloat(document.getElementById('flowRate').value);
var head = parseFloat(document.getElementById('headHeight').value);
var sg = parseFloat(document.getElementById('specificGravity').value);
var eff = parseFloat(document.getElementById('efficiency').value);
// Validation
if (isNaN(flow) || isNaN(head) || isNaN(sg) || isNaN(eff)) {
alert("Please enter valid numbers in all fields.");
return;
}
if (eff 100) {
alert("Efficiency must be between 0 and 100.");
return;
}
var hydraulicPower = 0;
var shaftPower = 0;
var unitLabel = "";
var decimalEff = eff / 100;
// Calculate Hydraulic Power
if (system === 'metric') {
// Formula: kW = (Q(L/s) * H(m) * 9.81 * SG) / 1000
hydraulicPower = (flow * head * 9.81 * sg) / 1000;
unitLabel = "kW";
} else {
// Formula: HP = (Q(GPM) * H(ft) * SG) / 3960
hydraulicPower = (flow * head * sg) / 3960;
unitLabel = "HP";
}
// Calculate Shaft/Brake Power based on Machine Type
if (type === 'pump') {
// Pump: We need MORE power input than the hydraulic work done
shaftPower = hydraulicPower / decimalEff;
document.getElementById('shaftLabel').innerHTML = "Required Shaft Power:";
} else {
// Turbine: We get LESS power output than the available hydraulic energy
shaftPower = hydraulicPower * decimalEff;
document.getElementById('shaftLabel').innerHTML = "Generated Power Output:";
}
// Display Results
var resultsDiv = document.getElementById('results');
resultsDiv.style.display = "block";
document.getElementById('hydraulicPowerResult').innerHTML = hydraulicPower.toFixed(2) + " " + unitLabel;
document.getElementById('brakePowerResult').innerHTML = shaftPower.toFixed(2) + " " + unitLabel;
var fluidText = (sg === 1) ? "Water (SG 1.0)" : "Fluid (SG " + sg + ")";
document.getElementById('fluidTypeDisplay').innerHTML = fluidText;
}