Dimensional Analysis of Transmissivity Equations and Comparison of Dependent Variables Using Birnin Gwari Aquifer Characteristics in Northern Nigeria

Abstract

This study established relationship among three transmissivity equations using dimensional analysis, comparing three dependent variables inherent in the transmissivity equations, and use correlation analysis to examine the nature of interrelationship between drawdown and specific capacity in the Birnin-Gwari local government area of Kaduna State, Nigeria between October 2018 and October 2019. Relationship between three transmissivity equations, namely, Jacob, Logan and Babuskin was determined using dimensional analysis. The equations and the outcome were applied to the hydraulic data obtained from 26 producing boreholes in the study area. Comparison of the dependent variables, namely discharge, drawdown and hydraulic conductivity, was carried out to observe the relationship among them. The Correlation analysis was used to examine the nature of interrelationship between drawdown and specific capacity, while the plots of depth-to-water table and depth-to-basement were made to provide pictorial comparison between positions of water table and the underlying Basement. The results showed that the values computed from the Jacob method are the lowest among the three, while Logan method gave higher values, although they all trend in similar manner. The study revealed an inverse trend in the drawdown versus discharge and hydraulic conductivity. Correlation analysis between drawdown and specific capacity gave a regression coefficient of -0.593 and correlation coefficient of 0.352, indicating a weak relationship between them. The graphical relation of water level versus basement rock surfaces portend a near-parallel trend possibly determined by the underlying geology. Transmissivity values computed from the Babuskin method gave almost average values among the three methods. Both the regression and correlation coefficients gave low to average values between drawdown and specific capacity. The depth-to-basement versus depth-to-water plots showed that water table variations are probably controlled by the type and trend of basement topography.