.gp-calculator-wrapper {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
max-width: 800px;
margin: 20px auto;
padding: 20px;
border: 1px solid #e0e0e0;
border-radius: 8px;
background-color: #f9f9f9;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.gp-calc-header {
text-align: center;
margin-bottom: 25px;
}
.gp-calc-header h2 {
color: #2c3e50;
margin: 0;
font-size: 24px;
}
.gp-input-group {
margin-bottom: 20px;
background: #fff;
padding: 15px;
border-radius: 6px;
border: 1px solid #ddd;
}
.gp-input-row {
display: flex;
flex-direction: column;
margin-bottom: 15px;
}
.gp-input-row label {
font-weight: 600;
color: #444;
margin-bottom: 8px;
}
.gp-input-row select, .gp-input-row input {
padding: 12px;
font-size: 16px;
border: 1px solid #ccc;
border-radius: 4px;
width: 100%;
box-sizing: border-box;
}
.gp-input-row input:focus {
border-color: #3498db;
outline: none;
}
.gp-btn {
width: 100%;
padding: 15px;
background-color: #2980b9;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background 0.3s;
}
.gp-btn:hover {
background-color: #2471a3;
}
.gp-results {
margin-top: 25px;
padding: 20px;
background-color: #e8f6f3;
border: 1px solid #d1f2eb;
border-radius: 6px;
display: none;
}
.gp-result-item {
display: flex;
justify-content: space-between;
margin-bottom: 10px;
font-size: 16px;
border-bottom: 1px solid #d1f2eb;
padding-bottom: 5px;
}
.gp-result-item:last-child {
border-bottom: none;
margin-bottom: 0;
padding-bottom: 0;
font-weight: bold;
font-size: 18px;
color: #16a085;
}
.gp-content-article {
max-width: 800px;
margin: 40px auto;
font-family: inherit;
line-height: 1.6;
color: #333;
}
.gp-content-article h2 {
color: #2c3e50;
border-bottom: 2px solid #3498db;
padding-bottom: 10px;
margin-top: 30px;
}
.gp-content-article h3 {
color: #34495e;
margin-top: 25px;
}
.gp-content-article ul {
margin-bottom: 20px;
}
.gp-content-article li {
margin-bottom: 10px;
}
.gp-formula-box {
background: #eee;
padding: 15px;
border-left: 4px solid #3498db;
font-family: monospace;
margin: 15px 0;
}
@media (min-width: 600px) {
.gp-input-row {
flex-direction: row;
align-items: center;
}
.gp-input-row label {
width: 40%;
margin-bottom: 0;
}
.gp-input-row input, .gp-input-row select {
width: 60%;
}
}
var currentUnit = "imperial";
function updateLabels() {
var unitSelect = document.getElementById("unitSystem");
var dispLabel = document.getElementById("labelDisplacement");
var dispInput = document.getElementById("displacement");
currentUnit = unitSelect.value;
if (currentUnit === "imperial") {
dispLabel.innerText = "Displacement (in³/rev):";
dispInput.placeholder = "e.g. 1.5";
} else {
dispLabel.innerText = "Displacement (cm³/rev):";
dispInput.placeholder = "e.g. 25";
}
// Hide results when units change to avoid confusion
document.getElementById("resultContainer").style.display = "none";
}
function calculateFlowRate() {
// Get Input Values
var disp = parseFloat(document.getElementById("displacement").value);
var rpm = parseFloat(document.getElementById("rpm").value);
var eff = parseFloat(document.getElementById("efficiency").value);
// Validation
if (isNaN(disp) || isNaN(rpm) || isNaN(eff)) {
alert("Please enter valid numeric values for all fields.");
return;
}
if (eff > 100 || eff < 0) {
alert("Efficiency must be between 0 and 100.");
return;
}
var theoreticalFlow = 0;
var actualFlow = 0;
var slip = 0;
var unitLabel = "";
// Calculation Logic
if (currentUnit === "imperial") {
// Formula: GPM = (Displacement (in3) * RPM) / 231
theoreticalFlow = (disp * rpm) / 231;
unitLabel = " GPM";
} else {
// Formula: LPM = (Displacement (cc) * RPM) / 1000
theoreticalFlow = (disp * rpm) / 1000;
unitLabel = " LPM";
}
// Apply Efficiency
// Actual Flow = Theoretical * (Efficiency / 100)
actualFlow = theoreticalFlow * (eff / 100);
// Calculate Slip (Difference)
slip = theoreticalFlow – actualFlow;
// Display Results
document.getElementById("theoResult").innerHTML = theoreticalFlow.toFixed(2) + unitLabel;
document.getElementById("slipResult").innerHTML = slip.toFixed(2) + unitLabel;
document.getElementById("actualResult").innerHTML = actualFlow.toFixed(2) + unitLabel;
document.getElementById("resultContainer").style.display = "block";
}
Understanding Gear Pump Flow Rate Calculations
Gear pumps are a type of positive displacement pump extensively used in hydraulic fluid power applications. Accurate flow rate calculation is critical for sizing components such as valves, cylinders, and motors within a hydraulic circuit. This calculator determines both the theoretical output (assuming no leakage) and the actual output based on the volumetric efficiency of the pump.
The Flow Rate Formulas
The output flow of a gear pump is determined by its displacement (the volume of fluid ejected per revolution) and its rotational speed (RPM). Because units of measurement vary by region, two distinct formulas are used.
1. Imperial Formula (GPM)
To calculate flow in Gallons Per Minute (GPM) using displacement in cubic inches per revolution (in³/rev or CIR):
Flow (GPM) = (Displacement × RPM) / 231
Note: The constant 231 represents the number of cubic inches in one US gallon.
2. Metric Formula (LPM)
To calculate flow in Liters Per Minute (LPM) using displacement in cubic centimeters per revolution (cm³/rev or cc/rev):
Flow (LPM) = (Displacement × RPM) / 1000
Volumetric Efficiency and Slip
No gear pump is 100% efficient. As pressure increases at the outlet, a small amount of fluid flows back internally from the high-pressure side to the low-pressure side. This phenomenon is known as "slip" or internal leakage.
Volumetric Efficiency ($\eta_v$) is the ratio of actual flow to theoretical flow.
- New Pumps: Typically operate at 90% – 95% efficiency.
- Worn Pumps: Efficiency may drop to 80% or lower, significantly reducing flow at high pressures.
- Formula: Actual Flow = Theoretical Flow × (Efficiency % / 100).
Example Calculation
Let's assume you have a hydraulic gear pump with a displacement of 1.5 in³/rev running at 1750 RPM (a standard 4-pole electric motor speed) with a volumetric efficiency of 90%.
- Calculate Theoretical Flow: (1.5 × 1750) / 231 = 11.36 GPM.
- Apply Efficiency: 11.36 × 0.90 = 10.22 GPM.
In this scenario, the pump is theoretically moving 11.36 GPM, but only 10.22 GPM is actually leaving the outlet port to do work in the system.
Factors Affecting Flow Rate
- RPM: Flow is directly proportional to speed. Doubling the RPM doubles the theoretical flow.
- Viscosity: Thinner fluids (low viscosity) increase internal leakage (slip), reducing volumetric efficiency.
- Pressure: Higher system pressure forces more fluid through internal clearances, increasing slip and reducing actual flow output.
- Wear: As gear teeth and housing wear down, clearances increase, leading to a permanent drop in flow rate over time.