Calculate Hydraulic and Shaft Power based on Flow Rate and Head
Unit: Cubic meters per hour (m³/h)
Unit: Meters (m)
kg/m³ (Water ≈ 1000)
Percentage (%)
Please enter valid positive numbers for all fields.
Required Shaft Power0 kW
Hydraulic Power (Theoretical):0 kW
Shaft Power (Horsepower):0 HP
Fluid Specific Gravity:1.0
function calculatePumpPower() {
// 1. Get input elements by ID
var flowRateInput = document.getElementById("flowRate");
var totalHeadInput = document.getElementById("totalHead");
var fluidDensityInput = document.getElementById("fluidDensity");
var pumpEfficiencyInput = document.getElementById("pumpEfficiency");
// 2. Parse values
var Q_m3h = parseFloat(flowRateInput.value); // Flow in m3/h
var H_m = parseFloat(totalHeadInput.value); // Head in meters
var rho = parseFloat(fluidDensityInput.value); // Density in kg/m3
var eta_percent = parseFloat(pumpEfficiencyInput.value); // Efficiency in %
// 3. Validation
var errorMsg = document.getElementById("errorMsg");
var resultsArea = document.getElementById("results-area");
if (isNaN(Q_m3h) || isNaN(H_m) || isNaN(rho) || isNaN(eta_percent) ||
Q_m3h <= 0 || H_m <= 0 || rho <= 0 || eta_percent <= 0) {
errorMsg.style.display = "block";
resultsArea.style.display = "none";
return;
} else {
errorMsg.style.display = "none";
resultsArea.style.display = "block";
}
// 4. Constants
var g = 9.81; // Gravity m/s^2
// 5. Conversions
// Convert Flow from m3/h to m3/s
var Q_m3s = Q_m3h / 3600;
// Convert Efficiency to decimal
var eta_decimal = eta_percent / 100;
// 6. Calculation Logic
// Hydraulic Power (P_hyd) in Watts = rho * g * Q * H
var pHyd_watts = rho * g * Q_m3s * H_m;
// Convert Hydraulic Power to Kilowatts
var pHyd_kW = pHyd_watts / 1000;
// Shaft Power (P_shaft) = P_hyd / efficiency
var pShaft_kW = pHyd_kW / eta_decimal;
// Convert Shaft Power to Horsepower (1 kW = 1.34102 HP)
var pShaft_HP = pShaft_kW * 1.34102;
// Specific Gravity (SG) = Density / Density of Water (1000)
var sg = rho / 1000;
// 7. Update DOM elements
document.getElementById("hydraulicPowerResult").innerHTML = pHyd_kW.toFixed(2) + " kW";
document.getElementById("shaftPowerResult").innerHTML = pShaft_kW.toFixed(2) + " kW";
document.getElementById("hpResult").innerHTML = pShaft_HP.toFixed(2) + " HP";
document.getElementById("sgResult").innerHTML = sg.toFixed(2);
}
How to Calculate Pump Power from Flow Rate
Calculating the power required to drive a pump is a fundamental task in fluid mechanics and engineering. Whether you are sizing a water pump for an irrigation system or an industrial chemical pump, understanding the relationship between flow rate, head, and power is essential to ensure system efficiency and longevity.
The Basic Pump Power Formula
The power transferred to the fluid (Hydraulic Power) is calculated using the following physics formula:
Phyd = ( ρ × g × Q × H ) / 1000
Where:
Phyd = Hydraulic Power in kilowatts (kW)
ρ (rho) = Fluid Density in kg/m³ (Water is approx 1000 kg/m³)
g = Acceleration due to gravity (9.81 m/s²)
Q = Flow rate in cubic meters per second (m³/s)
H = Total Differential Head in meters (m)
From Hydraulic Power to Shaft Power
The formula above calculates the theoretical power required if the pump were 100% efficient. However, in the real world, pumps lose energy due to friction and mechanical losses. To find the actual motor size required (Shaft Power), you must account for the pump's efficiency (η).
Pshaft = Phyd / η
Where η is the pump efficiency expressed as a decimal (e.g., 75% efficiency = 0.75). The Shaft Power will always be higher than the Hydraulic Power.
Step-by-Step Calculation Example
Let's calculate the power required for a water pump with the following specifications:
Account for Efficiency:
2.725 kW / 0.75 = 3.63 kW.
Therefore, the required Shaft Power is 3.63 kW.
Why Specific Gravity Matters
The calculator allows you to input fluid density because pumping heavier fluids requires more power. Water has a specific gravity of 1.0 (1000 kg/m³). If you are pumping brine (SG 1.2) or fuel oil (SG 0.85), the power requirement changes directly in proportion to the density.
Choosing the Right Motor
Once you calculate the Shaft Power (e.g., 3.63 kW), you should select a standard motor size that exceeds this value to provide a safety margin, typically by 10% to 15%, ensuring the motor does not overheat during operation.