Subject Code: 2142305
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE - SEMESTER- IV (New) EXAMINATION - WINTER 2019
Date: 16/12/2019
Subject Name: Applied Mathematics in Plastic Industry
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
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- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q.1 (a) Give detail classification of Non Newtonian fluids. [03]
(b) Derive Rheological models for Polymer melt flow. [04]
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(c) Explain cone and plate viscometer to obtain flow data on polymer melts. [07]Q.2 (a) Explain short term testing of Plastics. [03]
(b) Discuss Hooke model and Newton Model showing Elongation —Time and Stress-strain behavior. [04]
(c) Explain the mathematical model using Maxwell model for Viscoelastic behavior. [07]
OR
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Q.2 (a) Explain the radius of gyration of linear ideal chain. [07]
(b) Define drag flow, pressure flow, leakage flow. [03]
(c) Discuss Swelling ratios due to Shear Stresses for long capillary. [04]
Q.3 (a) In a particular extruder screw the channel depth is 2.4 mm, the screw diameter is 50mm, the screw speed is 100 rev/min, the flight angle is 17°42' and the pressure varies linearly over the screw length of 1000 mm from zero at entry to 20 MN/m? at the die entry. Estimate (a) the drag flow (b) the-pressure flow (c) the total flow. the plastic has a viscosity of 210Ns/m? [07]
OR
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Q.3 (b) The output of polythene from an extruder is 30 x10-6 m3/s. If the breaker plate in this extruder has 80 holes, each being 4 mm diameter and 12 mm long, estimate the pressure drop across the plate ‘assuming the material temperature is 170°C at this point. The shear stress is-1.2 x 106 N/m? [03]
(c) Draw the creep curve and-explain its various stages. [04]
Q.4 (a) With neat diagram explain Ram extruder to obtain flow data on polymer melt. [07]
(b) Which are the different forms of Fiber reinforcement in composites? Discuss. [03]
(c) Applying the Carteau model to PP, the following constants are known at 190°C. ?0=2350 Ns/m?, A1=0.05, n=0.33, Estimate the viscosity of PP at 230 °C and a shear rate of 1000 s-1 The glass transition temperature for the PP is -10 °C. [04]
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OR
Q.4 (a) Derive the expression for drag flow in detail for analysis of flow in extruder. [07]
(b) A polypropylene beam is 100 mm long, simply supported at each end and is subjected to a load W at its mid-span. If the maximum permissible strain in the material is to be 1.5%, calculate the largest load which may be applied so that the deflection of the beam does not exceed 5 mm in a service life of 1 year. For the beam I =28 mm4 and Modulus is 347 MN/m?. [03]
(c) Write a note on: Kelvin/Voigt model [04]
Q.5 (a) Explain the analysis of heat transfer during polymer processing. [07]
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Q.5 (a) The density of a composite made from unidirectional glass fibers in an epoxy matrix is 1950 kg/m3. If the densities of the glass and epoxy are known to be 2540 kg/m3 and 1300 kg/m3, calculate the weight fraction of fibers in the composite [04]
(b) Describe the analysis of continuous fiber composite having the longitudinal properties. [07]
OR
Q.5 (a) PEEK is to be reinforced with 30% by volume of unidirectional carbon fibers and the properties of the individual materials are given below. Calculate the density, modulus and strength of the composite in the fiber direction. [03]
| Material | Density (kg/cm3) | Tensile Strength (GN/m2) | Modulus (GN/m2) |
|---|---|---|---|
| PEEK | 1300 | 0.058 | 3.8 |
| Carbon Fiber | 1800 | 2.1 | 400 |
Q.5 (b) A ball-point pen made from polypropylene has the clip design shown in Figure. When the pen is inserted into a pocket, the clip is subjected to a deflection of 2 mm at point A. If the limiting strain in the material is to be 0.5% calculate (i) a suitable thickness, d, for the clip (ii) the initial stress in the clip when it is first inserted into the pocket. The short term modulus of Polypropylene is 1.6 GN/m2. [04]
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