Download SGBAU (Sant Gadge Baba Amravati university) B-Tech/BE (Bachelor of Technology) 8th Sem Chemical Engineering System Modelling Previous Question Paper
11676 : System Modelling : 8 CH 03
1" Page? 4 tmnmmummm ?'34?
Time : Three Hours . o a 1 3 . Max. Marks : 80
Notes : 1. A11 question carry marks as indicated. ,
2. Answer three question from Section A and three question from Section B.
3. Due credit will be given to neatness and adequate dimensions.
4. Assume suitable data wherever necessary.
5. Diagrams and chemical equations should be given wherever necessary.
6. Illustrate your answer necessary with the help of neat sketches.
7. Use of cell phone is not allowed in the exam-
8. Use of pen Blue/Black ink/refill only for writing the answer book.
SECTION - A
1 a) What do you mean by modelling of process/ system? Explain brie?y with suitable 6
examples the mathematical modelling and physical modelling.
b) When is the system at steady state? Explain with example. 3
c) Distinguish between deterministic models and probabilistic models. 5
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.Water enters at volumetric ?ow rate F0 into a cylindrical tank with cross sectional area A.
out ?ow rate Fl of water from the tank depends upon the height of liquid as shown in figure.
It is given by the equation F] = Kx/E
F0
?1
h
F. = NE
a) List the dependent variables, independent variables and constant parameters of the 3
system.
b) What ?mdamental law would you use to model the above process. 2
c) Derive the mathematical model for the process. 5
d) What type of model is it? Why? I 2
0) Is it possible to obtain the steady state model from the model you derived. If yes, 2
how? ?
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A tank contains 20 m5 of hater. A stream of brine containing 2 kg/m3 of salt is fed into a
tank at a rate of 0.05 m-?xmin. Liquid ?ows from the tank at a rate of 0.033 m3/min. 1f tank
is well agitated, what is the concentration of salt in the tank when the tank contains 30 m3
uf brine?
OR
Water containing 15 gm of pollutant! litre ?ows through a treatment tank at the rate ot?2
m3/min. In the tank the treatment removes 2% of pollutant per minute and water is
thoroughly stirred. The tank holds 40 m3 of water. 0n the day the treatment plant opens, the
tank is ?lled with pure water. Determine the concentration pro?le of the tank ef?uent.
Consider the following elementary reaction in series.
K K .e
A ? ?-'?> B ?l?> L
is taking place in isothermal CS?I'R. A feed containing A and B at concentration C A0 and
C B.) respectively. enters into the tank at volumetric ?ow rate F0 Product stream leaves the
tan]; at volumetric ?ow rate F, (F0 at F] ) Assume constant density. List the various variables
and constant parameters involved in the system. Model the system.
??
PO~CAC ?CHQ
V\(.ASCU9CC ?>
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'l'hree CSTR are connected in series as shown ?gure. Reaction A a B is taking place in
each reactor. Each reactor is maintained at different constant temperatures and rate constant
in each reactor is K1,K: and K3. Volume ofcach reactor is V1,V2 and V3 respectively. A
reat?tant A is fed to the ?rst reactor at concentration C An and volumetric ?ow rate F0
product is withdrawn from the last reactor at volumetric ?ow rate F3 . Assume constant
volume of each reaction and constant temperature in each reactor. Also assume constant
density of ?uid. Derive the mathematical model of the system.
FO?CAO
V '2~CA2 - VS?CA3 ?>
F1 F2 F3
SECTION - B
A supply of hot air is obtained by drawing cool air through a heated cylindrical pipe. The
pipe is 0.1 m in diameter and 1.2 m long and is maintained at temperature of Tw = 300? C
throughout its length. The average values of properties ol?air are as follows: heat capacity
C9 = 1005 J/kg ?C Thermal conductivity, K = 0.037 W/m2 ?C, density, p = 0.809kg/m3
Flow rate, u=8x10"3m3 t?sec. Inlet temperature = 21? C and overall heat transfer
k)
13
13
l3
l4
10.
coef?cient h = 52.3x(?1"2)W/ m2 ?C , where x is distance measured in meters from pipe
inlet. Assuming heat transfer takes place by conduction with in the gas in the axial direction
by mass ?ow of gas and by above mentioned variable heat transfer coef?cient from the
walls of tube. develop the mathematical model for temperature distribution in the axial
direction in the form of differential equations for steady state conditibns.
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GN+1 kgmole/ sec of wet gas containing YN+1 mole of solute 1 kg mole of wct gas is fed
into base of plate absorption column where the solute is to be stripped from the gas by
absorption in L0 kg mole/sec uflcan oil which is fed at top of column. The solute in entering
oil is X0 kg mole/kg. mole of lean oil and the solute in exit gas is Y, kg. mole/ kgmole of
wet gas. The equilibrium constant Km is given as Km = Ym /Xm, where Ym and Xm are
mole fraction of solute in gas and liquid phases respectively. So that performance of the
absorber can be expressed in terms of the absorption factor
A = (L0 / K GN+1) and number of ideal stages (N) by Kremser - Brown Equation:-
YN+1 ?\(I _ AN? ?A
YN+1?Y0 AN??I ?1
The temperature distribution across a large concrete 50 cm thick slab heated from one side,
as measured by thermocouples, approximates to the following relation:
?1?: 60? 50x + 12x2 + 20x3 +15x4 where, T is in ?C and x is in metres. considering an
area of 5 m2. compute the following:-
a) A heat entering and leaving slab in unit time.
b) The heat energy stored unit time.
c) The rate of temperature change at both sides of slab.
d) The point at which rate ofcooling or heating is maximum.
Take the following data for concrete:
Thermal conductivity, K = 1.2 w/m ?C
Thermal diffusivity a = 1.77 x10?3 in2 /sec
OR
Mode] the system for the heat loss through pipe ?anges as shown in diagram below. 'l'wo
thin wall metal pipes of 2.5 cm external diameter and joined by ?anges 1.25 cm thick and
10 cm diameter are carrying steam at 120? C. If the conductivity of the ?ange metal K =
400 W/m ?C and the exposed surfaces of the ?anges lose heat to the surroundings at
T1 = 15?C according to a heat transfer coef?cient h = 12 W/m2 ?C determine the rate of heat
loss from the pipe and the proportion which leaves the rim of the ?ange.
?6':
Pipe Flange
14
13
13
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11.
12.
The relationship bcmccn shear stress I and shear rate ' y ' for pseudoplastic ?uid can be 13
cxprcsscd by equation
I = 117" Following data are collected for certain pscudoplastic ?uid.
Using the method of least squares estimates the values of parameters uand n.
T(N rml) [ 5.99 7.45 8.56 9.15 11.30
y(lr? s) , 55 75 100 120 140
?1
1
I
OR
A11 investigator reponed the data tabulated below. If is known that such a data can be 13
modelled by following equation:-
x = 43?h)!? where a and b are constant parameters Linearize this equation and employ
linear regression to determine a and b. Based on your analysis predict y at x = 2.9.
{11?1719 4 5 1? 6
L3_i_0.6 1 1.9 3.1_ __?.8 5.2 1 7.9
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This post was last modified on 10 February 2020