Faculty of Engineering ENGG952 Engineering Computing This paper is for students studying at: X Wollongong Batemans Bay Bega Loftus Moss Vale Shoalhaven Sydney Distance

SAMPLE of FINAL EXAMINATION - This is only sample paper, the 2009 questions will be TOTALLY different

- The 2009 final exam cover all lecture topics (week 1 to 13, except SIMULINK) Time Allowed: 2 hours 15 minutes Number of Questions: Four (4)

DIRECTIONS TO CANDIDATES

1. All questions are to be answered. 2. The questions are of EQUAL value.

3. Examination paper is printed on both sides. 4. Start each question on a new page.

EXAMINATION MATERIALS/AIDS ALLOWED - Calculators - One two-sided A4 page of notes

Family Name ....................................................... First Name ....................................................... Student Number ....................................................... Table Number .......................................................

THIS EXAMINATION PAPER MUST NOT BE REMOVED FROM THE EXAMINATION ROOM

ENGG952 Engineering Computing Spring Session 2007

2

Question 1 (25 marks) Suppose you are designing a spherical tank, as shown in Figure 1, to hold water for a small village. The volume of liquid it can hold can be computed as

3)3(2 2 hRhV −

= π

where V = volume [m3], h = depth of water in tank [m], and R = the tank radius [m].

Figure 1 Schematic of a spherical tank system. If R = 3 m, to what depth must the tank be filled so that it holds 30 m3.

(a) Use three iterations of the Bisection method to determine your answer ( Rhh ul == ,0 ).

(11 marks) (b) Compute the approximate relative error after each iteration (if existing). (4 marks) (c) Write a MATLAB script M-file, by making use of the Newton-Ralphson method, to solve

this problem ( %,1=sε and 22 hRhdhdV ππ −= ). (10 marks)

Question 2 (25 marks) A double integral, as given below, has an analytical value of 2.67.

∫ ∫−+−

1

1

2

0

322 )2( dydxxyyx

Evaluate the above double integral numerically using :

(a) The composite trapezoidal rule with n = 2, or 1=Δ=Δ yx . (9 marks) (b) The Simpon’s 1/3 rule with n = 2, or 1=Δ=Δ yx . (12 marks) (c) For (a) and (b), compute the true percent relative error. (4 marks)

ENGG952 Engineering Computing Spring Session 2007

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Question 3 (25 marks) The ordinary differential equation boundary-value problem y′′ = -5 y′ – 4 y + x 0 ≤ x ≤ 1 is subject to the boundary conditions: y(0) = 0 and y(1) – 0.5 y′ (1) = 0.5. Using the Linear Finite-Difference method with step size, h = 0.25:

(a) Obtain the system of linear equations. (15 marks) (b) Calculate the unknown nodal values. (10 marks)

Question 4 (25 marks) The steady-state distribution of concentration (c) for the tank shown in Figure 2 is governed by the PDE

0yx 2

2

2

2

=−⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂ ccc 1.05.0

If the tank is subject to the boundary conditions shown in the figure:

Figure 2 Schematic of the concentration field in the tank.

(a) Derive the difference equation of the PDE. (5 marks) (b) Obtain the system of linear equations. (15 marks)

(c) If c1=2.317, c4=14.85 ,c5=1.10 ,c6=3.59 and c7=4.22 , determine the c values at nodes 2

and 3. (5 marks)