长江科学院院报
長江科學院院報
장강과학원원보
JOURNAL OF YANGTZE RIVER SCIENTIFIC RESEARCH INSTITUTE
2015年
8期
51-56
,共6页
半立方抛物线形断面%平方抛物线形断面%立方抛物线形断面%共轭水深%显式计算公式
半立方拋物線形斷麵%平方拋物線形斷麵%立方拋物線形斷麵%共軛水深%顯式計算公式
반립방포물선형단면%평방포물선형단면%립방포물선형단면%공액수심%현식계산공식
semi-cubic parabola-shaped channel%square parabola-shaped channel%cubic parabola-shaped chan-nel%conjugate depth%explicit calculation formula
为了得到半立方、平方、立方抛物线形渠道共轭水深的显式计算公式,对这3种抛物线形渠道的水跃方程进行恒等变形,利用临界水深介于跃前水深和跃后水深之间的性质,得到了无量纲跃前水深 x 和无量纲跃后水深 y之间的关系式,进一步分别得到其迭代公式。在工程常用范围内,利用 excel 拟合得到其迭代初值,提出了一套抛物线类渠道共轭水深的显式计算公式。最后,实例及误差分析表明:半立方、平方、立方抛物线形断面无量纲跃前水深 x、无量纲跃后水深 y 最大相对误差分别为0.25%,-0.23%;0.17%,-0.29%;0.31%,0.39%。公式物理概念清晰,计算简捷,精度高,适用范围广。
為瞭得到半立方、平方、立方拋物線形渠道共軛水深的顯式計算公式,對這3種拋物線形渠道的水躍方程進行恆等變形,利用臨界水深介于躍前水深和躍後水深之間的性質,得到瞭無量綱躍前水深 x 和無量綱躍後水深 y之間的關繫式,進一步分彆得到其迭代公式。在工程常用範圍內,利用 excel 擬閤得到其迭代初值,提齣瞭一套拋物線類渠道共軛水深的顯式計算公式。最後,實例及誤差分析錶明:半立方、平方、立方拋物線形斷麵無量綱躍前水深 x、無量綱躍後水深 y 最大相對誤差分彆為0.25%,-0.23%;0.17%,-0.29%;0.31%,0.39%。公式物理概唸清晰,計算簡捷,精度高,適用範圍廣。
위료득도반립방、평방、립방포물선형거도공액수심적현식계산공식,대저3충포물선형거도적수약방정진행항등변형,이용림계수심개우약전수심화약후수심지간적성질,득도료무량강약전수심 x 화무량강약후수심 y지간적관계식,진일보분별득도기질대공식。재공정상용범위내,이용 excel 의합득도기질대초치,제출료일투포물선류거도공액수심적현식계산공식。최후,실례급오차분석표명:반립방、평방、립방포물선형단면무량강약전수심 x、무량강약후수심 y 최대상대오차분별위0.25%,-0.23%;0.17%,-0.29%;0.31%,0.39%。공식물리개념청석,계산간첩,정도고,괄용범위엄。
In order to get the explicit calculation formula of conjugate depth for semi-cubic,square,and cubic para-bolic-shaped channels,the jump equations of the three parabola-shaped channels were transformed identically and the relationships between the dimensionless water depth x before jump and the dimensionless water depth y after jump were obtained according to the property that the critical depth was between the pre-jump depth and the post-jump depth.Their iterative formulas were further obtained respectively.Hence,a set of explicit calculation formu-las of conjugate depth for semi-cubic,square,and cubic parabolic-shaped channels were obtained by fitting the it-erative initial value through excel in common engineering scope.Finally,example and error analysis shows that the absolute value of maximum relative error of dimensionless water depth x before jump was 0.25%,0.1 7%,and 0.31 % respectively for the semi-cubic,square,and cubic parabolic-shaped channel,and that of dimensionless wa-ter depth y after jump was respectively -0.23%, -0.29%,and 0.39%.The formulas were convenient and highly accurate with clear physical meaning and wide application scope.