DYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON
Siphon is a pipe design, which generally an inverted U-shape that is used to flow fluid through a certain height by utilizing the pressure difference and gravitational potential energy. The work mechanism of a siphon becomes interesting discussion up to date. Based on the research of Richert and Bin...
Saved in:
Main Author: | |
---|---|
Format: | Theses |
Language: | Indonesia |
Online Access: | https://digilib.itb.ac.id/gdl/view/20371 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Institut Teknologi Bandung |
Language: | Indonesia |
id |
id-itb.:20371 |
---|---|
spelling |
id-itb.:203712017-09-27T14:40:54ZDYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON (NIM: 20211010), NURHAYATI Indonesia Theses INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/20371 Siphon is a pipe design, which generally an inverted U-shape that is used to flow fluid through a certain height by utilizing the pressure difference and gravitational potential energy. The work mechanism of a siphon becomes interesting discussion up to date. Based on the research of Richert and Binder (2011) with four simple experiments; both gravity and pressure play important roles. More recently, Nanayakkara and Rosa (2012) discussed the behavior of the siphon action at different hydrostatic pressure and different atmospheric pressure. A review of the siphon is a complex system by considering various aspects that influences the dynamics of fluid flow. Another interesting feature of the siphon is that the dynamics of fluid flow in the semi-circle pipe is nonlinear. In this study, the dynamics has been observed experimentally; the dynamics has been modeled, and the solution to the dynamics has been addressed analytically and numerically. Three siphons made of transparent glass with inner diameter (d) of 4, 6, and 8 mm have been prepared and used in the experiment. The siphon has three different segments; all of the segments are connected to each other. Segment I is a vertical straight pipe which has an adjustable length, since it is constructed of several small parts with length of about 2 cm. Segment II is a semicircle with radius 1 cm. Segment III is also a vertical straight segment with length of 15 cm. The segment I plays important role for the flow occurrence. Segment I has length of L+H, where L is the length above the water surface, and H is the length below the water surface in water container. The siphon equation of motion is derived by considering the influence of earth gravitational force, water friction, and hydrostatic pressure, which solved by Newton equation of motion. The equation of motion in the form of linear inhomogeneous second order differential equation is solved analytically on segments I and III by summing the general solutions and particular solutions, while the equation of motion in the form of nonlinear inhomogeneous second order differential equation is solved numerically using Euler method on segment II. To obtain numerical solution for segment II, an initial condition of time, position and velocity are required and can be obtained from the segment I. Therefore, an experiment was conducted on an open vertical pipe to obtain the time and the position. Analytical solution obtained in the segment I is fitted with the experimental results using Least Square Fitting to obtain a Δh (thickness of fluid volume element). This value of Δh is then used in the numerical solution of the siphon. The result from the numerical solution is then fitted to the analytical solution to obtain a corresponding Δt. Initial hypothesis was that the Δh and Δt which are obtained in the segment I can be applied in the numerical solution of segment II. To determine the validity of these values, a much smaller values of Δh and Δt are also applied in the numerical solution of segment II. Based on the results, we can conclude that the Δh and Δt obtained on segment I are not compatible to be applied to the segment II because the value of Δh is larger than the length of segmen II, where the length of segment II is π×r or equal to 3.14 cm. . The value of Δh and Δt for siphon with inner diameter of 4, 6, and 8 mm that simulate the occurrence of flow which conform with the experimental result are 10-4 m and 10-7 s, respectively. text |
institution |
Institut Teknologi Bandung |
building |
Institut Teknologi Bandung Library |
continent |
Asia |
country |
Indonesia Indonesia |
content_provider |
Institut Teknologi Bandung |
collection |
Digital ITB |
language |
Indonesia |
description |
Siphon is a pipe design, which generally an inverted U-shape that is used to flow fluid through a certain height by utilizing the pressure difference and gravitational potential energy. The work mechanism of a siphon becomes interesting discussion up to date. Based on the research of Richert and Binder (2011) with four simple experiments; both gravity and pressure play important roles. More recently, Nanayakkara and Rosa (2012) discussed the behavior of the siphon action at different hydrostatic pressure and different atmospheric pressure. A review of the siphon is a complex system by considering various aspects that influences the dynamics of fluid flow. Another interesting feature of the siphon is that the dynamics of fluid flow in the semi-circle pipe is nonlinear. In this study, the dynamics has been observed experimentally; the dynamics has been modeled, and the solution to the dynamics has been addressed analytically and numerically. Three siphons made of transparent glass with inner diameter (d) of 4, 6, and 8 mm have been prepared and used in the experiment. The siphon has three different segments; all of the segments are connected to each other. Segment I is a vertical straight pipe which has an adjustable length, since it is constructed of several small parts with length of about 2 cm. Segment II is a semicircle with radius 1 cm. Segment III is also a vertical straight segment with length of 15 cm. The segment I plays important role for the flow occurrence. Segment I has length of L+H, where L is the length above the water surface, and H is the length below the water surface in water container. The siphon equation of motion is derived by considering the influence of earth gravitational force, water friction, and hydrostatic pressure, which solved by Newton equation of motion. The equation of motion in the form of linear inhomogeneous second order differential equation is solved analytically on segments I and III by summing the general solutions and particular solutions, while the equation of motion in the form of nonlinear inhomogeneous second order differential equation is solved numerically using Euler method on segment II. To obtain numerical solution for segment II, an initial condition of time, position and velocity are required and can be obtained from the segment I. Therefore, an experiment was conducted on an open vertical pipe to obtain the time and the position. Analytical solution obtained in the segment I is fitted with the experimental results using Least Square Fitting to obtain a Δh (thickness of fluid volume element). This value of Δh is then used in the numerical solution of the siphon. The result from the numerical solution is then fitted to the analytical solution to obtain a corresponding Δt. Initial hypothesis was that the Δh and Δt which are obtained in the segment I can be applied in the numerical solution of segment II. To determine the validity of these values, a much smaller values of Δh and Δt are also applied in the numerical solution of segment II. Based on the results, we can conclude that the Δh and Δt obtained on segment I are not compatible to be applied to the segment II because the value of Δh is larger than the length of segmen II, where the length of segment II is π×r or equal to 3.14 cm. . The value of Δh and Δt for siphon with inner diameter of 4, 6, and 8 mm that simulate the occurrence of flow which conform with the experimental result are 10-4 m and 10-7 s, respectively. |
format |
Theses |
author |
(NIM: 20211010), NURHAYATI |
spellingShingle |
(NIM: 20211010), NURHAYATI DYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON |
author_facet |
(NIM: 20211010), NURHAYATI |
author_sort |
(NIM: 20211010), NURHAYATI |
title |
DYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON |
title_short |
DYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON |
title_full |
DYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON |
title_fullStr |
DYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON |
title_full_unstemmed |
DYNAMIC MODEL OF WATER VOLUME ELEMENT IN SIPHON |
title_sort |
dynamic model of water volume element in siphon |
url |
https://digilib.itb.ac.id/gdl/view/20371 |
_version_ |
1822919831081451520 |