Appendix ADOE-HDBK-1015/1-93BASIC SEPARATION THEORYRev. 0CH-01Page A-9Because of their number and complexity, the mathematical formulas used in calculating thepressure points in Figure A-3 will not be presented. The operator will read and record onlythose values which are measured by instruments and will not be required to perform any of themathematical calculations involved in completing a circuit balance. However, the followingdiscussion will give an indication as to the procedures involved in determining these values.To calculate a circuit balance for Stage N in Figure A-3, pressures P and P and temperature1 2T are recorded. Then, knowing P and T and a constant previously determined in a test loop,1 1 1it is possible to calculate the flow W (N - 1). Since the "A" barrel of the compressor hasA essentially a constant suction volume in the normal operating range, the interstage flow isproportional to the compressor "A" suction pressure and temperature. Next, it is known thatthe flow in a cascade must operate at a steady state condition to prevent an accumulation ofdeficiency of inventory in any one section. It may therefore be assumed that the flowdownward to a stage is equal to the flow upward from the same stage. (This assumption isnot valid for all stages in a cascade but for practical applications the error is negligible.) Fromthis assumption, W is equal to W (N - 1). With P , W , and pressure drop data obtained inBA2Bthe test loop, P can be calculated.7In a test loop, data is taken on converters of different sizes and types to determine pressurevariations with different amounts of flow and cut. If W is found in the same manner as WAA(N - 1), it is then possible with the test loop data to calculate P . Also, with the converter data,band knowing W , P , and W (W = W + W ), P and subsequently, P are found.B7TTABofAgain using pressure drop data, P can be calculated from W and P . With P , P is calculated5To53by knowing the "B" pressure ratio of the compressor.From the calculated values obtained from a circuit balance, it is possible to make furthercalculations which indicate the operational and productive characteristics of the cascade. Forexample, P , P , and the flows through a converter must be known before the actualfbpermeability of the barrier can be calculated. Also, these values make it possible to accuratelypredict horsepower requirements under varying conditions of flow and pressure. Anotherimportant application of the circuit balance is in the determination of inventory in the cascadewhere pressures and temperatures not otherwise measured are required.