Mine Ventilation

Ventilation Networks, Survey & Planning

Series/parallel airway resistance, Kirchhoff's laws and the pressure survey — how a whole-mine ventilation network is analysed and planned.

PART 1

Topic Breakdown & Traps

The Engineering Principle

A mine ventilation system is a network of airways obeying laws analogous to electrical circuits. Each airway has a resistance

R

; the square law

P = R Q^{2}

links pressure drop to airflow (note the *square* — ventilation is non-linear). Airways combine in series (resistances add) and parallel (a softer combined resistance). Kirchhoff's laws apply: the node law (flow in = flow out at every junction) and the mesh law (pressure drops around any closed loop sum to zero). A pressure (ventilation) survey measures pressures and flows in the field to determine each airway's resistance, calibrating the network model used for planning fans and splits.

The Core Formula Matrix

Square law:

P = R Q^{2}

(pressure drop

P

, resistance

R

, airflow

Q

)

Series:

R_{e q} = R_{1} + R_{2} + \dots

(same

Q

through each)

Parallel:

\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots

(same

P

across each)

Kirchhoff: node

\sum Q = 0

; mesh

\sum P = \sum R Q^{2} = 0

around any loop.

The ‘IIT Traps’

⚠
**Ventilation parallel law uses $1/ R$ , not $1/ R$ **, because the square law makes flow scale with $1/ R$ .
⚠
**Pressure drop scales with $Q^{2}$ .** Doubling the airflow quadruples the pressure loss — never linear.
⚠
Two equal-resistance airways in parallel carry equal flow and give $R_{e q} = R /4$ (not $R /2$ ).
⚠
Survey resistances drift as airways age, fall or are obstructed; re-survey before major planning.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

In mine ventilation the pressure drop across an airway varies with the airflow as:

Q2MEDIUM2 Marks · NAT

An airway of resistance

0.5 N\cdots^{2} / m^{8}

(gaul) carries

40 m^{3} / s

. The pressure drop across it is ______ Pa. (Round to the nearest whole number.)

Q3HARD2 Marks · NAT

Two airways of resistance

0.8

and

0.8 N\cdots^{2} / m^{8}

are connected in parallel. The equivalent resistance of the combination is ______

N\cdots^{2} / m^{8}

. (Round off to two decimal places.)