Compressed Air Piping Pressure Drop Calculation

1. Basic Calculation Formulas

Darcy-Weisbach Formula

ΔP = (λ × L × ρ × v²) / (2 × D)
ΔP = Pressure drop (Pa)
λ = Friction coefficient (dimensionless)
L = Pipe length (m)
ρ = Air density (kg/m³)
v = Flow velocity (m/s)
D = Pipe inner diameter (m)

Simplified Empirical Formula

ΔP = 7.57 × 10⁴ × Q^1.85 × L / (d^5 × P)
Where ΔP in kPa, Q in m³/min at standard conditions, L in m, d in mm, P in kPa absolute.

Harris Formula (for turbulent flow):

ΔP = 1.6 × 10³ × Q^1.85 × L / (d^5.25 × P)

Isothermal Flow:

ΔP = (P₁² - P₂²) × π² × d⁴ / (32 × λ × L × ρ × Q²)

Industrial Piping

Compressed Air Distribution

2. Friction Coefficient Data

Pipe Material Roughness (Reference: ASHRAE Fundamentals)

Pipe Material	ε (mm)	Notes
Drawn copper	0.0015
Stainless steel, new	0.015
Commercial steel, new	0.045	Per Moody 1944
Commercial steel, 10yr service	0.15	Variable with conditions
Galvanized	0.15
Cast iron, new	0.25
Cast iron, corroded	0.8-1.5	Depends on service years
Aluminum	0.0015
PE/PVC	0.007

λ Values for Turbulent Flow

Reynolds number 10⁴ to 10⁶ range:

ε/D	Re=10⁴	Re=10⁵	Re=10⁶
0.0001	λ = 0.031	0.018	0.012
0.0005	λ = 0.033	0.020	0.017
0.001	λ = 0.035	0.023	0.020
0.002	λ = 0.038	0.026	0.024
0.005	λ = 0.043	0.033	0.031
0.01	λ = 0.050	0.039	0.038
0.02	λ = 0.059	0.049	0.049

For quick estimation in steel pipes, λ can be taken as 0.02-0.03 for most compressed air applications. Smaller pipes trend toward 0.027-0.028, larger pipes (DN100+) toward 0.018-0.020.

3. Local Resistance Equivalent Lengths

Base reference: DN50 steel pipe. Data compiled from Crane TP-410 and various manufacturer catalogs.

Elbows

90° long radius: 1.5m
90° short radius: 2.5m (some sources give 2.0-3.0m)
45°: 0.8m

Tees

Straight through: 0.5m
Branch flow: 3.0m

Valves

Gate, full open: 0.3m
Ball, full open: 0.1m
Check valve: 2.0m (swing type); disk type may reach 2.5-4.0m
Globe valve, full open: 8.0m
Butterfly, full open: 0.8m
Angle valve: 4.0m

Filters

Varies significantly by manufacturer and filtration grade:

Coarse (40μm): 3m
Standard (5-25μm): 4-5m
Fine (1μm): 6-8m
Coalescing type: 8-12m

Note: Filter equivalent length increases as element loads with contaminants. Values above are for clean elements.

Other fittings: Reducer 0.5m, Union 0.2m, Coupling 0.3m

Diameter Scaling

Multiply DN50 values by these factors:

DN15: 0.30 | DN20: 0.40 | DN25: 0.50 | DN32: 0.64 | DN40: 0.80
DN65: 1.30 | DN80: 1.60 | DN100: 2.00 | DN125: 2.50 | DN150: 3.00 | DN200: 4.00

K-Value Method Alternative

ΔP = K × ρ × v² / 2

90° elbow long radius K=0.3, short radius K=0.75
45° elbow K=0.2
Tee straight K=0.1, branch K=1.0
Sudden expansion K=(1 - A₁/A₂)²
Sudden contraction K=0.5×(1 - A₂/A₁)
Sharp entrance K=0.5, rounded entrance K=0.05
Exit K=1.0

4. Pipe Sizing Tables

Recommended Diameters at 7 bar (Reference: Atlas Copco, Kaeser sizing guides)

Q (m³/min)	DN	v (m/s)	ID (mm)
0.5	15	10.2	16.1
1.0	20	9.5	21.7
1.5-2.0	25	8.6-9.1	27.3
3.0-4.0	32	8.4-8.9	35.9
5.0-6.0	40	8.5-8.9	41.9
8.0-10.0	50	7.2-9.0	53.1
15-20	65	8.0-8.5	68.9
25-35	80	7.0-7.8	80.9
45-60	100	6.4-8.5	105.3
80-100	125	7.3-9.1	130.7
130+	150	8.2	155.1
180+	200	8.1	206.5

Velocity Guidelines

Main headers: 6-10 m/s, target 8 m/s
Branch lines: 6-12 m/s
Distribution: 8-15 m/s
Drop pipes: 10-20 m/s
High pressure (>10 bar): keep below 8 m/s
Low pressure (<3 bar): can go to 12-15 m/s

Noise reference: Below 10 m/s generally acceptable. At 15 m/s expect 75-80 dB. Above 15 m/s noise becomes problematic in occupied areas.

5. Air Properties

Density vs Pressure at 20°C

Gauge (bar)	Abs (kPa)	ρ (kg/m³)
0	101.3	1.20
1	201	2.38
2	301	3.56
3	401	4.74
4	501	5.92
5	601	7.10
6	701	8.28
7	801	9.46
8	901	10.64
10	1101	13.00
12	1301	15.4
15	1601	18.9

Temperature Correction

Multiply standard density by: 1.16 at -20°C, 1.08 at 0°C, 1.04 at 10°C, 1.00 at 20°C, 0.93 at 40°C, 0.87 at 60°C, 0.77 at 100°C.

Humidity correction minor: 0.990-1.000 across 0-100% RH range, often ignored in practice.

6. Design Criteria

Pressure drop limits (per Compressed Air & Gas Institute recommendations):

Total system: not to exceed 5% of supply pressure
Main header: 2% max
Individual branch: 1%
Distribution piping: 3%

ΔP per 100m at 7 bar

Pipe Size	Flow	ΔP (kPa)
DN25	1 m³/min	8.2
DN25	2 m³/min	28.5
DN32	2 m³/min	7.8
DN32	4 m³/min	27.1
DN40	4 m³/min	9.5
DN40	6 m³/min	19.4
DN50	6 m³/min	5.8
DN50	10 m³/min	14.5
DN65	10 m³/min	4.2
DN65	20 m³/min	14.8
DN80	20 m³/min	5.1
DN80	35 m³/min	14.2
DN100	35 m³/min	4.0
DN100	60 m³/min	10.8

These values assume clean steel pipe. Add 10-20% margin for aging effects.

7. Reference Data

Standard conditions: 20°C, 101.325 kPa, ρ = 1.20 kg/m³

Conversions:

1 bar = 100 kPa = 14.5 psi
1 m³/min = 35.31 CFM
1 inch = 25.4 mm

Reynolds number: Re = ρvD/μ, where μ = 1.81×10⁻⁵ Pa·s at 20°C

Flow regime: Laminar Re<2300, Transition 2300-4000, Turbulent >4000. Compressed air systems operate turbulent under normal conditions.

Compression ratio at gauge pressure (bar): 1→1.99, 3→3.96, 5→5.94, 7→7.91, 10→10.87

FAD = Compressed flow × Compression ratio

Sources referenced: Crane TP-410 Flow of Fluids, ASHRAE Fundamentals Handbook, Compressed Air & Gas Institute Handbook, Moody L.F. (1944) Friction Factors for Pipe Flow, Atlas Copco Compressed Air Manual, Kaeser Compressors Technical Documentation.