Instrument air tubing is the circulatory system of a pneumatic control loop. Undersized tubing starves actuators of air, causing slow valve response and control problems. Oversized tubing wastes material and adds unnecessary volume that slows response time. The goal is to select tubing that delivers the required flow rate at the required pressure with acceptable pressure drop and velocity.
Unlike process piping where the fluid is moving continuously, instrument air tubing handles intermittent demand. A control valve actuator sits at steady state most of the time, consuming zero flow. When the valve strokes, the tubing must deliver enough air to fill the actuator volume in the required stroke time. This intermittent, high-demand pattern makes instrument air line sizing different from sizing continuous-flow air distribution headers.
This guide covers the Harris formula for calculating pressure drop in compressed air lines, compares tubing materials, explains equivalent length calculations for fittings, and addresses the 30 FPS velocity limit that protects against noise and erosion in instrument air systems.
The Harris Formula for Compressed Air Pressure Drop
The Harris formula is the standard calculation for pressure drop in compressed air piping and tubing. It is simpler than the Darcy-Weisbach equation because it uses empirical constants specific to air at typical instrument air conditions: ΔP = C × L × Q² / (d&sup5; × P) where ΔP is pressure drop in PSI, L is equivalent pipe length in feet (including fittings), Q is flow rate in SCFM, d is inside diameter in inches, and P is the average absolute pressure in PSIA.
The constant C depends on the formula version and units. For the standard ISA form: ΔP = 0.1025 × L × Q² / (3600 × d&sup5; × P_avg). The critical takeaway is that pressure drop is proportional to the fifth power of diameter. Doubling the tubing diameter reduces pressure drop by a factor of 32. This extreme sensitivity means that going up one tubing size often solves a pressure drop problem completely.
For instrument air applications, the acceptable pressure drop from the header to the instrument is typically 1-2 PSI maximum. If the header is at 20 PSI and the I/P converter or positioner needs 18 PSI minimum, you have 2 PSI of budget for tubing and fittings. Exceeding this budget causes the instrument to operate below its minimum supply pressure, resulting in reduced output range and control accuracy.
The flow rate Q in the formula is the actual flow demand during valve stroking, not the average flow. A 6-inch Fisher ED actuator filling in 5 seconds requires about 8 SCFM during the stroke. This peak demand is what you size the tubing for, even though the average consumption over an hour might be only 0.5 SCFM.
ΔP = 0.1025 × L × Q² / (3600 × d&sup5; × P_avg)ΔP = pressure drop (PSI)
L = equivalent length including fittings (ft)
Q = flow rate (SCFM)
d = inside diameter (inches)
P_avg = average absolute pressure (PSIA)
Instrument Air Line Sizing Calculator
Size instrument air tubing and piping using Harris formula. Compare copper, black iron, and stainless options with pressure drop and velocity checks.
Copper vs Stainless Steel vs Black Iron
Copper tubing (ASTM B75 or B280) is the most common material for instrument air runs. It is easy to bend, solder, or use with compression fittings, and it has a smooth internal surface with low friction. Standard sizes are 1/4-inch, 3/8-inch, and 1/2-inch OD with wall thicknesses of 0.030 to 0.049 inches. The inside diameter of 3/8-inch OD copper with 0.032 wall is 0.311 inches. Copper does not rust, so it does not introduce particulate contamination into the air stream. Disadvantage: copper work-hardens from vibration and can crack at stress points.
Stainless steel tubing (316 SS or 304 SS) is specified for corrosive environments, offshore platforms, and high-purity applications. It costs 3-5 times more than copper and requires specialized bending tools. The advantage is superior vibration resistance and corrosion immunity. In chemical plants with chlorine, acid vapors, or saltwater exposure, stainless is the only material that will survive long-term. Standard sizes match copper OD dimensions.
Black iron pipe (Schedule 40 or Schedule 80) is common for instrument air distribution headers and branch lines in older installations. It is inexpensive and strong but rusts internally, generating scale particles that plug I/P nozzles, positioner orifices, and relay passages. New black iron pipe should be blown out and pickled before instrument air service. As the pipe ages, internal corrosion progressively reduces the effective diameter and increases surface roughness, both of which increase pressure drop.
Plastic tubing (polyethylene, nylon, or polyurethane) is used for short connections in non-hazardous areas. It is lightweight, flexible, and resistant to corrosion. However, most plants restrict plastic tubing to runs under 10 feet due to fire risk. In a fire, plastic tubing melts and the air supply is lost, causing all pneumatic actuators on that run to fail. Copper and stainless steel maintain integrity much longer in fire conditions.
Equivalent Length of Fittings
Every fitting in an air line adds resistance equivalent to a certain length of straight tubing. A 90-degree elbow in 3/8-inch tubing adds roughly 1.5 feet of equivalent length. A tee used as an elbow adds about 3 feet. A union or coupling adds about 0.3 feet. Compression fittings with internal restrictions can add 2-5 feet each depending on design quality.
The equivalent length method works by adding all the fitting equivalent lengths to the actual straight-run length to get the total equivalent length for the pressure drop calculation. A 50-foot run with six 90-degree elbows, two tees, and a filter adds: 50 + (6 × 1.5) + (2 × 3.0) + 2.0 = 67 feet equivalent length. This 34% increase over straight-run length is typical for real installations.
Quick-connect fittings (push-to-connect style) are convenient but often have smaller internal passages than the tubing they connect. A 3/8-inch push-to-connect fitting may have an internal bore of only 0.250 inches versus the 0.311-inch bore of the tubing. This restriction acts like a smaller tube diameter at that point and can add significant equivalent length. For critical instrument air runs, use compression fittings with full-bore internal passages.
Minimize the number of fittings by bending tubing instead of using elbows where possible. A bent tube has less restriction than a fitting. Use a proper tube bender for the material (copper benders are different from stainless benders) and maintain the minimum bend radius specified by the tubing manufacturer, typically 3-5 times the tube OD.
90° elbow: 1.5 ft
45° elbow: 0.8 ft
Tee (thru): 1.0 ft
Tee (branch): 3.0 ft
Union/coupling: 0.3 ft
Ball valve (full bore): 0.5 ft
Globe valve: 8.0 ft
Filter/regulator: 2.0-5.0 ft
The 30 FPS Velocity Rule
Air velocity in instrument tubing should not exceed 30 feet per second (FPS). This limit exists for three reasons: noise, erosion, and pressure drop stability. Above 30 FPS, the air flow becomes turbulent enough to generate audible noise in the tubing and fittings. In environments where instrument air lines run through control rooms or near operator workstations, this noise is a practical nuisance.
The velocity is calculated from: V = Q / (A × 60) × (14.7 / (P + 14.7)) × 144 where V is velocity in FPS, Q is flow in SCFM, A is the cross-sectional area of the tube bore in square inches, and the pressure correction converts from standard conditions to actual conditions in the tube. At higher pressures, the actual velocity is lower than it would be at atmospheric pressure because the air is compressed.
For quick calculations at 80 PSI supply: the actual velocity is approximately 23% of what it would be at atmospheric pressure. So 10 SCFM through a 3/8-inch tube (0.311 ID) has an atmospheric velocity of about 60 FPS but an actual velocity at 80 PSI of about 14 FPS — well within the limit. The same 10 SCFM through 1/4-inch tube (0.190 ID) would have an actual velocity of about 37 FPS — above the limit.
In practice, the 30 FPS rule naturally prevents excessive pressure drop. If the velocity is within limits, the pressure drop is usually acceptable for typical instrument air run lengths (under 200 feet). When you encounter a line sizing problem, checking velocity first is a quick screening tool. If velocity is above 30 FPS, the line is undersized regardless of what the pressure drop calculation shows.
Aged Pipe Roughness Factor
Internal pipe roughness increases with age due to corrosion, scale buildup, and deposit accumulation. New black iron pipe has an absolute roughness of about 0.0018 inches. After 10 years of service with marginal air quality, that roughness can increase to 0.01-0.03 inches. After 20+ years, heavy scale can reduce the effective bore diameter by 10-20%.
The impact on pressure drop is dramatic. The Moody chart shows that friction factor increases significantly with roughness, especially in the transition and turbulent flow regimes where instrument air operates. A pipe with 10x the roughness of new pipe can have 2-3x the friction factor, which directly multiplies the pressure drop.
For existing installations with aged black iron pipe, apply a roughness multiplier to the calculated pressure drop. A conservative approach is to double the calculated pressure drop for pipe that is 10-15 years old, and triple it for pipe over 20 years old. Better yet, measure the actual pressure drop in the field with a gauge at the header and a gauge at the instrument during a valve stroke. This measurement captures the real condition of the piping including partially closed valves, plugged filters, and corroded sections.
When retrofitting or replacing aged instrument air lines, consider replacing black iron runs with copper or stainless tubing. The initial cost is higher but the long-term maintenance savings from eliminating corrosion contamination often justify the investment, especially for runs feeding critical control valves.
New pipe: 1.0x calculated pressure drop
5-10 years: 1.5x
10-15 years: 2.0x
15-20 years: 2.5x
20+ years: 3.0x or measure in field
These factors assume black iron pipe with standard air quality. Copper and stainless do not degrade significantly.