Mine Ventilation — Airway Resistance & Fan Selection

Atkinson equation (IDs 56–57) · Series & parallel circuits · MHSA Reg. 5.15.1 compliance · SA deep-level mining

Air Conditions

Mine depth (m)

Surface temperature (°C)

Surface pressure (kPa)

ρ at depth1.2308 kg/m³

T at depth30.0 °C

P at depth107.08 kPa

Airway 1

Label

Cross-section shape

Width W (m)

Height H (m)

A = 12.000 m² · Per = 14.00 m · D_h = 3.43 m

Length L (m)

Lining / k-factor

R = 0.06648 N·s²/m⁸

Circuit Configuration

All airways in chain — R_total = ΣR_i. Same Q flows through each.

Fan H-Q Curve Data

Enter from fan datasheet. H must decrease with Q. Min 2 points.

H unit:

Q (m³/s)

H (Pa)

Fan Arrangement

Fan efficiency η (%)

MHSA Compliance (optional)

Reg. 5.15.1 — min. airflow for diesel = 0.06 m³/s per kW. Reg. 5.15.2 — min. velocity per area type.

Total diesel kW installed underground

Min. velocity threshold (m/s)

Dev. headings 0.5 · Haulages 0.25 · Working places 0.5

Target Q for fan sizing (m³/s)

Shows required fan ΔP = R × Q² below.

✓

Q = 55.48 m³/s · ΔP = 205 Pa (20.9 mmWg) · P_shaft = 16.2 kW · SFP = 292 W/(m³/s)

System R = 0.06648 N·s²/m⁸ · series circuit · Single fan

System resistance R

0.06648

N·s²/m⁸ · series

Operating airflow Q

55.48 m³/s

199733 m³/h

Fan total pressure ΔP

205 Pa

20.9 mmWg · 0.205 kPa

Fan shaft power

16.2 kW

η = 70% · SFP = 292 W/(m³/s)

Air density ρ

1.2308 kg/m³

μ = 1.861 × 10⁻⁵ Pa·s · T = 30.0 °C

Fan arrangement

Single fan

1 airway(s) · series · η = 70%

System Curve & Fan Characteristic

System H = R·Q²Fan H-QOp. point

Airway Calculation Detail

Parameter	Airway 1
Shape	rectangular
Area A (m²)	12.000
Perimeter (m)	14.00
D_h (m)	3.429
Length L (m)	500
k (N·s²/m⁴)	0.01600
R_std (N·s²/m⁸)	0.06481
R_ρ (N·s²/m⁸)	0.06648
V at op. point (m/s)	4.62
V ≥ 0.5 m/s? (MHSA)	✓
Reynolds number Re	1050000
Flow regime	Turbulent ✓

Full Calculation Summary

Air density ρ (kg/m³)

1.2308

Air temp. at depth (°C)

30.0

Barometric P at depth (kPa)

107.08

Air dynamic viscosity μ (Pa·s)

1.861 × 10⁻⁵

Total system R (N·s²/m⁸)

0.06648

Circuit mode

series

Fan arrangement

Single

Fan efficiency η

70 %

Operating Q (m³/s)

55.481

Operating Q (m³/h)

199733

Fan ΔP at duty (Pa)

204.6

Fan ΔP at duty (mmWg)

20.9

Fan ΔP at duty (kPa)

0.2046

Fan shaft power (kW)

16.22

Specific fan power SFP (W/(m³/s))

292

MHSA diesel Q_req (m³/s)

N/A

MHSA compliance

N/A

Target Q (m³/s)

N/A

Required fan ΔP at target Q (Pa)

N/A

Required fan ΔP at target Q (mmWg)

N/A

Validity & Limitations

Atkinson's equation assumes steady, fully turbulent flow — valid for Re > 4000 in most mine airways.
k-factors are from McPherson (2009) & MHSA literature; actual values depend on surface finish, obstructions, and services in the airway.
Auto-compression temperature rise (~1 °C/100 m) is for dry air. Wet airways (spray cooling, evaporation) rise at ~0.5 °C/100 m.
Parallel circuit formula (1/√R_eq = Σ1/√Rᵢ) assumes each branch shares the same total pressure — correct for independent airways from common junctions.
Fan curve entered by the user — always verify against the manufacturer's certified test curve at the actual site density.
Fan hump (rising portion of H-Q curve) indicates potential operating instability if the system resistance curve intersects the rising portion.
MHSA Reg. 5.15.1 diesel dilution: 0.06 m³/s per kW diesel is the minimum — check actual CO and NO_x levels for compliance.
For leakage, shock losses at junctions, and multi-district networks use dedicated ventilation software (VentSim, VUMA, 3D-Canvent).

Parameter

Airway 1

Shape

rectangular

Area A (m²)

12.000

Perimeter (m)

14.00

D_h (m)

3.429

Length L (m)

500

k (N·s²/m⁴)

0.01600

R_std (N·s²/m⁸)

0.06481

R_ρ (N·s²/m⁸)

0.06648

V at op. point (m/s)

4.62

V ≥ 0.5 m/s? (MHSA)

✓

Reynolds number Re

1050000

Flow regime

Turbulent ✓