GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-IV (NEW) EXAMINATION - WINTER 2018
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Subject Code:2142305 Date:12/12/2018Subject Name:Applied Mathematics in Plastic Industry
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
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2. Make suitable assumptions wherever necessary.3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Define: Newtonian fluid, Shear stress and Shear Strain 03
(b) Give detail classification of Non Newtonian fluids along with 04
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example.(c) Explain the mathematical model using Maxwell model for 07
Viscoelastic behavior.
Q.2 (a) Discuss short term test methods for Plastics. 03
(b) Write a note on: Swelling ratios due to Shear Stresses. 04
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(c) Explain cone and plate viscometer to obtain flow data on polymer melts. 07OR
(c) In a particular extruder screw the channel depth is 2.4 mm, the screw 07
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
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mm from zero at entry to 20 MN/m² at the die entry. Estimate (a) thedrag flow (b) the pressure flow (c) the total flow. the plastic has a
viscosity of 210Ns/m²
Q.3 (a) Discuss forms of Fiber reinforcement in composites. 03
(b) With neat diagram explain Ram extruder to obtain flow data on 04
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polymer melt.(c) Explain: Iso thermal flow in channels: Non Newtonian fluids -flow of 07
power law fluid along a channel of uniform circular cross-section.
OR
Q.3 (a) The output of polythene from an extruder is 30 x10?6 m³/s. If the 03
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breaker plate in this extruder has 80 holes, each being 4 mmdiameter 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 10³ N/m²
(b) Draw the creep curve and explain its various stages. 04
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(c) Explain concentric cylinder viscometer to obtain flow data on polymer 7melts.
Q.4 (a) Draw graphs for Hooke model, Newton Model and Voigt model 03
showing Elongation —Time and Stress-strain behaviour.
(b) The density of a composite made from unidirectional glass fibers in 04
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an epoxy matrix is 1950 kg/m³. If the densities of the glass and epoxyare known to be 2540 kg/m³ and 1300 kg/m³, calculate the weight
fraction of fibers in the composite
(c) Discuss Residence Time and Relaxation Time. 07
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Q.4 (a) Discuss about Melt fracture and Sharkskin flow defects in polymer 03
melt.
(b) Write a short note on strength of composites for Fiber reinforced 04
materials.
(c) Explain the analysis of heat transfer during polymer processing. 07
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Q.5 (a) Define drag flow, pressure flow, leakage flow 03
(b) Applying the Carreau model to PP, the following constants are known 04
at 190°C. ?0=2250 Ns/m², ?=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.
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(c) Explain the analysis of continuous fiber composite having the 07longitudinal properties.
OR
Q.5 (a) PEEK is to be reinforced with 20% by volume of unidirectional 03
carbon fibers and the properties of the individual materials are given
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below. Calculate the density, modulus and strength of the compositein the fiber direction.
| Material | Density (kg/cm³) | Tensile Strength (GN/m²) | Modulus (GN/m²) |
|---|---|---|---|
| PEEK | 1300 | 0.058 | 3.8 |
| Carbon Fiber | 1800 | 2.1 | 400 |
(b) Derive Rheological models for Polymer melt flow. 04
(c) Explain the radius of gyration of an ideal branched polymer using 07
Kramers Theorem.
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