Calculation Formula for Normal Water Depth of Parabolic Index n> 2-shaped Cross Section
Chen Pin
Abstract
Chen Pin
Abstract
Since the normalwaterdepth solution of parabolic section(n 2)involves the computing problems of non-integrable function and transcendental equation,by introducing quadratic parabolic approximate integration and optimal fitting, and through successive approximation fitting, the approximate calculation formula is obtained which is simple in form, concise in computational process, wide in application, and convenient for project design staff to practically use. The error analysis and case calculation showthat in the scope of projectuse, the formula'smaximum relative calculation error isonly 0.841%.It could completelymeetthe requirementsof projectdesign precision and have the value forpopularization and application.
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Since the normalwaterdepth solution of parabolic section(n 2)involves the computing problems of non-integrable function and transcendental equation,by introducing quadratic parabolic approximate integration and optimal fitting, and through successive approximation fitting, the approximate calculation formula is obtained which is simple in form, concise in computational process, wide in application, and convenient for project design staff to practically use. The error analysis and case calculation showthat in the scope of projectuse, the formula'smaximum relative calculation error isonly 0.841%.It could completelymeetthe requirementsof projectdesign precision and have the value forpopularization and application.
Key concepts: Mathematics, Transcendental function, Approximation error, Quadratic equation, Section (typography), Mathematical analysis, Cross section (physics), Simple (philosophy)