浅谈微积分“抽水做功”相关物理应用问题

doi:10.16854 / j.cnki.1000-0712.200025

大学物理 ›› 2020, Vol. 39 ›› Issue (12): 20-27.doi: 10.16854 / j.cnki.1000-0712.200025

浅谈微积分“抽水做功”相关物理应用问题

庞国楹，刘　俊，郭　彦，刘　佳

陆军军事交通学院基础部数学教研室，天津　300161

收稿日期:2020-01-22 修回日期:2020-03-31 出版日期:2020-12-20 发布日期:2020-12-01
作者简介:庞国楹(1983—)，男，山东肥城人，陆军军事交通学院讲师，硕士，主要从事高等数学和数学建模工作.
基金资助:
学院教育教学改革重大基金项目(JYYJYB2019020)和(413GZ10107)资助

Study of the application physics problem of pumping work in infinitesimal calculus

PANG Guoying，LIU Jun，GUO Yan，LIU Jia

Mathematical Teaching Room，General Courses Department，Army Military Transportation University，Tianjin 300161，China

Received:2020-01-22 Revised:2020-03-31 Online:2020-12-20 Published:2020-12-01

摘要/Abstract

摘要：

针对微积分中的抽水做功相关物理问题，结合实际生活场景和工程背景，以微元法和三重积分方法，考虑容器竖直

放置和倾斜放置两种情况，建立了容器竖直放置以及吸管不同位置的做功模型，容器倾斜液体未流出的做功模型，以及容器

倾斜液体流出情形的做功模型，并进行数值仿真，得出的相关理论具有较强的实际应用和理论参考价值.

关键词: 微元法, 三重积分, 抽水做功

Abstract:

Considering the physical problem of pumping power，infinitesimal method and triple integral are used in this paper，combined scenes of real life and engineering background. Considering the container placed vertically and tilted，the model of vertical condition and the different positions of the straw，the model of tilted condition and liquid not flowing out，and the model of tilted condition and liquid flowing out of the container are established. Through numerical simulation，the strong practical application and the value of theoretical reference are pointed out.

Key words: infinitesimal method, triple integral, pumping work

庞国楹, 刘　俊, 郭　彦, 刘　佳. 浅谈微积分“抽水做功”相关物理应用问题[J]. 大学物理, 2020, 39(12): 20-27.

PANG Guoying, LIU Jun, GUO Yan, LIU Jia. Study of the application physics problem of pumping work in infinitesimal calculus [J]. College Physics, 2020, 39(12): 20-27.

浅谈微积分“抽水做功”相关物理应用问题

Study of the application physics problem of pumping work in infinitesimal calculus

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