A Simple Calculation Method for the Normal Water Depth of Tunnel with Egg-shaped Section
Teng Ka
Abstract
Teng Ka
Abstract
The normal water depth of tunnel with egg-shaped cross-section involves the solution of complex transcendental equations,and it cannot be calculated directly by analytical method. It's redundant and inaccurate to calculate by conventional method of looking-up tables and diagrams which would cause man-made errors. Meanwhile by trial method,the formulas are partitioned and the equations are complicated with heavy work load and low efficiency. In this research,an approximate formula was obtained by optimal fitting in the range of parameters applicable to practical engineering with the minimum standard residual difference as the objective function. The formula is convenient,practical,and simple in expression. Its precision also meets design requirements( maximum error0. 729%). It is of practical promotion significance.
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The normal water depth of tunnel with egg-shaped cross-section involves the solution of complex transcendental equations,and it cannot be calculated directly by analytical method. It's redundant and inaccurate to calculate by conventional method of looking-up tables and diagrams which would cause man-made errors. Meanwhile by trial method,the formulas are partitioned and the equations are complicated with heavy work load and low efficiency. In this research,an approximate formula was obtained by optimal fitting in the range of parameters applicable to practical engineering with the minimum standard residual difference as the objective function. The formula is convenient,practical,and simple in expression. Its precision also meets design requirements( maximum error0. 729%). It is of practical promotion significance.
Key concepts: Transcendental equation, Simple (philosophy), Range (aeronautics), Transcendental function, Expression (computer science), Section (typography), Mathematics, Function (biology)