Mining - Pressure Changes at Splits and Junctions in Mine Ventilation Circuits

The estimation of the magnitude of pressure changes which occur in mine ventilation circuits is of primary importance to the mining engineer in making changes in an existing mine or in projecting the ventilation requirements of a new mine. It is a formidable task in many cases, because no adequate theory is available and empirical data are unreliable or even lacking. The common practice of increasing one's estimate of the mine static pressure by an arbitrary "safety factor" to compensate for the unknown is a poor substitute for accuracy. Generally little difficulty is encountered in calculating friction losses in mine airways. As long as the friction factor can be reliably estimated, the well-known Atkinson formula gives accurate results. However, it is in the determination of shock losses that the ventilation engineer encounters difficulty and is apt to resort to an arbitrary allowance. Shock losses may constitute as little as five or as much as twenty-five percent or more of the overall pressure drop in the mine, and such allowances are generally completely unsatisfactory. Since other shock losses have been covered by McElroy (1), this paper deals with a long-neglected source of shock and pressure change in ventilation circuits, divergence and convergence of airflows, here referred to by their more common mining terms, splits and junctions. PREVIOUS WORK There is practically no fundamental information available in ventilation literature on the splitting and junction of airflows, either in mining or mechanical engineering periodicals or handbooks. Fluid mechanics textbooks seemingly avoid the subject of divergence and convergence, except for brief empirical treatment. The only investigation reported for mine ventilation systems was by Weeks, et a1 (21), in 1933. Although applicable to the case of line brattices in coal mines, it cannot be applied to the general case of mine splitting and junctions involving change of direction with little or no area change. In dealing briefly with the subject of shock losses at splits and junctions, McElroy (1) suggests only that they be considered comparable to bends, with losses at junctions being increased 50 pct to allow for interference of merging streams. He recognizes the importance of quantity ratio but concludes that exact quantitative data are lacking to compute losses at splits and junctions. A very capable summary and analysis of the state of knowledge in industrial ventilation and fluid mechanics regarding losses due to divergence has recently been reported by Gilman (3). In considering all earlier work dealing with both air and water as fluids, he compares results on a common basis and obtains good empirical agreement. For divergent flow, the controlling variable in each branch is the quantity ratio, although the deflection angle is of secondary importance. Empirical equations are presented for straight and 90-deg branches with varying velocity ratios, assuming branches smaller than the main duct. These formulas are modifications of the Borda equation for abrupt contraction and expansion. The only information available on shock losses in convergent flow are approximate experimental data presented by Alden (4) and the Manual of Recommended Practice for Industrial Ventilation of the American Conference of Governmental Industrial Hygienists. Alden considers the effects of both quantity ratio and deflection angle. The data indicate an effect opposite to that observed in divergence, the shock loss varying directly with quantity ratio. SHOCK LOSS THEORY Because pressure losses due to shock have been found to bear a constant relation to the mean velocity of flow in a given conduit, they are frequently expressed as a dimensionless function of the velocity head, termed the shock loss factor. For airflow in ducts and mine airways, the shock loss may be represented by the formula (1): Hx - XHv, (1)