Abstract:Converting the balance equation of the branch of a mine ventilation network into an equivalent nonlinear programming problem,this paper proves that the total sum of the energy loss in every branch will be a minimum when the airflow distribution in the networks is in a balanced state.The energy means of solving the network equations by nodal methods is also noted,and a theorem for the unique existence of the solution for a network balance equation is give.An example is used to explain these conclusions.

Key words: nonlinear programming; mine ventilation; energy airflow; Distribution