7/21/2019 es1840_exam.pdf

1/6

ES1840

THE UNIVERSITY OF WARWICK

First Year Examinations : Summer 2014

MECHANICS, STRUCTURES AND THERMODYNAMICS

Candidates should answer the TWO COMPULSORY QUESTIONS.

The TWO compulsory questions are each worth 50% of the available marks.

Time Allowed : 3 hours.

Only calculators that conform to the list of models approved by the School of Engineering

may be used in this examination. The Engineering Databook, Thermodynamic tables and

standard graph paper will be provided. Thermodynamic Equation sheets are appended to the

end of this examination paper.

Read carefully the instructions on the answer book and make sure that the particulars required are

entered on each answer book.

USE A SEPARATE ANSWER BOOK FOR EACH SECTION

7/21/2019 es1840_exam.pdf

2/6

ES1840

Question 1 Continued Overleaf ....

1

_________________________________________________________________________________________

SECTION A: MECHANICS

_________________________________________________________________________________________

1. Answer all parts. Note that numerical solutions lacking units are incomplete. You may use the

approximation for the gravitational acceleration at the Earths surface, g = 10 m s -2.

(a) Figure 1.a shows a plane pin-jointed frame supported by a pin-joint at A and a roller

joint at E. Angles between the members are always either 45 or 90. Lengths AF, CF

and EF are all 2 m. It is subjected to horizontal forces of 40 kN at C and D and a vertical

force of 50 kN at F, as shown.

(i) Determine the reaction forces at A and E. (6 marks)

(ii) Find the forces in members DE, DF and EF, stating explicitly whether they are in

tension or compression (8 marks)

(b) An astronaut training system uses a rocket-propelled sled that moves along a straight,

horizontal track. When the rocket is fired, it generates a constant 40 kN thrust until the

fuel runs out after 8 s. The fully laden sled has mass 800 kg of which 75% is fuel.

Assuming that the sled is at rest when the rocket first fires, write down an expression for

its mass as a function of time and hence estimate its speed after 6 s. (7 marks)

2 m

50 kN

A

B

C

D

EF

40 kN

40 kN

Figure 1.a

7/21/2019 es1840_exam.pdf

3/6

ES1840

Question 1 Continued Overleaf

2

Question 1 Continued

(c) A flywheel having a second moment of mass of 5 kg m 2 is rotating at 40 rad s -1.

Consider each of the following situations starting from this condition.

(i) At some instant, a steady braking torque of 40 N m is applied. What is the speed

of the flywheel after it has completed two full revolutions from then? (3 marks)

(ii) At time t = 0 s a spring applies an acceleration to the flywheel, initially at 6 rad s -2

and reducing at constant rate to zero at t = 2 s. How far has the wheel rotated at

t = 1.0 s? (7 marks)

(d) Figure 1.b shows a beam of length L. The point load P is acting at the mid-length of the

beam.

(i) Provide the equations of equilibrium and calculate the unknown reactions.

(4 marks)

(ii) Derive the equations and draw the diagrams of the internal shear force and

bending moment. (6 marks)

Fig. 1.b

(e) Figure 1.c shows a beam of length L. A triangular distributed load is acting along the

length of the beam and has a maximum intensity w. Derive the equations and draw thediagrams of the internal shear force and bending moment. (9 marks)

P

L

7/21/2019 es1840_exam.pdf

4/6

ES1840

Continued.

3

Question 1 Continued

Fig. 1.c

(Total 50 marks)

________________________________________________________________________________

w

L

7/21/2019 es1840_exam.pdf

5/6

ES1840

Question 2 Continued Overleaf.

4

_________________________________________________________________________________________

SECTION B: THERMODYNAMICS

_________________________________________________________________________________________

2 Answer all seven parts (2(a), 2(b) 2(g) inclusive). Marks will be deducted for incorrect or

missing units and for incorrect signs.

(a) Helium is contained by a piston and cylinder. Its initial pressure is 4 bar gauge, initial

temperature is 100 C and initial volume is 0.5 m 3. It is compressed reversibly to half its

initial volume, during which process its temperature is kept constant.

(i) What is the final pressure? (2 marks)

(ii) What is the work done by the helium on the piston? (4 marks)

(iii) What is its mass? (2 marks)

(iv) What is the heat input? (2 marks)

[You may assume that R = 2077 J kg -1 K -1 and c p = 5195 J kg -1 K -1 for helium]

(b) A refrigerator has a COP of 2.5 and consumes 0.5 kW of mechanical power. What is the

cooling power and power of the rejected heat? (3 marks)

(c) Steam enters an adiabatic nozzle at a speed of 20 m s -1, a temperature of 600 C and

pressure of 10 bar absolute. It exits at 400 C and 1 bar absolute.

(i) What is the exit speed? . (5 marks)

(ii) Show that the process is irreversible. (4 marks)

(d) Air enters a reversible adiabatic turbine at 8 bar absolute and 400 C, and expands it to 2

bar absolute. The flow rate is 3 kg s -1.

(i) What is the outlet temperature? (4 marks)

(ii) What is the work output per kg air? (2 marks)

7/21/2019 es1840_exam.pdf

6/6

ES1840

5

Question 2 Continued

(iii) What is the mechanical power output? (2 marks)

For air, c p = 1.005 kJ kg -1 K -1 and = 1.4.

(e) A reversible cyclic device takes in 500 J of heat from a source at 250 K, 300 J of heat

from a source at 400 K and exchanges heat with a thermal reservoir at 200K. It also has

an input or output of mechanical work

(i) Use the second law to calculate the quantity of heat exchanged at 200K (4 marks)

(ii) Use the first law to calculate the work input or output. (3 marks)

(f) Helium has a molecular weight of 4 and the ratio of its specific heats ( ) is 5/3. Given

that the universal gas constant is 8.315 kJ kg -1 K -1 calculate both the specific heat at

constant volume and the specific heat at constant pressure. (5 marks)

(g) A stream of oil, (0.01 kg s -1 , c p = 2.1 kJ kg-1 K -1 ), is to be cooled from 120 C to 80 C

by a stream of water (0.02 kg s -1 , c p = 4.18 kJ kg-1 K -1) entering an in-line counterflow

heat exchanger at 50 C. The heat exchanger overall U-value is 200 Wm-2

K -1

.

(i) What is the heat transfer rate? (2 marks)

(ii) What is the water outlet temperature? (2 marks)

(iii) What is the required heat exchanger area? (4 marks)

_________________________________________________________________________________________

END