GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University
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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- III (New) EXAMINATION — WINTER 2019
Subject Code: 3132306 Date: 26/11/2019
Subject Name: Applied mathematics in Plastic Industry
Time: 02:30 PM TO 05:00 PM Total Marks: 70
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Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
| Marks | |
|---|---|
| Q.1 (a) Define i)Stress ii)Strain iii)Creep | 03 |
| (b) Explain the Hooke’s model along with stress-strain and elongation-time plots. | 04 |
| (c) Determine the expressions of the creep, relaxation and recovery for the Maxwell mathematical model. | 07 |
| Q.2 (a) Explain the viscoelastic behavior of plastics. | 03 |
| (b) Write a short note on the Ram extruder. | 04 |
| (c) Explain the Maxwell & Voigt models for visco-elasticity along with their stress-strain and elongation-time plots. | 07 |
| OR | |
| (c) Determine the expressions of the creep, relaxation and recovery for the Kelvin or Voigt mathematical model. | 07 |
| Q.3 (a) Explain the General behaviour of polymer melts. | 03 |
| (b) Explain the Newton’s model along with stress-strain and elongation-time plots. | 04 |
| (c) Explain the deformation behavior of Polymeric Materials. | 07 |
| OR | |
| Q.3 (a) Discuss briefly the isometric & isochronous graph | 03 |
| (b) Explain the creep curve in detail. | 04 |
| (c) A ball-point pen made from polypropylene has the clip design shown in Fig. 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 | 07 |
| Q.4 (a) 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 10° N/m? . | 03 |
| (b) Explain the types of fibre reinforcement in composites. | 04 |
| (c) Discuss about the experimental methods used to obtain flow data and explain the cone and plate viscometer. | 07 |
| OR | |
| Q.4 (a) Explain the Melt Fracture flow defect. | 03 |
| (b) Discuss about the short term testing of plastics. | 04 |
| (c) Explain the analysis of heat transfer during polymer processing and state the equations of Fourier number and Temperature Gradient. | 07 |
| Q.5 (a) Discuss the Sharkskin flow defect. | 03 |
| (b) Explain briefly the Pseudo elastic design methods of plastics. | 04 |
| (c) PEEK is to be reinforced with 30% by volume of unidirectional carbon fibres and the properties of the individual materials are given below. Calculate the density, modulus and strength of the composite in the fiber direction. | 07 |
| Material | Density (kg/m3) | Tensile Strength (GN/m2) | Modulus (GN/m2) |
|---|---|---|---|
| PEEK | 1300 | 0.058 | 3.8 |
| Carbon | 1800 | 2.1 | 400 |
| OR | |
| Q.5 (a) Discuss about concentric cylinder viscometer. | 03 |
| (b) Explain the analysis of longitudinal properties for continuous fibre composites. | 04 |
| (c) The constants for a four- parameter model are E=5x107 N/m2, M = 5x 1010 N.s/m2, E3 = 104 N/m2 and 3 = 5x109 N.s/m2 For creep and creep recovery experiments calculate: a. The instantaneous elastic strain b. The recoverable retarded elastic strain c. The permanent set | 07 |
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