Pressure loss in a pipe, also known as friction loss, is the reduction in fluid pressure that occurs as the fluid flows through a pipe. This loss is primarily due to the friction between the fluid and the inner walls of the pipe, as well as internal friction within the fluid itself (viscosity).
Several factors contribute to pressure loss:
Flow Rate: Higher flow rates increase turbulence and shear forces, leading to greater pressure loss.
Pipe Diameter: Smaller diameter pipes have a higher surface area to volume ratio, resulting in more friction and thus higher pressure loss for the same flow rate.
Pipe Length: Longer pipes offer more surface area for friction, so pressure loss increases proportionally with length.
Fluid Properties:
Viscosity: More viscous fluids (thicker) create more internal resistance and thus higher pressure loss.
Density: While less directly impactful on friction loss itself, density affects the kinetic energy of the fluid and is crucial for calculating Reynolds number and related factors.
Pipe Roughness: Rougher internal pipe surfaces create more turbulence and impede flow more significantly than smooth surfaces.
Flow Regime: Whether the flow is laminar (smooth, orderly) or turbulent (chaotic, swirling) dramatically affects pressure loss. Turbulent flow causes significantly higher losses.
The Darcy-Weisbach Equation
The most widely accepted method for calculating pressure loss due to friction in a pipe is the Darcy-Weisbach equation. It's expressed as:
ΔP = f * (L/D) * (ρ * v^2 / 2)
Where:
ΔP is the pressure loss (Pascals, Pa)
f is the Darcy friction factor (dimensionless)
L is the pipe length (meters, m)
D is the pipe inner diameter (meters, m)
ρ (rho) is the fluid density (kg/m³)
v is the average fluid velocity (m/s)
Calculating the Friction Factor (f)
The friction factor 'f' is not a constant and depends on the flow regime (laminar or turbulent) and the relative roughness of the pipe. For turbulent flow, it's typically determined using the Colebrook-White equation or Moody diagram, which often requires iterative calculation or approximations. A common and widely used approximation is the Swamee-Jain equation:
f = 0.25 / [log10( (ε/D)/3.7 + 5.74/Re^0.9 )]^2
Where:
ε (epsilon) is the pipe absolute roughness (meters, m)
Re is the Reynolds number (dimensionless)
Reynolds Number (Re)
The Reynolds number is a dimensionless quantity used to predict flow patterns. It's calculated as:
Re = (ρ * v * D) / μ
Where:
μ (mu) is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
Practical Considerations
Units: It's crucial to maintain consistent units throughout the calculation. This calculator converts input units to SI units (meters, kilograms, seconds, Pascals) for calculation and then presents the result in a common unit like kPa (kilopascals).
Fluid Properties: Density and viscosity vary with temperature. The calculator uses approximate values for common fluids at standard temperatures and adjusts slightly based on user input.
Fittings and Valves: This calculation typically only accounts for friction loss along straight pipe sections. Additional pressure losses occur due to fittings (elbows, tees), valves, and changes in pipe diameter. These are often calculated separately using equivalent length methods or K-factors.
Assumptions: This calculator assumes fully developed, single-phase flow in a straight, constant-diameter pipe. It uses the Swamee-Jain equation as an approximation for the friction factor, which is generally accurate for turbulent flow.
Example Calculation
Let's calculate the pressure loss for:
Flow Rate: 150 L/min
Pipe Inner Diameter: 32 mm
Pipe Length: 75 m
Fluid Type: Water
Fluid Temperature: 15 °C
Pipe Absolute Roughness: 0.015 mm (typical for steel pipes)
Step 1: Convert inputs to SI units
Flow Rate = 150 L/min = 0.0025 m³/s
Diameter = 32 mm = 0.032 m
Length = 75 m
Roughness = 0.015 mm = 0.000015 m
Step 2: Determine fluid properties for Water at 15°C
Density (ρ) ≈ 999.1 kg/m³
Dynamic Viscosity (μ) ≈ 1.138 x 10⁻³ Pa·s
Step 3: Calculate fluid velocity (v)
Area = π * (D/2)² = π * (0.032/2)² ≈ 0.000804 m²
v = Flow Rate / Area = 0.0025 m³/s / 0.000804 m² ≈ 3.11 m/s
Step 4: Calculate Reynolds Number (Re)
Re = (ρ * v * D) / μ = (999.1 kg/m³ * 3.11 m/s * 0.032 m) / (1.138 x 10⁻³ Pa·s) ≈ 87,000
Since Re > 4000, the flow is turbulent.
Step 5: Calculate Friction Factor (f) using Swamee-Jain
Relative Roughness (ε/D) = 0.000015 m / 0.032 m ≈ 0.000469
f = 0.25 / [log10( (0.000469)/3.7 + 5.74/(87000)^0.9 )]^2
f = 0.25 / [log10( 0.0001267 + 5.74/25990 )]^2
f = 0.25 / [log10( 0.0001267 + 0.00022 )]^2
f = 0.25 / [log10( 0.0003467 )]^2
f = 0.25 / [-3.46]^2 = 0.25 / 11.97 ≈ 0.0209
Step 6: Calculate Pressure Loss (ΔP) using Darcy-Weisbach
ΔP = f * (L/D) * (ρ * v² / 2)
ΔP = 0.0209 * (75 m / 0.032 m) * (999.1 kg/m³ * (3.11 m/s)² / 2)
ΔP = 0.0209 * 2343.75 * (999.1 * 9.67 / 2)
ΔP = 49.0 * (9655 / 2)
ΔP = 49.0 * 4827.5 ≈ 236,547 Pa
Step 7: Convert to kPa
Pressure Loss ≈ 236.5 kPa
The calculator performs these steps automatically to provide a quick estimate.
function calculatePressureLoss() {
var flowRateLpm = parseFloat(document.getElementById("flowRate").value);
var pipeDiameterMm = parseFloat(document.getElementById("pipeDiameter").value);
var pipeLengthM = parseFloat(document.getElementById("pipeLength").value);
var fluidType = document.getElementById("fluidType").value;
var fluidTempC = parseFloat(document.getElementById("fluidTemp").value);
var pipeRoughnessMm = parseFloat(document.getElementById("pipeRoughness").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous result
// — Input Validation —
if (isNaN(flowRateLpm) || isNaN(pipeDiameterMm) || isNaN(pipeLengthM) || isNaN(fluidTempC) || isNaN(pipeRoughnessMm) ||
flowRateLpm <= 0 || pipeDiameterMm <= 0 || pipeLengthM <= 0 || fluidTempC < -273.15 || pipeRoughnessMm 100) density = 958.4; // Steam at 100C
if (fluidTempC < 0) density = 999.8; // Ice/subcooled water
density = Math.max(density, 1.0); // Avoid 0 or negative density
} else if (fluidType === "oil") { // Assuming SAE 30 Oil
// Approximate values for SAE 30 oil at typical industrial temps
// These can vary significantly! For precise calculations, specific oil data sheets are needed.
if (fluidTempC < 10) { viscosity = 1.0; density = 900; } // Very viscous cold
else if (fluidTempC < 20) { viscosity = 0.2; density = 895; }
else if (fluidTempC < 40) { viscosity = 0.05; density = 890; }
else { viscosity = 0.02; density = 880; } // Warmer
viscosity = viscosity * 0.001; // Convert 1 to 1000 cP approx to Pa·s
} else if (fluidType === "air") {
// Approximate properties for air (standard atmospheric pressure)
// Density = P / (R*T) where P=101325 Pa, R=287 J/(kg*K), T in Kelvin
var tempKelvin = fluidTempC + 273.15;
density = 101325 / (287 * tempKelvin);
// Dynamic Viscosity (Pa·s) – Sutherland's Law approximation
var T0 = 291.15; // Reference temperature (18°C)
var mu0 = 1.827e-5; // Viscosity at T0
var S = 110.4; // Sutherland constant for air
viscosity = mu0 * (T0 + S) / (tempKelvin + S) * Math.pow(tempKelvin / T0, 1.5);
} else {
resultDiv.innerHTML = "Unsupported fluid type.";
return;
}
// — Calculations —
var pipeArea = Math.PI * Math.pow(pipeDiameterM / 2.0, 2);
var velocity = m3PerSec / pipeArea; // m/s
// Reynolds Number
var reynoldsNumber = (density * velocity * pipeDiameterM) / viscosity;
var frictionFactor = 0;
if (reynoldsNumber 0
var logArg = Math.max(1e-9, (relativeRoughness / 3.7) + (5.74 / Math.pow(reynoldsNumber, 0.9)));
frictionFactor = 0.25 / Math.pow(Math.log10(logArg), 2);
}
// Darcy-Weisbach Equation
var pressureLossPa = frictionFactor * (pipeLengthM / pipeDiameterM) * (density * Math.pow(velocity, 2) / 2.0);
// Convert pressure loss to kPa
var pressureLossKpa = pressureLossPa / 1000.0;
// — Display Result —
if (isNaN(pressureLossKpa) || !isFinite(pressureLossKpa)) {
resultDiv.innerHTML = "Calculation resulted in an invalid number. Check inputs.";
} else {
resultDiv.innerHTML = "Pressure Loss: " + pressureLossKpa.toFixed(2) + " kPa";
}
}