Abstract: The Buckingham equation expresses the relationship between laminarflow velocity and resistance of the Bingham fluid. The Soviet scholarproposed an approximate formula for calculating flow resistance, based onwhich the maximum deviation relative to the exact solution was 6.7%. Inthis paper, with the mathematical analysis and three-dimensionsoptimization, and the change of the parameter of the approximate formula, the deviation isdecreased to a great extent. The deviation is the function of theparameter and thecore-flow relative radius r0. By means of the limiting value, the continuous points and interrupted points in the \bar r0 closedregion are determined, which provides a basis for reducing the deviationin the wholeregion. In the three-dimensional figure of the deviations, the problem toseek the max-value on multi-peak curved surface can be resolved by the useof the cutting plane. Finally, with the optimized parameter, the maximumdeviation of the approximate equation becomes 2.6%, a reduction of 4.1%comparing to 6.7%.