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\title{Study of Minor Loss Coefficient of Flexible Pipes for Different Bend Angles and Different Bend Radius by Experiment and Simulation}
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             \author[1]{M. S.  Islam}

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\date{\small \em Received: 7 December 2015 Accepted: 2 January 2016 Published: 15 January 2016}

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\begin{abstract}
        


The aim of this work is to investigate the minor loss for locally available bended flexible pipes of different dimensions. Minor loss coefficients for different bend angles and different bend radius of these pipes are ascertained, using both experimental method and numerical analysis. Different parameters on which Minor Loss depend were observed and their relations to the Minor Loss were analyzed. Minor loss coefficient for different bend angles and two bend radiuses were determined. Minor losses were measured under different flow rates. The Minor Loss Co-efficient was also determined by solving Navier-Stokes Equation, with the help of standard computer program. For Turbulent Stresses Boussinesq assumption is used. As Turbulence model k ?-? is implemented. Navier-Stokes equations for viscous, incompressible flow shows mixed ellipticparabolic behavior. So, semi-implicit method for pressure linked equation (SIMPLE) was used.

\end{abstract}


\keywords{Minor Loss Co-Efficient, Bends, ?? ? -? Turbulence Model.}

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\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
he losses that occur in pipelines due to bends, elbows, joints, valves etc are called minor losses. Minor loss in a bend is due to flow separation on the curved walls and a swirling secondary flow arising from the centripetal acceleration. Since the flow pattern in valves, bends and fittings are quite complex, the theory is very weak. The losses are usually measured experimentally and correlated with the pipe flow parameters. In turbulent flow, the Minor Loss varies as the square of the velocity. The form of Darcy's equation used to calculate minor losses of individual fluid system components is expressed by the equation h m = k v\textasciicircum 2/2g ????????. \hyperref[b0]{(1)} Where, h m = minor loss for a fitting, k = minor loss coefficient, ? = velocity of the fluid for the time. Bends are provided in pipes to change the direction of flow through it. An additional loss of head, apart from that due to fluid friction, takes place in the course of flow through pipe bend. The fluid takes a curved path while flowing through a pipe bend as shown in figure \hyperref[fig_0]{1}. Whenever a fluid flows in a curved path, there must be a University of Engineering \& Technology, Dhaka, Bangladesh. e mails: Jony06\textunderscore buet@yahoo.com,rashid@me.buet.ac.bd inward acceleration, known as centripetal acceleration. This results in an increase in pressure near the outer wall of the bend, starting at some point A and rising to a maximum at some point B. There is also a reduction of pressure near the inner wall giving a minimum pressure at C and a subsequent rise from C to D.\par
Therefore, between A and B and between C and D the fluid experiences an adverse pressure gradient (the pressure increases in the direction of flow). Losses also take place due to a secondary flow in the radial plane of the pipe because of a change in pressure in the radial depth of the pipe. This flow, in conjunction with the main flow, produces a typical spiral motion of the fluid which persists even for a downstream distance of fifty times the pipe diameter from the central plane of the bend. This spiral motion of the fluid increases the local flow velocity and the velocity gradient at the pipe wall, and therefore results in a greater frictional loss of head than that which occurs for the same rate of flow in a straight pipe of the same length and diameter.\par
In the context of our study, there are some contributions of particular importance. Khan and Islam \hyperref[b0]{[1]} made an experimental investigation of flow through flexible pipes and bends. In their work they used metal made pipes. Two manometers were used: one for trough to trough and one for crest to crest readings. Khan, Ahmed, Jonayat \hyperref[b1]{[2]} determined friction factor of flow through flexible pipes and minor loss coefficient of flexible bends. Ahmed, Chakraborty and Fattah \hyperref[b2]{[3]} did their work on locally manufactured PRR pipes bends to measure friction factor and minor loss coefficient respectively. In 1895 Reynolds \hyperref[b3]{[4]} rewrote Navier-Stokes equation in time averaging form. Jones and Launder \hyperref[b4]{[5]} and Harlow and Nakayama \hyperref[b5]{[6]} developed k ? -? turbulence around 1970 model. In 1972 Caretto, Patanker and Spalding \hyperref[b6]{[7]} introduced SIMPLE algorithm for solving Navier-Stokes Equations for viscous, incompressible flow. Jaiman, Oakley and Adkins \hyperref[b7]{[8]} did CFD modeling of corrugated flexible pipes. In their work they constructed a numerical model of the corrugated flexible pipes and did simulation to show variation of velocity distribution throughout the pipe, 2011). ? One PVC pipe (1 inch) is selected corresponding to the diameter of reducer and threads were cut at the end of the PVC pipe to be fitted with reducer. 
\section[{II. Setup \& Data Collection}]{II. Setup \& Data Collection}\par
? The end of the PVC pipe which was to be matched with the flexible pipes was smoothened and chamfered.\par
? Now using drill machine, two drills transverse to the flexible pipe's length were made at two modes where manometer are required to be connected with pipe nipples With help of two pipe tubes (1.5mm diameter).\par
? Steps 1 to 4 were repeated for pipe bends. To hold the bended flexible pipes in the desired position stand were used.\par
? Now that required machining operations are done; specimen were properly washed and cleaned to eliminate dirt, oil and other undesirable internal surface matter.\par
c) Construction Setup ? One end of the flexible pipe was connected with the corresponding PVC pipe with the help of reducer (reducer is fitted with the gate valve). ? Thread tapes were used to ensure proper sealing in different connections. ? The other end of the flexible pipe was directed to the bucket. ? After preparing the manometer, manometric fluid (CCl4) was injected to it. ? The limbs of manometer were connected to the nipples attached to the specimen through flexible tubes (1.5mm diameter) and fine wires were used to ensure proper sealing. ? Priming of the manometer was performed. ? Two stands were used to maintain the specimen horizontal and wood piece was used to keep the discharge end at elevated height to ensure full flow of water. 
\section[{d) Data Collection Procedure}]{d) Data Collection Procedure}\par
In order to collecting data working fluid (water) was allowed to flow through the experimental setup for three different dimensions of the flexible pipe. Differential Manometer was used to measure pressure drop through the bend. As manometric fluid, Carbon Tetra-Chloride (CCL4) was used.\par
At first, the inner diameter of the specimen was measured.\par
The room temperature was observed. Mass of empty bucket was measured.\par
The zero level of the manometer was checked. By opening the gate valve water was allowed to flow through the testing section and all the sealing was checked. Now stop-watch was turned on and water flowing through the pipe was collected to the bucket. Steady state manometer readings were collected. After a time, stop-watch was turned off and mass of water filled bucket was measured by platform scale. Stop-watch reading was taken. By changing the gate valve opening flow rate was varied and reading were taken at these flow rates by repeating step six to nine. These way four readings were taken for each bend angle. The above procedure was performed for three different diameters and two different bend radius. 
\section[{III. Theory}]{III. Theory}\par
The simulation of water flow in a flexible bend pipe of different diameter, bend radius and angle was done by solving the Navier-Stokes Equation, with the help of commercial simulation software ANSYS 13 (WORLBENCH and FLUNET). Here the terms ???? ? 2 ???? , ???????? ????? etc are called turbulent stresses.\par
According to Boussinesq assumption [9]   ????? ?? ??? ?? ??????? = 2?? ?? ?? ???? ? According to k ? -? model [5][6]   ?? ?? =?? ?? ??(?? ? ) 2 ??\textbf{(7)}\par
Here, ?= Dissipation rate. The transport equation for kinetic energy of turbulence ?? ? ,?? ??? ? ???? ? ???? + ??? ???? ? ???? + ?? ? ???? ? ???? ? = ?? ???? ?? ???? + ?? ?? ???? ?? ? ???? ? ???? ?? ? ? ???? + ?2?? ?? ?? ???? ? 2 3 ???? ? ?? ???? ? ???? ?? ???? ??\textbf{(8)}\par
The transport equation for Dissipation rate ?,?? ??? ? ???? ? ???? + ??? ???? ? ???? + ?? ? ???? ? ???? ? = ?? ???? ?? ???? + ?? ?? ???? ?? ? ???? ? ???? ?? ? + ?? ??1 ?? ?? ? ?2?? ?? ?? ???? ? 2 3 ???? ? ?? ???? ? ???? ?? ???? ?? ? ?? ??2 ?? ?? 2 ?? ?\textbf{(9)}\par
Where,?? ?? , ?? ??1 , ?? ??2 , ???? ?? are constant. The values used in simulation are 0.09, 1.44, 1.92 and 1.0 respectively. And water density and viscosity used are 995.325 ??ð??"ð??" ?? ? and 7.9 × 10 ?4 ???? ?? 2  ? respectively. Boundary condition for simulating water flow in bends are listed below, 1. At velocity inlet u=w=0;v=0.625 m?s 2. At pressure outlet p(gage)=0; 3. At wall no-slip condition.\par
Navier-Stokes equations for viscous, incompressible flow shows mixed elliptic-parabolic behavior. So, semi-implicit method for pressure linked equation (SIMPLE) \hyperref[b6]{[7]}, \hyperref[b11]{[12]}, \hyperref[b12]{[13]}  The susceptible reasons for the error in experimental data are described briefly below (a) The pipes used for the experiment may have variable roughness and cross-sectional area. This may have caused error. (b) Basically, the channels to fit the pipes were made by curving the wooden structure and these channels were not smooth enough to ensure precise data readings. (c) Traditional Multiple-lever weighting system (bucket platform) was used for measuring water mass. This method has very poor accuracy. (d) Priming of manometer was one of the major concerns. As inaccurate priming leads to erroneous pressure drop reading. It is a difficult task. Every time the pipe was changed, manometer had to be primed. It was very time consuming. Even after all the efforts, may be priming was not accurate to its desired level. (e) Despite all the effort, experimental setup wasn't leak proof. This introduced additional pressure in the system. And in this type of experimental thesis work a small pressure variation can induce a large discrepancy from standard value. (f) The water flow was controlled by a Gate valve, incorporated with the main water supply line of the laboratory. It is not quite accurate method for flow control. Moreover, while the data was taken from Bend Radius = 120mm, the flow was fluctuating. This induced large error which can be clearly seen from the large difference between experimental and simulation data. (g) Pipes were flexible. When bend was formed with them, there cross-sectional area got distorted slightly, from uniform circular section to elliptical section. This also caused variable cross-sectional area in the bend. (h) As CCl4 has low density, it showed large deflection due to small pressure variation. In the setup Manometer scale has limited range. This forced to limit the flow rate to narrow range, as manometric deflection increased with flow rate. (i) Experiment was done with limited number of pipe, bend radius and bend angle.  
\section[{a) Experimental Results}]{a) Experimental Results}\par
The experimental data has some inevitable errors which affects the result in a little degree. These errors can be classified into two types b) Graph Analysis i. Minor Loss Co-efficient Vs. Reynolds Number   
\section[{VI. Conclusion}]{VI. Conclusion}\par
This section concludes the study of the minor losses in locally available flexible pipes of diam eter 5.2mm, 7.2mm and 8.3mm for bend angle of 300, 600,900,1200,1500,1800 and bend radius 12cm and 8cm. ? Minor loss coefficient in general shows a decreasing trend with respect to Reynolds number for a given angle and pipe diameter. ? For a given Pipe Diameter and Bend Radius increase in bending angle increases Minor loss coefficient. ? For a given Bend angle Minor loss coefficient increases with the ratio of Pipe Diameter and Bend Radius until it reaches a maximum value, then it decreases.\par
VII. Scope for Future Works Some guideline for future work is as follows,\par
1. The thesis work center on the minor losses occurred in locally available flexible pipes. Therefore it will be beneficial to determine total head loss, both minor and frictional loss, developed in a piping system using flexible pipes and finally required power of the piping system. 2. The simulation was done using SIMPLE solution method, other solution method can be employed to see whether more accurate results are obtained or not. \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
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\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_3}}\end{figure}
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\noindent\textbf{3}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure 3 :}\end{figure}
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\noindent\textbf{45}\includegraphics[]{image-7.png}
\caption{\label{fig_5}?Figure 4 :Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.6237726098191214\textwidth}P{0.025258397932816534\textwidth}P{0.10213178294573644\textwidth}P{0.09883720930232558\textwidth}}
= 0\tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{3}{l}{The under-relaxation Constant and Spatial}\tabcellsep \\
\multicolumn{3}{l}{Discretization Method are as follows,}\tabcellsep \\
Parameter Pressure\tabcellsep Under-relaxation 0.3\tabcellsep Spatial Discretization Method Second Order\tabcellsep Year 2016\\
Momentum\tabcellsep 0.7\tabcellsep Second Order Upwind\tabcellsep 29\\
\multicolumn{3}{l}{Turbulent Kinetic Energy Turbulent Dissipation Rate Equation 0.8 0.8 continuity x \& y -momentum z-momentum, kinetic energy, dissipation Second Order Upwind Second Order Upwind Residual 0.0001 0.00001 rate 0.001 IV. Results The values of Minor Loss Co-efficient are tabulated for different Pipe Diameter, Bend Radii and Bend Angles. Both data from experiment and simulation are mentioned below. And the Stopping Criterion for different equation are given below,}\tabcellsep Global Journal of Researches in Engineering A ( ) Volume XVI Issue IV Version I\\
\tabcellsep \tabcellsep © 2016 Global Journals Inc. (US)\tabcellsep \end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.10986394557823129\textwidth}P{0.04336734693877551\textwidth}P{0.09829931972789116\textwidth}P{0.11853741496598638\textwidth}P{0.09829931972789116\textwidth}P{0.20816326530612245\textwidth}P{0.08673469387755102\textwidth}P{0.08673469387755102\textwidth}}
\multicolumn{2}{l}{No. Bend RadiD (mm)}\tabcellsep Pipe Dia. d (mm)\tabcellsep Ratio ?? ??\tabcellsep 30 0\tabcellsep \multicolumn{3}{l}{Minor Loss Co-efficient k 60 0 120 0 180 0}\\
1\tabcellsep 80\tabcellsep 5.2\tabcellsep 0.065\tabcellsep 7.494\tabcellsep 4.568\tabcellsep 12.38\tabcellsep 20.01\\
2\tabcellsep 80\tabcellsep 7.2\tabcellsep 0.090\tabcellsep 5.221\tabcellsep 2.830\tabcellsep 6.066\tabcellsep 10.68\\
3\tabcellsep 80\tabcellsep 8.3\tabcellsep 0.104\tabcellsep 4.465\tabcellsep 2.128\tabcellsep 5.240\tabcellsep 11.69\\
4\tabcellsep 120\tabcellsep 5.2\tabcellsep 0.043\tabcellsep 1.156\tabcellsep 1.696\tabcellsep 2.718\tabcellsep 3.734\\
5\tabcellsep 120\tabcellsep 7.2\tabcellsep 0.060\tabcellsep 0.773\tabcellsep 1.127\tabcellsep 1.827\tabcellsep 2.532\\
6\tabcellsep 120\tabcellsep 8.3\tabcellsep 0.069\tabcellsep 0.654\tabcellsep 0.963\tabcellsep 1.531\tabcellsep 2.123\\
\multicolumn{2}{l}{V. Discussion}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
  {\small\itshape [Note: a) Error Analysis? Error in experimental procedure ? Error due to inaccuracy of measuring Devices]} 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.85\textwidth}}
Year 2016\\
A\\
All the graphs, both\\
experimental and simulation, presented in this paper\\
are best fitted curve, based on quadratic regression.\\
(j) For simulation temperature variation is not\\
considered, as it complicated matter immensely\\
with only a little change in result. Besides, during\\
our experimentation temperature remained nearly\\
constant.\end{longtable} \par
 
\caption{\label{tab_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_3}}\end{figure}
 			\footnote{© 2016 Global Journals Inc. (US)} 		 		\backmatter  			 			 			  				\begin{bibitemlist}{1}
\bibitem[Streeter and Wylie]{b0}\label{b0} 	 		\textit{},  		 			V L Streeter 		,  		 			E Benjamin Wylie 		.  	 	 		Fluid Mechanics. First SI Metric Edition  		McGraw-Hill Book Co.  	 
\bibitem[Md et al.]{b2}\label{b2} 	 		\textit{},  		 			Md 		,  		 			A K Islam 		,  		 			Islam 		.  		 		 			Fluid Mechanics Laboratory Practice, World University Service Press 		 	 
\bibitem[Ahmed et al. (2011)]{b9}\label{b9} 	 		\textit{An Experimental Study of Loss Characteristics of Polypropylene Random (PPR) Pipes Pipe Elbows},  		 			Isfak Ahmed 		,  		 			Pranay Chakraborty 		,  		 			Md Fattah 		.  		February-2011. BUET.  	 
\bibitem[Jaiman et al.]{b4}\label{b4} 	 		\textit{CFD Modeling of Corrugated Flexible Pipe},  		 			R K Jaiman 		,  		 			O H OakleyJr 		,  		 			J D Adkins 		.  		p. .  	 
\bibitem[Md et al. (2011)]{b8}\label{b8} 	 		\textit{Determination of friction Factor of Flow through Flexible Pipes and Minor Loss Coefficient of Flexible Bends},  		 			Rokonuzzaman Md 		,  		 			Saad Khan 		,  		 			A S M Ahmed 		,  		 			Jonayat 		.  		February-2011.  		 			BUET 		 	 
\bibitem[Md et al. (2009)]{b7}\label{b7} 	 		\textit{Determination of Minor head Loss and Friction Factor for locally Available PVC pipe Reducers},  		 			Md 		,  		 			A K Hafizur Rahman 		,  		 			Roy 		,  		 			. S Md 		,  		 			Hossain 		.  		September-2009.  	 
\bibitem[Khan and Islam (1979)]{b3}\label{b3} 	 		 			M H Khan 		,  		 			Md Islam 		.  	 	 		\textit{An Experimental Investigation of Flow Through Flexible Pipes and Bends},  				 (Bangladesh, Vol7)  		July,1979.  	 
\bibitem[Modi and Seth ()]{b1}\label{b1} 	 		 			P N Modi 		,  		 			S M Seth 		.  		\textit{Hydraulic and Fluid Mechanics Including Hydraulic Machines},  				 (Standard Book House)  		2002.  	 	 (Fourteenth edition) 
\bibitem[Date ()]{b6}\label{b6} 	 		‘Prediction of Fully developed Flow in a Tube Containing a Twisted Tape’.  		 			A W Date 		.  	 	 		\textit{Int. J. Heat Mass Transfer}  		1974. Pergamon Press. 17 p. .  	 
\bibitem[Ayub and Al-Fahed (1993)]{b5}\label{b5} 	 		‘The effect of gap width between horizontal tube and twisted tape on the pressure drop in turbulent water flow’.  		 			Z H Ayub 		,  		 			S F Al-Fahed 		.  	 	 		\textit{Int. J. Heat and Fluid Flow}  		March 1993. 14  (1) .  	 
\bibitem[Jones and Launder ()]{b11}\label{b11} 	 		‘The prediction of laminarization with a two-equation model of turbulence’.  		 			W P Jones 		,  		 			B E Launder 		.  	 	 		\textit{Int. J. Heat Mass Transfer}  		1972. 15.  	 
\bibitem[Harlow and Nakayama ()]{b12}\label{b12} 	 		‘Transport of turbulence energy decay rate’.  		 			F H Harlow 		,  		 			P I Nakayama 		.  	 	 		\textit{Los Alamos Scientific Laboratory Report LA}  		1968. 3854.  	 
\bibitem[White ()]{b10}\label{b10} 	 		 			F M White 		.  		\textit{Fluid Mechanics},  				 (New York)  		2003. McGraw-Hill.  	 	 (5th ed.) 
\end{bibitemlist}
 			 		 	 
\end{document}
