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2003 Course Advanced Polymer Rheology

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Total No. of Questions : 12] [Total No. of Pages : 3 [3664] - 300 P 1375 B.E. (Polymer) ADVANCED POLYMER RHEOLOGY (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) All questions from Section I & II are compulsory. 2) Marks given on R.H.S. 3) Use of calculator allowed. 4) If any data is missing, assume any suitable data. SECTION - I Q1) a) b) c) d) Give egs. by which the normal stress generated in polymers can be understood. [4] Explain either continuity or Cauchys equation. [6] Give the shear rate & shear stress formulas for flow through circular, slit & annular c/s. [3] Give the velocity profile for Turbulent as well as laminar flow & explain the reason for their flat or parabolic profile. [5] OR Q2) a) b) c) Q3) a) b) Explain Navier stokes equation & its significance. [6] Explain how tensors are useful to understand Rheology. Also explain in [8] short with eg. stress tensors and strain tensors. Give classification of fluids and what are the parameters which are used [4] to study these fluids. What is meant by Reynolds number and what is its significance. Derive the equation giving relation between Zmax and Reynolds no. [8] Give equation for Ellis model and explain all the terms in its equation. [8] OR Q4) a) For a flow described by Ellis model, w = 20 N/m2. Calculate the velocity at the centre for the flow through a 10 mm diameter tube, zero shear viscosity and 1 2 value. = 1.707, 0 = 2.89 m2/NS & 1 = 0.28 m2/NS. [4] P.T.O. b) c) Q5) a) b) Explain the transition between laminar and turbulent flow given by Ryan & Johnson. [7] For an LDPE melt, value of n = 0.26. Find the critical Reynolds number and comment on the type of flow. [5] Explain the concept explained in Boltzmann superposition principle.[6] What is the role of the two elements used in Maxwell or Voigt model. For both models, explain in which condition do they satisfy the polymeric behaviour. Give all the possible combinations in which the two elements can be attached to give close behaviour like polymers, i.e. viscoelastic. [10] OR Q6) a) b) c) Give the limitations of Maxwell & Voigt model. Give the explanation of four element model that goes very close to the behaviour exhibited by [8] polymers. What concepts are explained by Doi-Edward theory? [4] What molecular theory was developed by Rouse for dilute solutions. Explain the meaning of Reptation. [4] SECTION - II Q7) a) b) c) What is the importance of WLF equation? [6] Derive activation energy of flow and state its relation with zero shear viscosity. Explain the method of calculation of activation energy graphically. [6] Explain the significance of flow behaviour index n . State its relation with activation energy of flow. [4] OR Q8) a) b) Q9) a) b) List various parameters affecting polymer melt viscosity. Describe the effect of MWD in details. [8] Discuss the effect of pressure on polymer melt viscosity. Also list all those parameters that have effect on melt viscosity. [8] Write down the classification of various rheometers. Explain how melt flow indexer is used to generate a rheogram. [8] Derive an expression for apparant viscosity in a cone and plate rheometer. For a Newtonian fluid with viscosity 0.15 Pa-s, find torque experienced if cone angle is 1o, angular velocity is 50 radians/min, and radius of cone as 12 cm. [8] [3664] - 300 -2- OR Q10)a) b) Derive an equation for apparent viscosity in concentric cylinders, when gap between the two cylinders is very small. [8] Derive an equation for shear stress at wall for flow through a capillary rheometer. Explain the constructional features of a capillary rheometer. [8] Q11)Attempt any 3 : [18] a) Derive an expression for minimum injection pressure necessary at the gate of a disc cavity which is centre gated. b) Derive an expression for compaction force in case of compression molding. c) Derive an expression for pressure drop for melt flow through calender rolls stating clearly the assumptions made. d) Derive an expression for flow length of power law fluid injected at constant pressure in a rectangular channel assuming non isothermal flow. OR Q12)a) b) c) Derive an expression to find the thickness of a blow molded container when die dimension are known. A blow molding die has outside diameter of 40 mm and die gap of 2 mm. It is used to produce a bottle of 70 mm diameter. If swelling ratio of melt in thickness direction is 1.8, estimate the parison dimensions, thickness of bottle and suitable inflation pressure [9] if melt fracture occurs at stress of 10 mN/m2. In a plunger type injection molding machine, the torpedo has a length of 30 mm and diameter 23 mm. If during injection, the plunger moves forward at 50 mm/s, estimate the pressure drop along the torpedo. Barrel diameter is 25 mm; & n = 0.33. [4] Calculate the pressure drop for melt flow through a quadratic section with length of side as 2.8 mm and channel length as 50 mm. Data : a = ke T . r n 1 k = 135900, n = 0.326 & = 0.00863 mass flow rate = 0.01 g/s. melt temperature = 200oC. melt density = 0.7 g/cm3. [3664] - 300 -3- [5]

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