Understanding Pressure Drop
Pressure drop is the reduction in fluid pressure that occurs as the fluid flows through a pipe, fitting, or any other component in a piping system. This loss of pressure is primarily due to friction between the fluid and the pipe walls, as well as turbulence created by changes in direction or obstructions (fittings).
Factors Affecting Pressure Drop:
- Flow Rate: Higher flow rates lead to increased friction and turbulence, resulting in a greater pressure drop.
- Pipe Diameter: Smaller pipe diameters restrict flow more, leading to higher velocities and increased pressure drop.
- Pipe Length: Longer pipes offer more surface area for friction, thus increasing the pressure drop.
- Fluid Properties: Viscosity and density play significant roles. Highly viscous fluids experience more friction. Denser fluids have higher momentum, which can contribute to pressure loss.
- Pipe Roughness: Rougher internal pipe surfaces create more turbulence and friction, leading to a higher pressure drop.
- Fittings: Elbows, valves, tees, and other fittings disrupt the flow, causing additional turbulence and pressure loss, quantified by loss coefficients (K).
Why is it Important?
Accurate pressure drop calculations are vital for:
- Pump and Fan Sizing: Ensuring that the selected equipment can overcome the system's resistance to maintain the desired flow rate.
- Energy Efficiency: Minimizing pressure drop reduces the energy required by pumps and fans, leading to cost savings.
- System Performance: Guaranteeing that sufficient pressure is available at the point of use.
- Material Selection: Choosing appropriate pipe materials and sizes to manage pressure and flow effectively.
Calculation Method (Darcy-Weisbach Equation & Minor Losses:
The pressure drop (ΔP) is typically calculated using the Darcy-Weisbach equation for friction losses and adding losses from fittings (minor losses).
1. Calculate Reynolds Number (Re): Re = (ρ * v * D) / μ, where ρ is density, v is velocity, D is diameter, and μ is dynamic viscosity.
2. Determine Friction Factor (f): This depends on Re and pipe roughness (ε/D). The Colebrook equation or Moody chart is often used for turbulent flow. For simplicity in this calculator, an approximation might be used or a lookup table implied.
3. Calculate Frictional Pressure Drop (ΔPf): ΔPf = f * (L/D) * (ρ * v²/2), where L is length.
4. Calculate Minor Loss Pressure Drop (ΔPm): ΔPm = K * (ρ * v²/2), where K is the total loss coefficient for fittings.
5. Total Pressure Drop (ΔP_total): ΔP_total = ΔPf + ΔPm.
Note: Velocity (v) is derived from Flow Rate (Q) and Pipe Diameter (D): v = Q / A, where A is the cross-sectional area of the pipe.
function calculatePressureDrop() {
var flowRate = parseFloat(document.getElementById("flowRate").value);
var pipeDiameterMm = parseFloat(document.getElementById("pipeDiameter").value);
var pipeLength = parseFloat(document.getElementById("pipeLength").value);
var fluidViscosity = parseFloat(document.getElementById("fluidViscosity").value); // in cP or mPa·s
var fluidDensity = parseFloat(document.getElementById("fluidDensity").value); // in kg/m³
var roughnessMicrons = parseFloat(document.getElementById("roughness").value); // in µm
var fittingLossCoefficient = parseFloat(document.getElementById("fittingLossCoefficient").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Input validation
if (isNaN(flowRate) || isNaN(pipeDiameterMm) || isNaN(pipeLength) ||
isNaN(fluidViscosity) || isNaN(fluidDensity) || isNaN(roughnessMicrons) ||
isNaN(fittingLossCoefficient)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (pipeDiameterMm <= 0 || pipeLength <= 0 || fluidViscosity <= 0 || fluidDensity <= 0 || roughnessMicrons < 0 || fittingLossCoefficient < 0) {
resultDiv.innerHTML = "Please enter positive values for dimensions, viscosity, and density. Roughness and fitting coefficients can be zero but not negative.";
return;
}
// — Conversions —
// Convert flow rate: Assuming common inputs like L/min or m³/hr. Let's standardize to m³/s for calculations.
var flowRateMs;
// This part is tricky without knowing the unit. For a robust calculator, you'd ask for units.
// For this example, let's assume the user inputs in m³/hr and convert.
// If you intend to support L/min, you'd need an additional input or logic.
// Assuming m³/hr for now:
flowRateMs = flowRate / 3600.0; // m³/hr to m³/s
// Convert pipe diameter from mm to meters
var pipeDiameterM = pipeDiameterMm / 1000.0;
// Convert viscosity from cP to Pa·s (1 cP = 0.001 Pa·s)
var fluidViscosityPaS = fluidViscosity * 0.001;
// Convert roughness from µm to meters
var roughnessM = roughnessMicrons / 1000000.0;
// — Calculations —
var pipeArea = Math.PI * Math.pow(pipeDiameterM / 2, 2);
var velocity = flowRateMs / pipeArea; // m/s
// Calculate Reynolds Number (Re)
var reynoldsNumber = (fluidDensity * velocity * pipeDiameterM) / fluidViscosityPaS;
// Calculate Friction Factor (f) using an approximation (e.g., Haaland equation for turbulent flow)
// This is a simplified approach. For higher accuracy, Colebrook-White or a Moody chart lookup is needed.
var frictionFactor;
var relativeRoughness = roughnessM / pipeDiameterM;
if (reynoldsNumber < 2300) { // Laminar Flow
frictionFactor = 64 / reynoldsNumber;
} else { // Turbulent Flow (using Haaland approximation)
var term1 = Math.pow((relativeRoughness / 3.7), 1.11);
var term2 = 6.9 / reynoldsNumber;
frictionFactor = Math.pow( (1 / (-1.8 * Math.log10(term1 + term2)) ), 2);
if (isNaN(frictionFactor) || frictionFactor <= 0) { // Fallback for potential issues with Haaland
frictionFactor = 0.02; // A typical value for turbulent flow if calculation fails
}
}
// Calculate Frictional Pressure Drop (ΔPf) using Darcy-Weisbach
// ΔPf = f * (L/D) * (ρ * v²/2)
var frictionalPressureDropPascals = frictionFactor * (pipeLength / pipeDiameterM) * (fluidDensity * Math.pow(velocity, 2) / 2);
// Calculate Minor Loss Pressure Drop (ΔPm)
// ΔPm = K * (ρ * v²/2)
var minorLossPressureDropPascals = fittingLossCoefficient * (fluidDensity * Math.pow(velocity, 2) / 2);
// Total Pressure Drop
var totalPressureDropPascals = frictionalPressureDropPascals + minorLossPressureDropPascals;
// Convert to more common units (e.g., kPa or bar)
var totalPressureDropKpa = totalPressureDropPascals / 1000.0;
var totalPressureDropBar = totalPressureDropPascals / 100000.0;
var totalPressureDropPsi = totalPressureDropPascals * 0.000145038; // Pascals to PSI
// Display results
resultDiv.innerHTML = "
Results:
" +
"
Reynolds Number (Re): " + reynoldsNumber.toFixed(2) + "" +
"
Friction Factor (f): " + frictionFactor.toFixed(4) + "" +
"
Fluid Velocity: " + velocity.toFixed(3) + " m/s" +
"
Frictional Pressure Drop: " + frictionalPressureDropPascals.toFixed(2) + " Pa" +
"
Minor Loss Pressure Drop: " + minorLossPressureDropPascals.toFixed(2) + " Pa" +
"
Total Pressure Drop:" +
"" +
totalPressureDropPascals.toFixed(2) + " Pa (" +
totalPressureDropKpa.toFixed(3) + " kPa / " +
totalPressureDropBar.toFixed(4) + " bar / " +
totalPressureDropPsi.toFixed(3) + " psi)";
}
.calculator-wrapper {
font-family: sans-serif;
max-width: 900px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
display: flex;
flex-wrap: wrap;
gap: 30px;
background-color: #f9f9f9;
}
.calculator-form {
flex: 1;
min-width: 300px;
background-color: #fff;
padding: 25px;
border-radius: 8px;
box-shadow: 0 2px 5px rgba(0,0,0,0.1);
}
.calculator-form h2 {
margin-top: 0;
color: #333;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
margin-bottom: 20px;
}
.calculator-form p {
color: #555;
line-height: 1.6;
margin-bottom: 15px;
}
.calculator-form .form-group {
margin-bottom: 15px;
}
.calculator-form label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #444;
}
.calculator-form input[type="number"],
.calculator-form input[type="text"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1rem;
}
.calculator-form input[type="number"]:focus,
.calculator-form input[type="text"]:focus {
border-color: #007bff;
outline: none;
box-shadow: 0 0 5px rgba(0,123,255,0.25);
}
.calculator-form button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 5px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
.calculator-form button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 25px;
padding: 15px;
background-color: #e9ecef;
border: 1px solid #ced4da;
border-radius: 5px;
text-align: center;
}
.calculator-result h3 {
margin-top: 0;
color: #333;
font-size: 1.3em;
}
.calculator-result p {
margin: 8px 0;
color: #333;
line-height: 1.5;
}
.calculator-result strong {
color: #0056b3;
}
.calculator-explanation {
flex: 1.5;
min-width: 300px;
background-color: #fff;
padding: 25px;
border-radius: 8px;
box-shadow: 0 2px 5px rgba(0,0,0,0.1);
}
.calculator-explanation h3,
.calculator-explanation h4 {
color: #333;
margin-bottom: 15px;
border-bottom: 1px solid #eee;
padding-bottom: 5px;
}
.calculator-explanation ul {
list-style: disc;
margin-left: 20px;
color: #555;
line-height: 1.6;
}
.calculator-explanation li {
margin-bottom: 10px;
}
.calculator-explanation code {
background-color: #e7f3ff;
padding: 2px 5px;
border-radius: 3px;
font-family: monospace;
color: #0056b3;
}