Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 4th Sem New 2142305 Applied Mathematics In Plastic Industry Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2142305 Date:12/12/2018
Subject Name:Applied Mathematics in Plastic Industry
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
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
example.
04
(c) Explain the mathematical model using Maxwell model for
Viscoelastic behavior.
07
Q.2 (a) Discuss short term test methods for Plastics. 03
(b) Write a note on: Swelling ratios due to Shear Stresses. 04
(c)
Explain cone and plate viscometer to obtain flow data on polymer melts.
07
OR
(c) 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
o
42' and the pressure varies linearly over the screw length of 1000
mm from zero at entry to 20 MN/m
2
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
2
07
Q.3 (a) Discuss forms of Fiber reinforcement in composites. 03
(b) With neat diagram explain Ram extruder to obtain flow data on
polymer melt.
04
(c)
Explain: Iso thermal flow in channels: Non Newtonian fluids -flow of
power law fluid along a channel of uniform circular cross-section.
07
OR
Q.3 (a) The output of polythene from an extruder is 30 x10
-6
m
3
/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
5
N/m
2
03
(b) Draw the creep curve and explain its various stages. 04
(c)
Explain concentric cylinder viscometer to obtain flow data on polymer
melts.
07
Q.4 (a)
Draw graphs for Hooke model, Newton Model and Voigt model
showing Elongation ?Time and Stress-strain behaviour.
03
(b) The density of a composite made from unidirectional glass fibers in
an epoxy matrix is 1950 kg/m
3
. If the densities of the glass and epoxy
are known to be 2540 kg/m
3
and 1300 kg/m
3
, calculate the weight
fraction of fibers in the composite
04
(c)
Discuss Residence Time and Relaxation Time.
07
www.FirstRanker.com www.FirstRanker.com
www.FirstRanker.com
FirstRanker.com - FirstRanker's Choice
www.FirstRanker.com
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2142305 Date:12/12/2018
Subject Name:Applied Mathematics in Plastic Industry
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
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
example.
04
(c) Explain the mathematical model using Maxwell model for
Viscoelastic behavior.
07
Q.2 (a) Discuss short term test methods for Plastics. 03
(b) Write a note on: Swelling ratios due to Shear Stresses. 04
(c)
Explain cone and plate viscometer to obtain flow data on polymer melts.
07
OR
(c) 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
o
42' and the pressure varies linearly over the screw length of 1000
mm from zero at entry to 20 MN/m
2
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
2
07
Q.3 (a) Discuss forms of Fiber reinforcement in composites. 03
(b) With neat diagram explain Ram extruder to obtain flow data on
polymer melt.
04
(c)
Explain: Iso thermal flow in channels: Non Newtonian fluids -flow of
power law fluid along a channel of uniform circular cross-section.
07
OR
Q.3 (a) The output of polythene from an extruder is 30 x10
-6
m
3
/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
5
N/m
2
03
(b) Draw the creep curve and explain its various stages. 04
(c)
Explain concentric cylinder viscometer to obtain flow data on polymer
melts.
07
Q.4 (a)
Draw graphs for Hooke model, Newton Model and Voigt model
showing Elongation ?Time and Stress-strain behaviour.
03
(b) The density of a composite made from unidirectional glass fibers in
an epoxy matrix is 1950 kg/m
3
. If the densities of the glass and epoxy
are known to be 2540 kg/m
3
and 1300 kg/m
3
, calculate the weight
fraction of fibers in the composite
04
(c)
Discuss Residence Time and Relaxation Time.
07
www.FirstRanker.com www.FirstRanker.com
www.FirstRanker.com
www.FirstRanker.com
2
OR
Q.4 (a) Discuss about Melt fracture and Sharksin flow defects in polymer
melt.
03
(b) Write a short note on strength of composites for Fiber reinforced
materials.
04
(c) Explain the analysis of heat transfer during polymer processing. 07
Q.5 (a) Define drag flow, pressure flow, leakage flow 03
(b)
Applying the Carreau model to PP, the following constants are known
at 190?C. ? 0=2250 Ns/m
2
, A T=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
(c) Explain the analysis of continuous fiber composite having the
longitudinal properties.
07
OR
Q.5 (a) PEEK is to be reinforced with 20% 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.
Material Density
(kg/cm
3
)
Tensile Strength
(GN/m
2
)
Modulus
(GN/m
2
)
PEEK 1300 0.058 3.8
Carbon Fiber 1800 2.1 400
03
(b) Derive Rheological models for Polymer melt flow. 04
(c) Explain the radius of gyration of an ideal branched polymer using
Kramers Theorem.
07
************
www.FirstRanker.com www.FirstRanker.com
www.FirstRanker.com
FirstRanker.com - FirstRanker's Choice
This post was last modified on 20 February 2020