Effect of Polymer Solutions on Efflux Time for Two Exit Pipe System

Transcription

1 Effect of Polyer Solutions on Efflux Tie for Two Exit Pipe Syste Abstract: A. UMA DEVI a, D.V. PADMA a & CH. V. SUBBARAO a a Departent of Cheical Engineering, MVGR College of Engineering, Vizianagara , Andhra Pradesh, India. E-ail address: subbaraochv@rediffail.co Experients are perfored for assessing the efflux tie when water soluble polyer solutions are added to a open cylindrical tank drained by two exit pipes (The flow in each of the pipes is assued to be turbulent). The polyer used is polyacrylaide (PAM). Experients are perfored for four different concentrations of polyer solutions and optiu concentration of polyer is found. A generalized correlation for friction factor is developed. Keywords: Efflux tie, Newtonian liquid, open storage tank, iniu tie Noenclature: A p A Area of each pipe, t Area of tank, D Diaeter of tank, d Diaeter of each exit pipe, f Friction factor, diensionless GV 1 & GV Gate Valves H Initial height of liquid in the tank at t0, ' H Final height of liquid in the tank on draining, L Length of the exit pipe, LI Level indicator V exp xperiental average velocity, /sec ρ Density of liquid, kg/ 3 μ θ Viscosity of liquid, kg/.sec Diensionless tie 1. Introduction: Processing and storage vessels in the cheical and related industries appear in a large variety of shapes. The tie required to drain these vessels off their liquid contents is known as efflux tie [1] and this is of crucial iportance in any eergency situations besides productivity considerations. This is of considerable interest in a variety of industries like cheical, food and pharaceutical []. Matheatical analysis and experiental work of gravity draining of a Newtonian liquid fro a storage tank through restricted orifice of different diaeters were reported by Jouse [3]. It was shown that the acceleration of free surface of a liquid is less than the acceleration due to gravity. Vandogen and Roche. Jr [4] carried out efflux tie analysis fro tanks with exit pipes and fittings in the Reynolds nuber range of 40,000-60,000 in the exit pipe. The effect of pipes and fittings were expressed in ters of equivalent lengths. ISSN : X Vol. 1 No. 1 Septeber-Noveber

2 Using coputational tools, Morrison [5] carried out efflux tie analysis through an exit pipe at around a Reynolds nuber of 6,000. The axiu efflux tie reported was only 35 seconds. The ratio of tank cross section to pipe cross section was only 8. This was uch less than the ratio subbarao et al [6]. Subbarao et al [6] carried out efflux tie analysis of draining a Newtonian liquid fro a cylindrical tank through a single exit pipe based on acroscopic balances. The efflux tie equation was siplified and written as ( H + L H L ) t ' g acceleration due to gravity g by eff +, where g is odified for of acceleration due to gravity and related to g 1, f is the friction factor, L and d are length and diaeter of the exit g L A 1 + t 4 f d Ap 3 pipe, A t and Ap is the cross sectional area of tank and pipe respectively. They used an exit pipe of 4X10 dia. Subbarao and other researchers [7] developed equation for efflux tie for two exit pipe syste for the case of turbulent flow in the exit pipe. They also studied the effect of polyer additions on drag reduction and discussed the saturation liit of Froude nuber. However, the authors failed to develop a generalized correlation for efflux tie. The present study is carried out to develop a generalized correlation for friction factor in the absence and presence of polyer solutions.. Experiental Procedure: Part A: Fig. 1: Cylindrical tank with two-exit pipes The Apparatus used for experientation consisted of a stainless steel cylindrical tank of known diaeter (Fig.1) provided with a level indicator (LI) and two ild steel pipes each of 4X10-3 I.D welded to the tank. One pipe is located at the centre of the botto of the tank and the other at c away fro the centre. Two gate valves (GV 1 & GV ) provided at the botto ost point served as the outlet for draining as shown in figure-1. Both the ISSN : X Vol. 1 No. 1 Septeber-Noveber

3 valves are closed and the tank is filled up to the ark and allowed to stabilize. The stopwatch is started iediately after the opening of the botto gate valves. The drop in water level is read fro the level indicator. The tie is recorded for a known drop in the liquid level. The easureents are continued till the water level reaches to a desired value just 0.0 above the tank botto. The experiental efflux tie is designated ast act. The experients are repeated to check the consistency of data Part B: Experients are also perfored for with four pre-ixed polyacrylaide (PAM) solutions of four different concentrations of 10, 5,.5 and 1 pp. The stock solution is prepared by dissolving 1.6X10-3 kgs of PAM in 0.4 liters of water. A sall quantity of isoproponal is added to serve as disinfectant. The solution is stirred for 4 hours and allowed to hydrate for 4 hours. The clear solution without any non hoogeneity is diluted suitably to prepared 10, 5,.5 and 1 pp solution. Since all the solutions are dilute, their density and viscosity are assued to be equal to that of water [7]. The pre-ixed solutions are added to the cylindrical tank and exit pipe syste and efflux ties are obtained in the anner described above in part-a. The list of variables covered are in the present study is copiled in table-1. Table 1: List of variables covered with two-exit pipe syste. S. No D, L, H, , 0.18, 0.16, , 0.8, 0.4, , 0.40, 0.3, Results and discussion Santosh kuar et al [8] used the following efflux tie equation for coparing the theoretical efflux tie with experiental values. H At θ * 1+ 1 L Ap L d (1) The above equation is derived by using the following friction factor equation as reported by Bird et al [9] Re f () The equation suggests that the plot of H At 1+ 1 L Ap vs t eff is a straight line. The equation even though suggests that coplete draining is possible, it is observed during experientation that coplete draining can t be achieved. Hence the equation is odified as H H ' θ * L L At A p L d The authors reported an average deviation of 16% in efflux tie in the absence of polyer solutions. ISSN : X Vol. 1 No. 1 Septeber-Noveber 011 3

4 This sae equation ( Eq.1) is used for coparing the efflux tie values in presence of different concentrations of polyer solutions as well. 7 H 3 / H ' The plot of L L fig,,3,4 &5 respectively. vs t eff for 10, 5,.5 and 1 pp polyer concentrations is shown in Fig.: Efflux tie coparison of two exit pipe syste for 10pp polyer solution D0.7 and L0.75 An average deviation of 4% is found between experiental and theoretical values. Fig.3: Efflux tie coparison of two exit pipe syste for 5 pp polyer solution D0.7 and L0.75 An average deviation of 6% is found between theoretical and experiental values. ISSN : X Vol. 1 No. 1 Septeber-Noveber

5 Fig.4: Efflux tie coparison of two exit pipe syste for.5 pp polyer solution D0.7 and L0.75 An average deviation of 9% is found between theoretical and experiental values. Fig.5: Efflux tie coparison of two exit pipe syste for 1 pp polyer solution D0.7 and L0.75 An average deviation of 13% is found between theoretical and experiental values. The trend is observed to be siilar for other tank diaeters of pipes for the polyer concentratinos considered. It can be concluded that the plots are well in agreeent with experiental efflux tie. Hence, Eq. is considered as generalized equation for friction factor for two exit pipe syste. The validity of the equation ( Eq.) is further verified for 0.3 & 0.34 dia. tanks for the concentratinos of polyer solutinos entioned above and found to be satisfactory. Since there are two exit pipes, the Reynolds nuber in each pipe is odified as: Re dv expρ. 3 μ ISSN : X Vol. 1 No. 1 Septeber-Noveber

6 V exp ( H H ') πd 4 πd t act Since the fluid is water, its density and viscosity are assued to be 1000 kg/ 3 and 1x10-3 kg/.sec cp respectively. The flow in each of the pipes is calculated using eq.3 and found to be turbulent only. A plot of polyer concentrations vs actual efflux tie for draining the liquid fro a given initial height of liquid in the tank is shown in Fig.6 Fig.6: Polyer concentration vs efflux tie for D0.7 and L0.75 H0.. Fro the figure, It can be concluded that optiu concentration of polyer is 10pp. The trend is observed to be siilar for other initial heights of liquid in the tank and diaeters of storage vessels. Conclusions 1. The friction factor equation reported by Bird et al can be considered as generalized friction factor equation for calculating the efflux tie for the polyer solutinos considered.. The optiu concentration of polyer is found to be 10pp. Acknowledgeents The authors gratefully acknowledges the Principal, Dr K.V.L.Raju and the Manageent of MVGR College of Engineering Vizianagara for providing the necessary infrastructural facilities for carrying out experients. The authors also would like to thank Prof Ch.Durgaprasada Rao, Retd. Professor of Cheical Engineering, IIT, Chennai, India and Prof C.Bhaskara Sara, Professor of Cheical Engineering, Gayatri Vidyaparishad College of Engineering, Visakhapatna, India for their useful discussions. REFERENCES 1. Hart, W. Peter and Soerfeld T, Expression for gravity drainage of annular and Toroidal containers, Process Safety Progress, 1995, pp Soerfeld, J.T and Stallybrass, M.P Elliptical integral solutions for drainage of horizontal cylindrical vessels with piping friction, Industrial Eng. Che.Res, 199, pp Jouse Njock Libii, Mechanics of slow draining of a large tank under gravity, Aerican Journal of Physics, 003, pp David B.Vondogen Edawrd c.roche, Jr., Efflux tie fro tanks with exit pipes and fittings, International journal of Engg. Ed, 1999, pp Ken R.Morrison, Modeling and coputation techniques for fluid echanics experients, International journal of Engg. Ed, 001, pp Subbarao Ch.V, King.P and Prasad, V.S.R.K, Effect of polyer additions on the echanics of slow draining of large tank under gravity, ARPN journal of Engineering and applied sciences, 008, pp ISSN : X Vol. 1 No. 1 Septeber-Noveber

7 7. Subbarao Ch.V, King.P and Prasad, V.S.R.K, Effect of polyer additives on the Dynaics of a Fluid for once through syste, International Journal of Fluid Mechanics Research, 008, pp G.Santosh kuar, Ch.V.Subbarao and P.King Efflux tie for two exit pipe syste, subitted to International journal of applied science and Engineering-in press. 9. R.Byron Bird, Warren E.Stewart and Edwin N. Lightfoot, Transport Phenoena, nd edition, John Wiley & sons (Asia) Pvt.Ltd., 005. ISSN : X Vol. 1 No. 1 Septeber-Noveber