COMPUTER APPLICATION IN CHEMICAL ENGINEERING JNTU UNIVERSITY PREVIOUS YEAR QUESTION PAPER COLLECTION final year second semester chemical engineering students

IV B.Tech II Semester Regular Examinations, Apr/May 2007

COMPUTER APPLICATION IN CHEMICAL ENGINEERING

(Chemical Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

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1. Apply Runge-Kutta third order method to find an approximate value of y when x
=0.2 in steps of 0.1, given that dy/dx = x+y2 and y = 1 when x = 0. [16]
2. Solve by Cramer’s rule, the equations:2x1+5x2+3x3 = 1,-x1+2x2+x3=2,x1+x3+x2=
0. [16]
3. Find the solution to the set of equations shown below. 2x1 − 3x2 − 3x3 + 6x − 4 =
15; 4x1+2x2+3x−3−4x4 = 10; 5x1+6x2+x3−12x−4 = 5; 3x1−x2+2x3+2x4 = 13
using Gauss Elimination method. [16]
4. (a) Solve the equation e−x - x = 0 by Newton-Raphson method.
(b) How does one choose the initial guess value of the root? [12+4]
5. An elementary liquid phase reaction A + B ! R+S is conducted in a multiple
reactor system in which 100liters capacity CSTR is used as the first unit and a
PFR is used as the second unit. Find the intermediate conversion between the
both the units using iterative method. Data: Initial molar ratio of B to A, M
=2, Reaction rate constant (k) =0.2 lit/gmol.min, CA0=0.5 gmol/lit and v0=93.3
lit/min. [16]
6. The specific heat of the Hexane was measured at various temperatures during the
heating and given in the following table
Temp(T),K 298 350 400 450 500 550
Cp/R 16.24 18.229 20.07 21.84 23.53 25.14
If the relationship between specific heat and temperature is of the form: Cp/R=A+BT+CT2+DT3
Estimate the coefficients using polynomial regression. What is the value of specific
heat at 700K. [16]
7. (a) Explain the necessary and sufficient conditions for the extreme of an uncon-
strained function.
(b) Determine the nature of stationary point of the function f(x) = -3x5 + 10x3 -
20
[8+8]
8. (a) Compare the Fibonacci method and modified Fibonacci method by computing
the number of experiments required to get an accuracy of α 0.01.
(b) Find the effectiveness of Fibonacci method and modified Fibonacci method
when the number of experiments is 10. [8+8]
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IV B.Tech II Semester Regular Examinations, Apr/May 2007

COMPUTER APPLICATION IN CHEMICAL ENGINEERING

(Chemical Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

⋆ ⋆ ⋆ ⋆ ⋆

1. Use Runge- Kutta 4th order method to approximate y at x = 0.1 and x = 0.2 for
dy/dx = x+y with x0 = 0 and y0 =1 and h = 0.1. [16]
2. Solve the following equations using Cramer’s rule: x+y+z = 3; x+2y+3z = 4;
x+4y+9z = 6. [16]
3. Solve by Gauss elimination method x + y + z = 6.6 x - y + z = 2.2 x + 2y + 3z
= 15.2. [16]
4. (a) Find a real root of the equation X3 −2X −5 = 0 by the Regula-falsi method
correct to three decimal places.
(b) How does one choose the initial value of the root . [12+4]
5. A gaseous mixture has the following composition (in mol◦/◦)CH4= 20◦/◦, C2H4
=30◦/◦, N2= 50◦/◦. Find the molar volume at 90 atm pressure and 100◦C using
Vander Waals equation of state with averaged constants of the following type V 3-
(b’ + RT/b)V 2 + (a’/P)V - a’.b’/P =0 where a’, b’ are the average constants a’=2.3
×106 atm(cm3/gmol)2 , b’=45.0 cm3/gmol. Use the Newton Raphson method. [16]
6. A new microorganism has been discovered which at each cell division yields three
daughter cells. The growth rate data during the batch cultivation is given below
Time(t),h 0 .5 1 1.5 2.0


Dry Wt(X),g/l 0.1 0.15 0.23 0.34 0.51
Fit the above data using least square regression in the exponential growth model
x=a.ebt where a and b are constants. [16]
7. (a) Describe the Newton-Raphson method of finding the extrema of an uncon-
strained single variable function.
(b) Minimize f(Q) = 4 Q + 16/Q using Newton Raphson method. Start with the
first estimate at Q = 1. [8+8]
8. (a) Compare the Fibonacci method and modified Fibonacci method by computing
the number of experiments required to get an accuracy of α ≤ 0.01.
(b) Find the effectiveness of Fibonacci method and modified Fibonacci method
when the number of experiments is 10. [8+8]
⋆ ⋆ ⋆ ⋆ ⋆

IV B.Tech II Semester Regular Examinations, Apr/May 2007

COMPUTER APPLICATION IN CHEMICAL ENGINEERING

(Chemical Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

⋆ ⋆ ⋆ ⋆ ⋆

1. Using Euler’s method, find an approximate value of y corresponding to x = 1, given
that dy/dx = x + y and y = 1 when x = 0. [16]
2. In a given electrical network, the equations for the currents i1, i2, i3 are 3i1+i2+i3=
8; 2i1 −3i2 −2i3 = -5; 7i1 +2i2 −5i3 = 0. Calculate i1 and i3 by Cramers rule.[16]
3. Develop a step-by-step computational procedure to solve the following equation by
Gauss elimination method x + 4y - z = -5; x + y - 6z = -12; 3x - y - z = 4. [16]
4. (a) Find the roots of X2
− 25 = 0 numerically using Regula-falsi method.
(b) Write the computational procedure to evaluate the roots of the equation.
[10+6]
5. For the reaction CO2 (g) + 4H2(g) ! 2H2O(g) + CH4(g) the standard heat of
reaction can be expressed as H0
T = H’ + αT + ( β/2)T2 + ( γ/3)T3 ; H’=-
148345 j; α=-62.54; β=46.3510−3 ; γ= −7.21 × 10−6 . Find the relevant
temperature at which standard heat of reaction is equal to -183950j using iterative
method. [16]
6. The specific heat of the Hexane was measured at various temperatures during the
heating and given in the following table
Temp(T),K 298 350 400 450 500 550
Cp/R 16.24 18.229 20.07 21.84 23.53 25.14
If the relationship between specific heat and temperature is of the form: Cp/R=A+BT+CT2+DT3
Estimate the coefficients using polynomial regression. What is the value of specific
heat at 700K. [16]
7. (a) Illustrate the importance of optimization techniques in chemical engineering
giving at least four examples.
(b) Given the function f(x) = 80/x + 20x + 20, find the stationary points and
test them for maxima or minima. [8+8]
8. Find the effectiveness of preplanned regular interval method, sequential two point
regular interval method, sequential dichotomous search and preplanned dichoto-
mous search when the number of experiments is 20. [16]
⋆ ⋆ ⋆ ⋆ ⋆

IV B.Tech II Semester Regular Examinations, Apr/May 2007

COMPUTER APPLICATION IN CHEMICAL ENGINEERING

(Chemical Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

⋆ ⋆ ⋆ ⋆ ⋆

1. Using Euler’s method, find an approximate value of y corresponding to x = 1, given
that dy/dx = x + y and y = 1 when x = 0. [16]
2. Solve by Cramer’s rule, the equations:2x1+5x2+3x3 = 1,-x1+2x2+x3=2,x1+x3+x2=
0. [16]
3. Find the solution to the set of equations shown below. 2x1 − 3x2 − 3x3 + 6x − 4 =
15; 4x1+2x2+3x−3−4x4 = 10; 5x1+6x2+x3−12x−4 = 5; 3x1−x2+2x3+2x4 = 13
using Gauss Elimination method. [16]
4. (a) Solve the equation X2 − 25 = 0 numerically using Newton-Raphson method.
(b) Write the computational procedure to evaluate the roots of the equation .
[10+6]
5. Calculate the molar volume of methanol vapor at 400 K and 8 bar by using Redlich-
Kwong equation of stateV = [RT/P + b − a(V − b)/{T0.5.PV(V + b)}] Where a=0.4278R2
Tc2.5 /Pc; b= 0.0867RTc/Pc ;Tc=512.6 K; Pc =81 bar. Use the regular falsi method.
[16]
6. A zero order liquid phase reaction A!R is conducted in a constant volume batch
reactor and the following data were reported. Fit the data in the zero order rate
equation using least square regression technique and find the rate constant(k).
Data: Initial reactant concentration CA0=2gmol/lit, -rA=-dCA/dt=k. [16]
Time(t),min 0 0.25 0.5 0.75 1.0 1.25 1.50
Conversion(X) 0 0.11 0.19 0.31 0.39 0.51 0.60
7. (a) Illustrate the importance of optimization techniques in chemical engineering
giving at least four examples.
(b) Given the function f(x) = 80/x + 20x + 20, find the stationary points and
test them for maxima or minima. [8+8]
8. Minimize y = (2x − 9)2
0 < x < 10 for 6 Fibonacci experiments. [16]
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