GUJARAT TECHNOLOGICAL UNIVERSITY
SEMESTER-IV(NEW) - EXAMINATION - SUMMER 2019
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Subject Code:2142305
Subject Name: Applied Mathematics in Plastic Industry
Time:02:30 PM TO 05:00 PM
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks
- Do not write anything on the question paper except seat no
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Q.1
(a) Define, 1) Newtonian Fluid, 2) Bingham plastic, 3) viscoelastic fluid [03]
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(b) Write a short note on Residence and Relaxation Times [04]
(c) Which are the different Mathematical Models available for Viscoelastic Behavior? Explain any one in detail. [07]
Q.2
(a) Describe Fourier number and temperature gradient [03]
(b) State and explain Power law. [04]
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(c) Explain the Rheological model for polymer melt flow [07]
OR
(c) Explain Enthalpy calculations for Injection moulding [07]
Q.3
(a) Write a short note on thermal conductivity on Plastics. [03]
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(b) Explain the radius of gyration of linear ideal chain [04]
(c) Explain the radius of gyration of an ideal branched polymer( kramers theorem) [07]
OR
Q3 (a) Derive the equation for Temperature Rise in Die, ?T = ?% where ? is the density of the fluid and Cp is its specific heat. [04]
(b) Explain Heat Transfer Phenomena in Plastic'Processing. [07]
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(c) Write a short note on radius of gyration of rod polymer. [03]
Q.4
(a) Write a short note on strength of composites for Fiber reinforced materials. [03]
(b) Write a short note on Creep. [04]
(c) Describe Mathematical Models of Visco-elastic Behavior through Maxwell model. [07]
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OR
Q.4
(a) Discuss the Stress Strain behaviour of plastic materials. [03]
(b) Write a short note on Isometric and Isochronous graphs with neat sketch. [04]
(c) Explain Kelvin Voigt Model. [07]
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Q.5
(a) Define Drag flow, Pressure flow and Leakage flows. [03]
(b) 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]
Date:25/05/2019
Total Marks: 70
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Q5
(a) Nylon Extruder Die [03]
Viscosity =420 Ns/m2 | Diameter = 30 mm Length =4 mm
Density (solid) = 1140 | Length = 750 mm Diameter = 5 mm
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kg/m3
Density (melt) = 790 | Screw flight angle =
kg/m3 17.7"
Metering channel depth =2.5mm
(b) A nylon extruder is to be used to produce a rod of 5 mm diameter at a production rate of 1.5 m/min. Using the following information, calculate the required screw speed. [04]
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(c) Die swelling effects may be ignored and the melt viscosity can be assumed to be constant. [07]
OR
(c) Discuss the analysis of Blow moulding operation, [07]
A polyethylene injection moulding is in the form of a flat sheet 100 mm square and 3 mm thick. If the melt temperature is 230°, the mould temperature is 30° and the plastics may be ejected at a centre line temperature of 90° estimate
a) The temperature of the material at the centre of the moulding after 7 seconds.
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b) The time taken for the centre of the moulding to reach the ejection temperature of 90°
Take temperature gradient (.58 and fourier number 0.59 & a= 1x 1077 M/,
A blow moulding die has an outside diameter of 30 mm and an inside diameter of 27 mm. The parison is inflated with a pressure of 0.4 MN/m?2 to produce a plastic bottle of diameter 50 mm. If the extrusion rate used causes a thickness swelling ratio of 2, estimate the wall thickness of the bottle. Comment on the suitability of the production conditions if melt fracture occurs at a stress of 6 MN/m2
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