Determination of Most Economical Airshaft Size

TO determine the optimum inside dimension of an airshaft, it is necessary to strike the proper balance between the cost of power for air friction and turbulence losses within the airshaft, on the one hand, and the cost of sinking the airshaft, on the other. An airshaft larger than necessary is extravagant because the increased amortization rate exceeds the reduction in power cost. Conversely, an airshaft smaller than is needed wastes more power than can be justified by the corresponding reduction in amortization rate. The airshaft power is a function of the air volume Q cu. ft. per min. and the air- pressure drop p in. water gauge across the airshaft The airshaft pressure drop is calculated by the formula: [ ] wherein R is the air-friction coefficient for the portion of the airshaft 1 ft. deep, 0 ft. in perimeter and A sq. ft. in area, when passing an air volume of Q cu. ft. per minute. The airpower w kw. dissipated within the airshaft is computed by the formula: [ ] With a combined over-all unit efficiency of the fan and drive of E per cent, the air- shaft power requirements become [ ] There are 8760 hours per year, so with energy at I cent per kilowatt-hour the annual cost per kilowatt for continuous operation is $87.60; therefore, with energy at C$ per kw-hr. the annual airshaft power cost MI dollars per year becomes: [ ] which, expressed by the component parts, becomes : [] The amortization rate a dollars per year per dollar invested includes both depreciation and interest on the investment. These in turn involve the expected useful life of the airshaft and available monetary interest rate. For the purpose of this discussion the cost of airshaft sinking is assumed to comprise a fixed move-in charge Y dollars, which covers the cost of transporting, erecting and removing the shaft-sinking equipment and is independent of the air- shaft size. Also, it is assumed that the cost of shaft lining, if any, is fixed at $X per cu. yd. of lining material and that excava-