Pressure Drop and Flow Rate Calculator

by

Pressure Drop and Flow Rate Calculator

Results

Total Pressure Drop: 0 kPa
Fluid Velocity: 0 m/s
Reynolds Number: 0
Friction Factor: 0

*Pressure drop calculations are based on the Darcy-Weisbach equation and Swamee-Jain approximation.

function calculatePressureDrop() { var Q = parseFloat(document.getElementById('flowRate').value); var D_mm = parseFloat(document.getElementById('pipeDiameter').value); var L = parseFloat(document.getElementById('pipeLength').value); var e = parseFloat(document.getElementById('roughness').value); var rho = parseFloat(document.getElementById('density').value); var mu_cp = parseFloat(document.getElementById('viscosity').value); if (isNaN(Q) || isNaN(D_mm) || isNaN(L) || isNaN(rho) || isNaN(mu_cp) || D_mm <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Conversions to SI var D = D_mm / 1000; // m var A = Math.PI * Math.pow(D / 2, 2); // m^2 var Q_s = Q / 3600; // m^3/s var V = Q_s / A; // m/s var mu = mu_cp / 1000; // Pa.s var epsilon = e / 1000; // m // Reynolds Number var Re = (rho * V * D) / mu; // Friction Factor (f) var f = 0; if (Re < 2300) { // Laminar Flow f = 64 / Re; } else { // Turbulent Flow – Swamee-Jain Equation var term1 = epsilon / (3.7 * D); var term2 = 5.74 / Math.pow(Re, 0.9); f = 0.25 / Math.pow(Math.log10(term1 + term2), 2); } // Darcy-Weisbach Equation: Delta P = f * (L/D) * (rho * v^2 / 2) var deltaP_pa = f * (L / D) * (rho * Math.pow(V, 2) / 2); var deltaP_kpa = deltaP_pa / 1000; // Output results document.getElementById('res-pressure-kpa').innerText = deltaP_kpa.toFixed(3); document.getElementById('res-velocity').innerText = V.toFixed(2); document.getElementById('res-reynolds').innerText = Math.round(Re).toLocaleString(); document.getElementById('res-friction').innerText = f.toFixed(5); document.getElementById('results-box').style.display = 'block'; }

Understanding Pressure Drop and Fluid Flow

In fluid dynamics, pressure drop is the result of frictional forces, caused by the resistance to flow, acting on a fluid as it travels through a pipe. Calculating the pressure drop accurately is critical for engineers and technicians to size pumps, select pipe diameters, and ensure the efficiency of industrial piping systems.

The Physics Behind the Math

This calculator primarily utilizes the Darcy-Weisbach equation, which is the most accurate formula for calculating pressure loss in pipes. The main factors influencing the result include:

  • Velocity (V): Higher flow rates in the same diameter pipe lead to higher velocities, which increase pressure drop exponentially ($V^2$).
  • Pipe Diameter (D): Narrower pipes create significantly more resistance than wider pipes.
  • Viscosity (μ): "Thicker" fluids (like oil) require more energy to move than "thinner" fluids (like water).
  • Pipe Roughness (ε): The internal texture of the pipe (e.g., rusted steel vs. smooth PVC) creates turbulence and friction.

Laminar vs. Turbulent Flow

The behavior of the fluid is determined by the Reynolds Number (Re). If the number is below 2,300, the flow is laminar (smooth and predictable). If it is above 4,000, the flow is turbulent (chaotic and swirling), which significantly increases the friction factor and subsequent pressure loss.

Practical Example: Water Transport

Imagine you are moving water through a 100-meter stainless steel pipe with an inner diameter of 50mm. At a flow rate of 10 m³/h:

  1. The fluid velocity will be approximately 1.41 m/s.
  2. The Reynolds number will be around 70,500 (Turbulent flow).
  3. The pressure drop will be roughly 18.5 kPa (0.18 bar).

If you were to double the flow rate to 20 m³/h, the pressure drop would jump to approximately 68 kPa—nearly a four-fold increase!

How to Reduce Pressure Drop

If your calculation shows a pressure drop that is too high for your pump's capacity, consider these adjustments:

  1. Increase Pipe Diameter: This is the most effective way to lower velocity and resistance.
  2. Reduce Pipe Length: Shorten the run or remove unnecessary elbows and fittings.
  3. Change Material: Use smoother piping (like HDPE or Copper) instead of rougher materials like cast iron.
  4. Increase Temperature: For many oils and chemicals, increasing temperature reduces viscosity, making the fluid easier to move.

Leave a Comment