Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 4th Sem New 2142305 Applied Mathematics In Plastic Industry Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2142305 Date: 16/12/2019
Subject Name: Applied Mathematics in Plastic Industry
Time: 10:30 AM TO 01:00 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) Give detail classification of Non Newtonian fluids. 03
(b) Derive Rheological models for Polymer melt flow. 04
(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
(c) Explain the radius of gyration of linear ideal chain.
07
Q.3 (a) Define drag flow, pressure flow, leakage flow. 03
(b) Discuss Swelling ratios due to Shear Stresses for long capillary. 04
(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
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) With neat diagram explain Ram extruder to obtain flow data on polymer melt. 07
Q.4 (a) Which are the different forms of Fiber reinforcement in composites? Discuss. 03
(b)
Applying the Carreau model to PP, the following constants are known at 190?C. ? 0=2350
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) Derive the expression for drag flow in detail for analysis of flow in extruder. 07
OR
Q.4 (a)
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 mm
4
and Modulus is 347
MN/m
2
.
03
(b) Write a note on: Kelvin/Voigt model 04
(c) Explain the analysis of heat transfer during polymer processing.
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2142305 Date: 16/12/2019
Subject Name: Applied Mathematics in Plastic Industry
Time: 10:30 AM TO 01:00 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) Give detail classification of Non Newtonian fluids. 03
(b) Derive Rheological models for Polymer melt flow. 04
(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
(c) Explain the radius of gyration of linear ideal chain.
07
Q.3 (a) Define drag flow, pressure flow, leakage flow. 03
(b) Discuss Swelling ratios due to Shear Stresses for long capillary. 04
(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
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) With neat diagram explain Ram extruder to obtain flow data on polymer melt. 07
Q.4 (a) Which are the different forms of Fiber reinforcement in composites? Discuss. 03
(b)
Applying the Carreau model to PP, the following constants are known at 190?C. ? 0=2350
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) Derive the expression for drag flow in detail for analysis of flow in extruder. 07
OR
Q.4 (a)
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 mm
4
and Modulus is 347
MN/m
2
.
03
(b) Write a note on: Kelvin/Voigt model 04
(c) Explain the analysis of heat transfer during polymer processing.
07
2
Q.5 (a) Discuss Residence Time and Relaxation Time. 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) 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.
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) 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/m
2
.
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
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This post was last modified on 20 February 2020