The document appears to be a set of exam questions for a Chemical Engineering course involving numerical methods and optimization techniques. It includes 8 questions related to topics like: 1) Using methods like Runge-Kutta, Cramer's rule, and Gauss elimination to solve systems of differential/algebraic equations. 2) Finding roots of equations numerically using methods like Regula-falsi and Newton-Raphson. 3) Modeling using techniques like polynomial regression and exponential growth models. 4) Describing optimization techniques like Newton-Raphson for finding extrema and comparing search methods.

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Code No: RR420803
Set No. 1
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. Apply Runge-Kutta third order metho d to nd 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. 2 1 - 3 2 - 3 3 + 6 - 4 =
15; 4 1+2 2+3 -3 -4 4 = 10; 5 1+6 2 + 3-12 -4 = 5; 3 1- 2+2 3 +2 4 = 13
using Gauss Elimination metho d. [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 rst 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 0=93.3
lit/min. [16]
6. The speci c 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 speci c heat and temperature is of the form: Cp/R=A+BT+C 2+D 3
Estimate the coe cients using polynomial regression. What is the value of speci c
heat at 700K. [16]
7. (a) Explain the necessary and su cient conditions for the extreme of an uncon-
strained function.
(b) Determine the nature of stationary point of the function f(x) = -3 5 + 10 3 -
20
[8+8]
8. (a) Compare the Fibonacci method and mo di ed Fibonacci method by computing
the number of experiments required to get an accuracy of = 0.01.
(b) Find the e ectiveness of Fibonacci method and modi ed Fibonacci metho d

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Code No: RR420803
Set No. 1

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Code No: RR420803
Set No. 2
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 ro ot of the equation 3 2 5 = 0 by the Regula-falsi metho d
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 / 2 4
=30 / , 2= 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 3-
(b’ + RT/b) 2 + (a’/P)V - a’.b’/P =0 where a’, b’ are the average constants a’=2.3
106 atm( 3 )2 , b’=45.0 3/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 nding the extrema of an uncon-
strained single variable function.
(b) Minimize f(Q) = 4 Q + 16/Q using Newton Raphson method. Start with the
rst estimate at Q = 1. [8+8]
8. (a) Compare the Fibonacci method and mo di ed Fibonacci method by computing
the number of experiments required to get an accuracy of 0.01.
(b) Find the e ectiveness of Fibonacci method and modi ed Fibonacci metho d
when the number of experiments is 10. [8+8]

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Code No: RR420803
Set No. 3
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, nd 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 3 1 + 2 + 3=
8; 2 1 - 3 2 - 2 3 = -5; 7 1 + 2 2 - 5 3 = 0. Calculate 1 and 3 by Cramers rule.[16]
3. Develop a step-by-step computational pro cedure 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 2 - 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 2 (g) + 4 2( ) 2 2 ( ) + 4( ) the standard heat of
reaction can be expressed as 0 T = H’ + T + ( /2) 2 + ( /3) 3 ; H’=-
148345 j; =-62.54; =46.3510-3 ; = -7 21 × 10-6 . Find the relevant
temperature at which standard heat of reaction is equal to -183950j using iterative
method. [16]
6. The speci c 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 speci c heat and temperature is of the form: Cp/R=A+BT+C 2+D 3
Estimate the coe cients using polynomial regression. What is the value of speci c
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, nd the stationary points and
test them for maxima or minima. [8+8]
8. Find the e ectiveness 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]

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Code No: RR420803
Set No. 4
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, nd 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. 2 1 - 3 2 - 3 3 + 6 - 4 =
15; 4 1+2 2+3 -3 -4 4 = 10; 5 1+6 2 + 3-12 -4 = 5; 3 1- 2+2 3 +2 4 = 13
using Gauss Elimination metho d. [16]
4. (a) Solve the equation 2 - 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=0.4278 2
Tc2.5 / c; b= 0.0867R c/ c ; c=512.6 K; c =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 nd the rate constant(k).
Data: Initial reactant concentration CA0=2gmol/lit, - A=-d A/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, nd the stationary points and
test them for maxima or minima. [8+8]
8. Minimize y = (2 - 9)2
0 x 10 for 6 Fibonacci experiments. [16]