Gujarat Technological UniversitySummer 2026 examination

GTU 3140510 Numerical Methods in Chemical Engineering Summer 2026 Question Paper & PDF

B.E. · Chemical Engineering · Semester 4 · Subject code 3140510
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 10:30 AM – 1:00 PM
Questions
5 with internal choice
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Q.1

14 Marks
(a)
3 marks
Differentiate between accuracy and precision with appropriate examples.
(b)
4 marks
Explain diagonal dominant condition and its importance in convergence of Gauss-sidel method.
(c)
7 marks
A chemical reaction A→B takes place in a CSTR. The following model describes the
system:
where, =1, =0.25, =1 and =0.25. Report obtained after fourth iteration of Secant method. Consider =0
and =1 as two initial guesses for Secant method

Q.2

14 Marks
(a)
3 marks
Explain about the system of ill-conditioned equations using appropriate example
(b)
4 marks

Define Following Terms

1Accuracy Numbers
2Inherent Errors
3Absolute, Relative and Percentage Errors
4Truncation Errors
(c)
7 marks

Amount of dissolved oxygen in a lake gives an estimate of its health. The saturation concentration of dissolved oxygen in freshwater can be calculated using: In the above equation, T is the temperature in Kelvins and is the saturation oxygen concentration. The typical saturation concentrations ranges from 14.621 mg/L at 273 K to 6.413 mg/L at 313 K. Using bisection method, find temperature of fresh water that gives = 8 mg/L

(c)
7 marks

Solve the following system of equations using Gauss elimination method. ,

Q.3

14 Marks
(a)
3 marks
Write significance of least square method
(b)
4 marks
Write an algorithm for false position method.
(c)
7 marks

Consider the following example of linear equations in four variables Please write the equations in the form Ax=b, and calculate the values of four variables using Gauss-Jordan method.

(a)
3 marks

Find a real root of the equation up to one decimal places using Newton- Raphson method. Take

(b)
4 marks

Find the root of the equation using the regula-falsi (false position) method up to two iterations.

(c)
7 marks

The relationship between stress ‘τ’ and the strain ‘γ’ for a pseudoplastic fluid can be expressed by the following equation: The following data come from a 0.5% hydroxethylcellulose in water solution. Using linear least square method, Estimate the parameters ‘μ’ and ‘n’. 50 70 90 110 130 6.01 7.48 8.59 9.19 10.21

Q.4

14 Marks
(a)
3 marks
Describe application of Newton’s divided difference formula.
(b)
4 marks

Apply Lagrange's interpolation formula to find the value of y when x=10, if the following values of x and y are given. x 5 6 9 11 y 12 13 14 16

(c)
7 marks

Find by Taylor’s series method, the values of y at x = 0.1 and x = 0.2 to five places of decimals from , y (0) = 1.

(a)
3 marks

Round off the number 75462 to four significant digits and then calculate the absolute error and percentage error.

(b)
4 marks
Using the modified Euler’s method, find given
(c)
7 marks
Consider the following data obtained from experiments:

x 1.0 1.1 1.2 1.3 1.4 1.5 y 2.0 2.3 2.6 2.95 3.34 3.76 The linear model is of the form: Obtain parameters and using method of group averages.

Q.5

14 Marks
(a)
3 marks
List out the methods used to solve ODEs using numerical method and also write its limitation.
(b)
4 marks

Given that evaluate Using any one method. x 4.0 4.2 4.4 4.6 4.8 5.0 5.2 log x 1.3863 1.4351 1.4816 1.5261 1.5686 1.6094 1.6487

(c)
7 marks

The following table gives the value of density (d) of a saturated water for various temperature (T) of saturated stream. Temp(T),˚C 100 150 200 250 300 Density(d),kg/m³ 958 917 586 799 712 Use Newton’s forward interpolation formula to find the density when the temperature is 270˚C.

(a)
3 marks
Write the significance of Newton Rapson/Secant method.
(b)
4 marks
Using Newton’s divided difference formula find f(8) from given table:

x 4 5 7 10 11 13 F(x) 48 100 294 900 1210 2028

(c)
7 marks

Using Runge-Kutta method of order 4, solve with initial condition y (0) = 1 , For x = 0.1, 0.2.

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Official Gujarat Technological University (GTU) examination paper for Numerical Methods in Chemical Engineering (Summer 2026, B.E. · Chemical Engineering, Sem 4). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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