Pressure Drop
Pressure drop (ΔP) is the reduction in fluid pressure between two points in a flow system due to frictional resistance from pipe walls, fittings, valves, packed beds, or other flow restrictions. It determines the pumping or compression power required to maintain flow and is a critical factor in the economic design of pipelines, heat exchangers, distillation columns, and catalytic reactors. For incompressible flow in pipes, the Darcy-Weisbach equation relates pressure drop to fluid velocity, pipe geometry, and friction factor.
Key Formula
ΔP = f_D × (L/D) × (ρv²/2)
LaTeX: \Delta P = f_D \cdot \frac{L}{D} \cdot \frac{\rho v^2}{2}
| Symbol | Meaning | Unit |
|---|---|---|
| ΔP | Pressure drop | Pa |
| f_D | Darcy friction factor | dimensionless |
| L | Pipe length | m |
| D | Pipe inner diameter | m |
| ρ | Fluid density | kg/m³ |
| v | Mean flow velocity | m/s |
Worked Example
Problem
Water (ρ = 1000 kg/m³) flows at v = 3 m/s through a steel pipe (D = 0.1 m, L = 50 m). The Darcy friction factor f_D = 0.018. Calculate the pressure drop and the pumping power if flow rate Q = 0.0236 m³/s.
Solution
Step 1: ΔP = f_D × (L/D) × (ρv²/2) = 0.018 × (50/0.1) × (1000 × 9/2). Step 2: ΔP = 0.018 × 500 × 4,500 = 9 × 4,500 = 40,500 Pa = 40.5 kPa. Step 3: Pumping power: P = Q × ΔP = 0.0236 × 40,500 = 955.8 W ≈ 0.96 kW.
Answer
Pressure drop ΔP = 40.5 kPa; pumping power ≈ 0.96 kW
Pressure Drop Contributions from Common Pipe Fittings (Equivalent Length L_eq/D)
| Fitting Type | L_eq/D (turbulent) | Approximate ΔP Factor | Notes | Common Use |
|---|---|---|---|---|
| Gate valve (fully open) | 13 | Low | Preferred for isolation | On/off service |
| Globe valve (fully open) | 350 | High | Avoid for flow control | Throttling |
| 90° elbow (standard) | 30 | Moderate | Common pipe turns | General piping |
| 90° elbow (long radius) | 16 | Lower | Preferred for slurries | Low pressure drop |
| Tee (through run) | 20 | Low–moderate | Straight flow | Branch lines |
| Check valve | 135 | High | Prevents backflow | Pump discharge |
Interactive Tools
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Related Terms
Dimensionless Group
A dimensionless group is a combination of physical variables and constants that yields a pure number with no units, enabling the comparison and scaling of physical phenomena independent of the system of measurement. In chemical engineering, dimensionless groups like the Reynolds, Nusselt, and Prandtl numbers are used to correlate experimental data, predict transport phenomena, and scale laboratory results to industrial equipment. They arise from dimensional analysis (Buckingham Pi theorem) and are fundamental to similarity theory and the development of engineering correlations.
Heat Transfer Coefficient
The heat transfer coefficient (h) is a proportionality constant that quantifies the rate of heat transfer per unit area per unit temperature difference between a surface and a fluid in contact with it. It combines the effects of conduction through the fluid boundary layer and convection driven by fluid motion, making it central to the design of heat exchangers, reactors, and process equipment. Higher values indicate more efficient heat transfer, and the coefficient depends strongly on fluid properties, flow velocity, geometry, and surface roughness.
Process Control (engineering)
Process control is the engineering discipline concerned with maintaining process variables (temperature, pressure, flow rate, composition) at desired setpoints by manipulating control variables through feedback and feedforward control strategies. A typical feedback control loop consists of a sensor, controller (commonly PID), and final control element (valve or pump) that continuously corrects deviations from setpoint. It is essential in chemical plants, oil refineries, pharmaceutical manufacturing, and food processing to ensure product quality, process safety, and energy efficiency.
"Pressure" from Latin "pressura" (a pressing), from "premere" (to press). The Darcy-Weisbach equation was developed by Henry Darcy (French engineer, 1857) and Julius Weisbach (German engineer, 1845). Lewis Moody (1944) compiled the famous Moody chart relating friction factor to Reynolds number and relative roughness.