UNIVERSITY OF BOLTON WESTERN INTERNATIONAL · PDF fileTHERMOFLUIDS AND CONTROL SYSTEMS MODULE NO: ... Formula Sheet . Page 2 of 14 Western International College, Ras Al Khaimah B.Eng(Hons)

OCD46

UNIVERSITY OF BOLTON

WESTERN INTERNATIONAL COLLEGE,

OFF CAMPUS DIVISION

B.ENG (HONS) MECHANICAL ENGINEERING

SEMESTER TWO EXAMINATION 2014/2015

THERMOFLUIDS AND CONTROL SYSTEMS

MODULE NO: AME5003

Date: Tuesday 09 June 2015 Time: 10:00 – 1:00 INSTRUCTIONS TO CANDIDATES: There are SIX questions on this

paper Answer ANY two questions from

PART A and ANY two questions from PART B

Marks for parts of questions are

shown in brackets. CANDIDATES REQUIRE : Property Tables Formula Sheet

Page 2 of 14

Western International College, Ras Al Khaimah B.Eng(Hons) Mechanical Engineering Semester 2 Examination 2014/2015 Thermofluids and Control Systems Module No. AME5003

PART A

Q1

a) Derive from Bernoulli’s theorem expressions for the theoretical velocity and

discharge through an orificemeter.

(15 marks)

b) The flow of oil of specific gravity 0.8 is measured using a horizontal venturimeter

having an inlet diameter of 20cm and throat diameter of 10cm.The discharge of

oil through the venturimeter is noted as 60litres/s. Determine the reading of the

oil-mercury differential manometer. Take cd =0.98

(5 marks)

c) A pitot–tube is inserted in a pipe of 250mm diameter. The static pressure in pipe

is 80mm of mercury (vacuum).The stagnation pressure at the centre of the pipe

recorded by the pitot-tube is 0.987N/cm2.If the mean velocity of flow is 0.8 times

the central velocity, determine the rate of flow of water through the pipe. Take cv

as 0.98.

(5 marks)

Total 25 marks

Q2

a) A pipe line carrying oil of specific gravity 0.85, changes in diameter from 250mm

diameter at first position A to 550mm diameter at second position B which is 4.5

metres at a higher level. If the pressures at A and B are 10.56N/cm2 and

6.86N/cm2 respectively and if the discharge is 250litres/s, determine the

following:

i. Loss of head

(7 marks)

ii. Direction of flow

(3 marks)

Q2 continued over the page…

Page 3 of 14


Q2 continued...

b) In a 45o bend a rectangular air duct of 1.5m2 cross-sectional area is gradually

reduced to 0.8m2 area as shown if FigureQ2(b) .If the velocity of flow at the

1.5m2 section is 12m/s and the pressure is 3.672N/cm2,determine the magnitude

and direction of the force required to hold the duct in position. Take density of air

as 1.16kg/m3.

FigureQ2(b)

(15 marks)

Total 25 marks

Q3

a) A piston cylinder arrangement contains 2kg of wet steam at 1.3 bar pressure and

1.963m3 initial volume. The piston is free to move up or down unless it reaches

the stops at the top. The steam is heated until the temperature reaches 4000C;

the piston is up against the stops and the volume becomes 3.098m3. Using

steam table make calculations for the amount of work and heat interactions.

(10marks)


Page 4 of 14


Q3 contd.

b) One kg of air at 2bar and 400K is compressed adiabatically till its pressure

becomes 5times the original pressure. Subsequently it is expanded at constant

pressure and finally cooled at constant volume to return to its original state.

Determine the following :

i. Sketch the process on P-V plot

(3marks)

ii. work done for each process and for the cycle

(4marks)

iii. heat interaction for each process and for the cycle

(4marks)

iv. Change in internal energy for each process and for the cycle

(4marks)

For Air take Cp=1.005kJ/kgK and Cv =0.718kJ/kgK

Total 25 marks

Please turn the page

Page 5 of 14


PART B

Q4. For the spring damper and mass system shown in figure Q4 (a), where

M1 = 1 Kg, K1 = 2 N/m, B1 = 4 Ns/m

M2 = 2 Kg, K2 = 1 N/m, B2 = 2 Ns/m

K3 = 3N/m.

Figure Q4. (a) Spring damper mass system

(a) Develop the differential equations for the system. (4 marks)

(b) Determine the Laplace transforms of the differential equations obtained

from Q4 (a) above

(4 marks) (c) Determine the transfer function G(s) = X1(s)/F(s), Assume that the

system is subjected to a unit step input and the initial conditions of the

system are zeros (i.e. at time = 0, x, x’, x’’ are all zeros).

(8 marks)


B1

K1

X1

K3

M2

M1

X2

F(t)

K2

B2

Page 6 of 14


Q4 continued…

(d) A thermal system used for heating flow of water is shown in figure Q4.d. An

electric heating element is provided in the storage tank to heat the flow of

water. The storage tank is insulated from surrounding atmosphere to reduce

heat loss.

Given : inlet water temperature as ɵi

outlet water temperature as ɵ0.

thermal resistance of the insulation as R (0C/Joule/sec).

energy input to the system as q (Joule/sec)

surrounding air temperature as ɵ.

Derive the mathematical model for the given thermal water heating system.

(9 marks)

Total 25 marks

Please turn the page

Page 7 of 14


Q5. (a). The forward path transfer function of a unity feedback control system is

given by

Obtain an expression for unit step response of the system. (6 marks)

(b). Determine the following for the system given in Figure Q5.(b) i) The characteristic equation for the system

(2 marks)

ii) Natural frequency of oscillation (ωn)

(1 mark)

iii) Damping Ratio ()

(1 mark)

iv) Damped frequency of oscillation (ωd)

(1 mark)

v) Rise time ( tr)

(1mark)

vi) Peak time ( tp)

(1 mark)

vii) Maximum Overshoot ( Mp)

(1 mark)

viii) Settling Time ( ts)

(1 mark)

Figure Q5. (b)


Page 8 of 14


Q5 continued… (c). A robot has an open loop transfer function for its angular position of

The input of the system is a ramp input changing at the rate 10 degrees and K has the values 1, 10,100.

i). Analyse the steady state errors for different K values when it is an open loop system.

(3 marks)

ii). Analyse the steady state errors for different K values when it is an closed loop system.

(3 marks) iii).Comment on the significance of increasing the value of K.

(4 marks) Total 25 marks Q6.

(a). Large welding robots are widely used in automobile assembly lines. The welding

head is moved to different positions on the automobile bode, and rapid accurate

response is required. The characteristic equation for the welding system is

s4 + 6s3 + 11s2 + 6s + 0.6K = 0

Using Routh-Hurwitz stability criterion determine the range of values of K

for the system which will result in stability.

(8 marks)

Q6 continued over the page...

Page 9 of 14


Q6 continued…

(b). Analyse the stability of control systems based on location of roots of

characteristic equation in S plane.

(8 marks)

(c). Reduce the following block diagram shown in Figure Q6.(c) and determine

the system transfer function.

Figure Q6. (c)

(9 marks)

Total 25 marks

END OF QUESTIONS

Page 10 of 14


FORMULA SHEET ρ water = 1000Kg/m3

R= 287 J/ Kg K P = F/A ρ = m/V m. = ρAV P = Pg + Patm P = ρgh

Q= A v Q=V/t

Q=

v= Cv

.ΔMΔt

ΔMF

Fx = ρQ( v1x –v2x) + (p1A1)x + (p2A2)x

Fy = ρQ( v1y –v2y) + (p1A1)y + (p2A2)y

FR = Q = W+ΔU + ΔPE + ΔKE Q=mC ΔT PV=mRT Cp – Cv =R

Page 11 of 14


H=U+PV

W = PdV P Vn = C W = P (v2 – v1)

V

V PV = W

1

2ln

1 -n

V P - V P =W 2211

h = hf + x hfg s = sf + x sfg

Page 12 of 14


Page 13 of 14


FORMULA SHEET: Control Systems Laplace Transforms A unit impulse function 1

A unit step function s

1

A unit ramp function 2

1

s

Block Diagram Reduction Blocks with feedback loop

G(s) = )()(1

)(

sHsGo

sGo

(for a negative feedback)

G(s) = )()(1

)(

sHsGo

sGo

(for a positive feedback)

Blocks G1(S) & G2(s) in series G(s) = G1(S) *G2(s) Blocks G1(S) & G2(s) in parallel G(s) = G1(S) +G2(s) Steady-State Error (Open Loop)

)]()1([lim 00

sGse is

ss

Steady-State Error (Closed Loop)

)]()(1

1[lim

0s

sGse i

os

ss

Page 14 of 14


Time Response for second-order systems

d = n (21( )

ᶲ = tan-1(

)1( 2 )

tr = ( - ᶲ)/d

tp = /d

n

4= ts

%100))1(

(exp = Mp.2

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UNIVERSITY OF BOLTON WESTERN INTERNATIONAL · PDF fileTHERMOFLUIDS AND CONTROL SYSTEMS MODULE NO: ... Formula Sheet . Page 2 of 14 Western International College, Ras Al Khaimah B.Eng(Hons)