Ventilation Networks

That a close analogy exists between the flow of air in mines and the flow of current in electrical networks- has been known for a long time. The laws that have been used to solve series and parallel electrical circuits have been used to solve for the equivalent resistance in mine ventilation problems. Kirchhoff's current and voltage laws have also been adopted in solving mine ventilation network problems. It will be best to define a few terms here regarding networks, and with reference to Figure 1, these definitions can be elucidated. Figure 1 can be represented by the network in Figure 2 without losing any essential details. 1. A junction is a point where two or more airways meet. 2. The segment of a roadway connecting any two junctions is known as a branch. 3. A mesh is a closed path through the network. In the above network, B, C, D and F are the junctions, CF and CD are two of the branches and CFDC is a mesh. Kirchhoff's current law states that the sum of currents entering a junction. Applying this law to the junctions in the ventilation network, one obtains for junctions C and F, the following relationships: JUNCTION C: Q1 = Q4 + Q3 (1) JUNCTION F: Q2 + Q3 = Q5 (2) Similar relationships can be drawn for other junctions. Kirchhoff's voltage law states that in any complete electric circuit, the algebraic sum of the emf's must equal the algebraic sum of the voltage drops. In mine ventilation, the square law (Atkinson's