On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium

Xie Cuili; Zhang Yunong

doi:doi:10.11648/j.ajpa.20231102.11

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On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium

Xie Cuili, Zhang Yunong

Published in American Journal of Physics and Applications (Volume 11, Issue 2)

Received: 16 March 2023 Accepted: 10 April 2023 Published: 27 April 2023

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Abstract

Falling motion of a sphere in the stationary medium is an important basic research and has a wide range of engineering application prospects. This paper studies the free fall motion of spheres in a stationary medium considering air drag. This paper calculates the acceleration, velocity and displacement of the falling process of the sphere by Excel, and discusses the influence of the density, diameter and Re on the motion. Some analysis and fitting of displacement over time are performed. The results show that the varied-acceleration motion of the falling spheres is similar for different sphere materials, namely, the falling acceleration, the velocity and falling displacement all can be divided into three segmentations and fitted with polynomial functions. The relationship between displacement h and time t during falling with varied- acceleration is also greatly affected by the density of the sphere, the greater the density of the sphere, the closer the relationship between h and t during the fall process is closer to no drag free fall, the smaller the density of the sphere is, the closer the relationship between h and t is nearer to linear relationship. The displacement data of different solid material sphere is located between the fall of water and the free drop without drag, but does not meet power function or the multi-relationship function. Some results are compared with the literature experiments, and are consistent with the experiments.

Published in	American Journal of Physics and Applications (Volume 11, Issue 2)
DOI	10.11648/j.ajpa.20231102.11
Page(s)	31-39
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fall of Sphere, Settlement, Kinematics, Varied Acceleration Motion, Nonlinear Motion

References

[1]	Phillip P. Brown1 and Desmond F. Lawler2. Sphere Drag and Settling Velocity Revisited. 2003, 129 (3). 222-230.
[2]	Dou Xiurong, Study on the working characteristics analysis and process parameter selection of air drilling. Master's Thesis. 2004, China Academy of Petroleum Exploration and Development.
[3]	Hagbart S. Alsos, Odd M. Faltinsen, 3D motion dynamics of axisymmetric bodies falling through water. Ocean Engineering 2018, 169, 442-456.
[4]	J. Gylys, R. Skvorcinskiene, L. Paukstaitis, M. Gylys, A. Adomavicius. Water temperature influence on the spherical body’s falling velocity, International Journal of Heat and Mass Transfer, 89 (2015), 913-919.
[5]	LIU Lei, YANG Jian-mina, LYU Hai-ninga, TIAN Xin-lianga, PENG Tao, Effects of Degrees of Motion Freedom on Free-Fall of A Sphere in Fluid. China Ocean Eng., 2018, Vol. 32, No. 5, P. 605–613.
[6]	A. Iranmanesh M. Passandideh Fard, Two dimensional modelling of free surface flows in presence of a spherical object using the Modifed Volume of Fluid technique. Marine Systems & Ocean Technology (2023) 17: 123–134.
[7]	Hadi Ahmadi •Saman Farzi Sizkow, Numerical analysis of ground improvement effects on dynamic settlement of uniform sand using DEM, SN Applied Sciences (2020) 2: 689-677.
[8]	E. Tempelman & M. M. S. Dwaikat & C. Spitás, Experimental and Analytical Study of Free-Fall Drop Impact Testing of Portable Products, Experimental Mechanics (2012) 52: 1385–1395.
[9]	M. M. Zdravkovich, Flow around circular cylinder. 2018. China Machine Press.
[10]	Wu Hualin, Shen Huanting, Li Zhongwei, Acceleration Motion of Sediment Particle, Ocean Engineering, 2000. 18 (1): 44-49.
[11]	Xu Falin, Excel Scatter Chart Processing of Free fall motion to explore experimental data, Middle School Physics Teaching Reference 2019, 48 (5), 66-67.
[12]	Chen Xianying, Three supplements to Galileo's research on free falling motion, Physics Teaching Discussion, 2012. Vol 30 (444), 13-15.
[13]	N. Mordant and J. F. Pinton, Velocity measurement of a settling sphere, Eur. Phys. J. B 18, 343-352 (2000).
[14]	P. V. D. Leeden Liem Djan Nw and P. C. Suratman, The velocity of free falling droplets. Appl. sci. Res 1955. Section A, Vol. 5, 342-347.

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APA Style

Xie Cuili, Zhang Yunong. (2023). On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium. American Journal of Physics and Applications, 11(2), 31-39. https://doi.org/10.11648/j.ajpa.20231102.11

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ACS Style

Xie Cuili; Zhang Yunong. On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium. Am. J. Phys. Appl. 2023, 11(2), 31-39. doi: 10.11648/j.ajpa.20231102.11

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AMA Style

Xie Cuili, Zhang Yunong. On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium. Am J Phys Appl. 2023;11(2):31-39. doi: 10.11648/j.ajpa.20231102.11

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@article{10.11648/j.ajpa.20231102.11,
  author = {Xie Cuili and Zhang Yunong},
  title = {On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium},
  journal = {American Journal of Physics and Applications},
  volume = {11},
  number = {2},
  pages = {31-39},
  doi = {10.11648/j.ajpa.20231102.11},
  url = {https://doi.org/10.11648/j.ajpa.20231102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20231102.11},
  abstract = {Falling motion of a sphere in the stationary medium is an important basic research and has a wide range of engineering application prospects. This paper studies the free fall motion of spheres in a stationary medium considering air drag. This paper calculates the acceleration, velocity and displacement of the falling process of the sphere by Excel, and discusses the influence of the density, diameter and Re on the motion. Some analysis and fitting of displacement over time are performed. The results show that the varied-acceleration motion of the falling spheres is similar for different sphere materials, namely, the falling acceleration, the velocity and falling displacement all can be divided into three segmentations and fitted with polynomial functions. The relationship between displacement h and time t during falling with varied- acceleration is also greatly affected by the density of the sphere, the greater the density of the sphere, the closer the relationship between h and t during the fall process is closer to no drag free fall, the smaller the density of the sphere is, the closer the relationship between h and t is nearer to linear relationship. The displacement data of different solid material sphere is located between the fall of water and the free drop without drag, but does not meet power function or the multi-relationship function. Some results are compared with the literature experiments, and are consistent with the experiments.},
 year = {2023}
}

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TY  - JOUR
T1  - On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium
AU  - Xie Cuili
AU  - Zhang Yunong
Y1  - 2023/04/27
PY  - 2023
N1  - https://doi.org/10.11648/j.ajpa.20231102.11
DO  - 10.11648/j.ajpa.20231102.11
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 31
EP  - 39
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20231102.11
AB  - Falling motion of a sphere in the stationary medium is an important basic research and has a wide range of engineering application prospects. This paper studies the free fall motion of spheres in a stationary medium considering air drag. This paper calculates the acceleration, velocity and displacement of the falling process of the sphere by Excel, and discusses the influence of the density, diameter and Re on the motion. Some analysis and fitting of displacement over time are performed. The results show that the varied-acceleration motion of the falling spheres is similar for different sphere materials, namely, the falling acceleration, the velocity and falling displacement all can be divided into three segmentations and fitted with polynomial functions. The relationship between displacement h and time t during falling with varied- acceleration is also greatly affected by the density of the sphere, the greater the density of the sphere, the closer the relationship between h and t during the fall process is closer to no drag free fall, the smaller the density of the sphere is, the closer the relationship between h and t is nearer to linear relationship. The displacement data of different solid material sphere is located between the fall of water and the free drop without drag, but does not meet power function or the multi-relationship function. Some results are compared with the literature experiments, and are consistent with the experiments.
VL  - 11
IS  - 2
ER  -

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Author Information

Xie Cuili

School of Petroleum Engineering, China University of Petroleum, Qingdao, China
Zhang Yunong

School of English Education, Guangzhou University of Foreign Studies, Guangzhou, China

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APA Style

Xie Cuili, Zhang Yunong. (2023). On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium. American Journal of Physics and Applications, 11(2), 31-39. https://doi.org/10.11648/j.ajpa.20231102.11

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ACS Style

Xie Cuili; Zhang Yunong. On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium. Am. J. Phys. Appl. 2023, 11(2), 31-39. doi: 10.11648/j.ajpa.20231102.11

Copy | Download

AMA Style

Xie Cuili, Zhang Yunong. On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium. Am J Phys Appl. 2023;11(2):31-39. doi: 10.11648/j.ajpa.20231102.11

Copy | Download

@article{10.11648/j.ajpa.20231102.11,
  author = {Xie Cuili and Zhang Yunong},
  title = {On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium},
  journal = {American Journal of Physics and Applications},
  volume = {11},
  number = {2},
  pages = {31-39},
  doi = {10.11648/j.ajpa.20231102.11},
  url = {https://doi.org/10.11648/j.ajpa.20231102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20231102.11},
  abstract = {Falling motion of a sphere in the stationary medium is an important basic research and has a wide range of engineering application prospects. This paper studies the free fall motion of spheres in a stationary medium considering air drag. This paper calculates the acceleration, velocity and displacement of the falling process of the sphere by Excel, and discusses the influence of the density, diameter and Re on the motion. Some analysis and fitting of displacement over time are performed. The results show that the varied-acceleration motion of the falling spheres is similar for different sphere materials, namely, the falling acceleration, the velocity and falling displacement all can be divided into three segmentations and fitted with polynomial functions. The relationship between displacement h and time t during falling with varied- acceleration is also greatly affected by the density of the sphere, the greater the density of the sphere, the closer the relationship between h and t during the fall process is closer to no drag free fall, the smaller the density of the sphere is, the closer the relationship between h and t is nearer to linear relationship. The displacement data of different solid material sphere is located between the fall of water and the free drop without drag, but does not meet power function or the multi-relationship function. Some results are compared with the literature experiments, and are consistent with the experiments.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - On the Variable Acceleration Motion of Falling Sphere in a Fluid Medium
AU  - Xie Cuili
AU  - Zhang Yunong
Y1  - 2023/04/27
PY  - 2023
N1  - https://doi.org/10.11648/j.ajpa.20231102.11
DO  - 10.11648/j.ajpa.20231102.11
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 31
EP  - 39
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20231102.11
AB  - Falling motion of a sphere in the stationary medium is an important basic research and has a wide range of engineering application prospects. This paper studies the free fall motion of spheres in a stationary medium considering air drag. This paper calculates the acceleration, velocity and displacement of the falling process of the sphere by Excel, and discusses the influence of the density, diameter and Re on the motion. Some analysis and fitting of displacement over time are performed. The results show that the varied-acceleration motion of the falling spheres is similar for different sphere materials, namely, the falling acceleration, the velocity and falling displacement all can be divided into three segmentations and fitted with polynomial functions. The relationship between displacement h and time t during falling with varied- acceleration is also greatly affected by the density of the sphere, the greater the density of the sphere, the closer the relationship between h and t during the fall process is closer to no drag free fall, the smaller the density of the sphere is, the closer the relationship between h and t is nearer to linear relationship. The displacement data of different solid material sphere is located between the fall of water and the free drop without drag, but does not meet power function or the multi-relationship function. Some results are compared with the literature experiments, and are consistent with the experiments.
VL  - 11
IS  - 2
ER  -

Copy | Download