The unitary aqueduct method: a new tool for the preliminary design of air chambers

Abstract

Modern aqueducts supply pressurized water from the available sources to the demanding urban-industrial or agricultural centers. Air chambers, in which air is stored at the pipeline pressure, are widely used in aqueducts, to reduce and to control the effects of the hydraulic transients produced immediately after the accidental or programmed stoppage of the pumps of the system. Dimensionless graphs have been proposed for the preliminary design of the air chambers: Allievi (1937), Angus (1937), Evans and Crawford (1954), Parmakian (1955), to name the classics. These graphs, obtained for the elastic and for the rigid column models of water hammer, allow the calculation of the initial air volume in the chamber and of the maximum and minimum pressures resulting from the hydraulic transients. However, dimensionless equations have not been proposed for the preliminary design of the air chambers. The method of the Unitary Aqueduct, for the preliminary design of the air chambers, is proposed in this paper, presenting dimensionless equations with only two dimensionless parameters, in which all aqueducts are represented, and design tables, from which the complete dimensions of the air chambers can be defined. The findings of this method are compared with the dimensions of a number of existing relevant aqueducts in Mexico, with very good correspondence. The Unitary Aqueduct is defined as a 10 km long aqueduct, with a flow of 2 m3/s, a water velocity of 2 m/s, and an absolute head of 110 m, typical of an aqueduct able to supply a city of 500 000 inhabitants. All possible aqueducts will be a multiple or a fraction of this aqueduct, and since a set of unitary air chambers for this unitary aqueduct can be completely pre-designed, for different relative minimum pressures, the design of an air chamber for a specific aqueduct will be a multiple or a fraction of one of the unitary air chambers of the prototype. Finally, the maximum possible upsurge is calculated and shown in a dimensionless figure. This maximum pressure can be compared with the maximum transient head desired, the difference between the two representing the head to be eliminated at the air chamber entrance or at the pipe connecting the returning flow with the air chamber. The method is also validated with the findings of a large number of experiments, carried out in an experimental installation.