.calculator-container {
font-family: 'Segoe UI', Roboto, Helvetica, Arial, sans-serif;
max-width: 800px;
margin: 0 auto;
background: #ffffff;
border: 1px solid #e0e0e0;
border-radius: 8px;
box-shadow: 0 4px 12px rgba(0,0,0,0.05);
padding: 20px;
}
.calc-header {
text-align: center;
background-color: #005a87;
color: white;
padding: 20px;
border-radius: 6px 6px 0 0;
margin: -20px -20px 20px -20px;
}
.calc-header h2 {
margin: 0;
font-size: 24px;
}
.form-group {
margin-bottom: 15px;
}
.form-group label {
display: block;
font-weight: 600;
margin-bottom: 5px;
color: #333;
}
.form-group input {
width: 100%;
padding: 10px;
border: 1px solid #ddd;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.form-group .help-text {
font-size: 12px;
color: #666;
margin-top: 4px;
}
.btn-calc {
width: 100%;
padding: 12px;
background-color: #0077b6;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
cursor: pointer;
transition: background-color 0.3s;
font-weight: bold;
}
.btn-calc:hover {
background-color: #005a87;
}
.result-box {
margin-top: 25px;
background-color: #f8f9fa;
border: 1px solid #dee2e6;
border-radius: 4px;
padding: 20px;
text-align: center;
display: none;
}
.result-value {
font-size: 32px;
color: #0077b6;
font-weight: bold;
margin: 10px 0;
}
.result-label {
font-size: 14px;
color: #555;
text-transform: uppercase;
letter-spacing: 1px;
}
.secondary-results {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 10px;
margin-top: 15px;
border-top: 1px solid #e0e0e0;
padding-top: 15px;
}
.sec-item strong {
display: block;
color: #333;
font-size: 18px;
}
.sec-item span {
font-size: 13px;
color: #666;
}
.calc-article {
margin-top: 40px;
line-height: 1.6;
color: #333;
}
.calc-article h3 {
color: #005a87;
margin-top: 25px;
}
.calc-article ul {
padding-left: 20px;
}
.calc-article li {
margin-bottom: 8px;
}
.alert-error {
color: #721c24;
background-color: #f8d7da;
border: 1px solid #f5c6cb;
padding: 10px;
border-radius: 4px;
margin-top: 15px;
display: none;
text-align: center;
}
function calculateFlowRate() {
// Get input elements
var pressureInput = document.getElementById('pressureDrop');
var diameterInput = document.getElementById('pipeDiameter');
var viscosityInput = document.getElementById('dynamicViscosity');
var lengthInput = document.getElementById('pipeLength');
// Get values
var pressurePa = parseFloat(pressureInput.value);
var diameterMm = parseFloat(diameterInput.value);
var viscosityCp = parseFloat(viscosityInput.value);
var lengthM = parseFloat(lengthInput.value);
var errorBox = document.getElementById('errorBox');
var resultsArea = document.getElementById('resultsArea');
// Reset UI
errorBox.style.display = 'none';
resultsArea.style.display = 'none';
// Validation
if (isNaN(pressurePa) || isNaN(diameterMm) || isNaN(viscosityCp) || isNaN(lengthM)) {
errorBox.innerText = "Please fill in all fields with valid numbers.";
errorBox.style.display = 'block';
return;
}
if (diameterMm <= 0 || viscosityCp <= 0 || lengthM <= 0) {
errorBox.innerText = "Diameter, Viscosity, and Length must be greater than zero.";
errorBox.style.display = 'block';
return;
}
// Unit Conversions for Formula (SI Units)
// Viscosity: cP to Pa.s (1 cP = 0.001 Pa.s)
var viscosityPaS = viscosityCp / 1000;
// Diameter: mm to radius in meters
// Radius = (Diameter / 2) / 1000
var radiusM = (diameterMm / 2) / 1000;
// Poiseuille's Law Calculation: Q = (PI * dP * r^4) / (8 * mu * L)
var numerator = Math.PI * pressurePa * Math.pow(radiusM, 4);
var denominator = 8 * viscosityPaS * lengthM;
var flowRateCubicMetersPerSecond = numerator / denominator;
// Result Conversions
var litersPerMinute = flowRateCubicMetersPerSecond * 60000; // m3/s to L/min
var litersPerSecond = flowRateCubicMetersPerSecond * 1000; // m3/s to L/s
var cubicMetersPerHour = flowRateCubicMetersPerSecond * 3600; // m3/s to m3/h
// Display Results
document.getElementById('mainResult').innerText = litersPerMinute.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " L/min";
document.getElementById('resM3').innerText = cubicMetersPerHour.toLocaleString(undefined, {minimumFractionDigits: 3, maximumFractionDigits: 3});
document.getElementById('resLPS').innerText = litersPerSecond.toLocaleString(undefined, {minimumFractionDigits: 3, maximumFractionDigits: 3});
resultsArea.style.display = 'block';
}
Viscosity vs. Flow Rate Calculator
Calculate Volumetric Flow Rate using Poiseuille's Law
The driving force pushing the fluid (Input 100000 for 1 Bar).
The internal width of the pipe or tube.
Water ≈ 1 cP, Olive Oil ≈ 80 cP, Honey ≈ 10000 cP.
Total length of the pipe segment.
Volumetric Flow Rate
–
0
m³/hour
0
Liters/second
Understanding the Relationship: Viscosity vs. Flow Rate
In fluid dynamics, the relationship between viscosity and flow rate is primarily governed by Poiseuille's Law (for laminar flow). This calculator helps engineers, students, and technicians determine how fast a fluid will flow through a pipe given specific conditions.
The Formula
The calculator uses the standard Hagen-Poiseuille equation to determine volumetric flow rate ($Q$):
Q = (π · ΔP · r⁴) / (8 · μ · L)
- Q: Volumetric flow rate ($m^3/s$)
- ΔP: Pressure difference between two ends of the pipe ($Pa$)
- r: Internal radius of the pipe ($m$)
- μ (mu): Dynamic viscosity of the fluid ($Pa\cdot s$)
- L: Length of the pipe ($m$)
Key Insights
1. Viscosity is Resistance: Viscosity acts as internal friction. The higher the viscosity (e.g., honey vs. water), the slower the flow rate, assuming pressure remains constant. It is inversely proportional to flow.
2. The Power of Diameter: The radius of the pipe is raised to the fourth power ($r^4$). This means a small increase in pipe diameter results in a massive increase in flow rate. Doubling the pipe width increases the flow rate by 16 times!
Example Calculation
Let's say you are pumping an oil with a viscosity of 100 cP through a pipe with an internal diameter of 50 mm and a length of 20 meters. The pump generates a pressure difference of 50,000 Pa (0.5 Bar).
- Radius ($r$): 0.025 meters
- Viscosity ($\mu$): 0.1 $Pa\cdot s$
- Result ($Q$): The flow rate would be approximately 0.0038 m³/s or roughly 230 Liters/minute.