Pressure Drop Compressed Air Pipes

Overview

Engineering reference data for Pressure Drop Compressed Air Pipes in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Formula Details

The primary empirical formula for pressure drop in compressed air lines is:

$dp = \frac{7.57 \cdot q^{1.85} \cdot L}{10^4 \cdot d^5 \cdot p}$

Where:

• dp = pressure drop
• q = air volume flow at atmospheric conditions (FAD)
• L = length of pipe
• d = inside diameter of pipe
• p = initial gauge pressure

Important Note: Pressure is force per unit area. Units like kg/cm² are technically mass-based; for precise work, pressure should be expressed in pascals (Pa) or bars.

Unit Conversions

Key pressure unit equivalences:

• 1 kg/cm² = 98068 Pa = 0.98 bar = 0.97 atm
• 1 kg/cm² = 14.2 psi (approx.)
• 1 kg/cm² = 10 m H₂O = 32.8 ft H₂O

Practical Calculation Guidance

1. Applicability Limit: The formula and calculators are generally not valid for pressure drops exceeding 1 kg/cm² (14-15 psi).

2. Iterative Method for Long Pipelines: For larger systems, divide the pipeline into segments. Calculate the pressure drop for each segment sequentially, using the outlet pressure of one segment as the inlet pressure for the next. The total pressure drop is the sum of the individual drops.

3. Reference Conditions: Calculations are typically based on Schedule 40 steel pipe and an initial gauge pressure of 7 kg/cm² (100 psig), as referenced in standard tables and diagrams.

Resources

• Nomogram: A graphical tool for estimating pressure drops at 7 bar (100 psig) is available for download.
• Spreadsheets: Pre-built spreadsheets for metric and imperial units (including different pipe types) are available.
• Online Calculators: Dedicated calculators for both metric (m³/min, m, mm, kg/cm²) and imperial (cfm, ft, in, psig) units are provided.

References

• Original Source