UNIVERSITY OF BOLTON
WESTERN INTERNATIONAL COLLEGE FZE
BENG (HONS) MECHANICAL ENGINEERING
SEMESTER ONE EXAMINATION 2016/2017
ADVANCED THERMOFLUIDS & CONTROL SYSTEM
MODULE NO: AME6005
Date: Tuesday 10 January 2017 Time: 2:00 – 4:00 INSTRUCTIONS TO CANDIDATES: There are 6 questions. Answer 4 questions. All questions carry equal marks. Attempt TWO questions from PART A
and TWO questions from PART B Marks for parts of questions are shown
in brackets. CANDIDATES REQUIRE : Thermodynamic properties of fluids
tables are provided Take density of water = 1000 kg/m3
Formula sheets provided
Page 2 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
PART A
Q1. a) The velocity distribution through a circular pipe as shown in Figure Q1a.
for laminar flow at any radius r is given by
Figure Q1a.
Prove that the momentum correction factor is
(14 marks)
b) A laminar flow is taking place in a pipe of diameter 220mm.The maximum
velocity is 2m/s.
Determine the following:
i) Mean velocity of flow (3 marks)
ii) Radius at which mean velocity occurs (4 marks)
iii) Velocity at 4cm from the wall as in FigureQ1b. (4 marks)
Figure Q1b.
Total 25 marks
Please turn the page
Page 3 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
Q2. a) Water at 25oC flows at a rate of 30 litres/s in a cast iron pipe of 35cm
diameter and 150m length. The system includes a sudden entrance
(ke= 0.5) and a gate valve (kg=0.15).Determine the head loss of the
pipe.
Given the kinematic viscosity of water at 25oC = 1 x 10-6 m2/s.
The surface roughness value for cast iron = 0.12mm.
(18 marks)
b) A shaft having a diameter of 60mm rotates centrally in a journal bearing
having a diameter of 60.25mm and length of 125mm.The angular
space between the shaft and the bearing is filled with oil having
viscosity of 0.9 poise. Determine the power absorbed in the bearing
when the speed of rotation is 700 r.p.m.
(7 marks)
Total 25 marks
Q3. (a) Steam enters an engine at a pressure of 10MPa absolute and 450oC.
It is exhausted at 1.5 bar. The steam at exhaust is 0.9 dry. Find the
following:
i) Drop in enthalpy (5 marks)
ii) Change in entropy (5 marks)
iii) Sketch the process in T-S diagram (2 marks)
Page 4 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
Please turn the page
Question 3 contd….
(b) Air at 200C and 1.05 bar occupies 0.045m3. The air is heated at
constant volume until the pressure is 4bar.Then it is cooled at constant
pressure back to original temperature. Determine the following:
i. Evaluate the work done for each process (3 marks)
ii. Evaluate the heat transfer for each process (3 marks)
iii. Evaluate the change in entropy for each process (3 marks)
iv. Represent the cycle on T-S and p-v plot. (4 marks)
Take Specific heat capacity at constant volume,Cv =0.718kJ/kgK
and gas constant,R= 287 J/kgK
Total 25 marks
Please turn the page
Page 5 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
PART B
Q4. An industrial manufacturing system using a sampled data controller is shown
in Figure Q4.
Figure Q4.
(a) Determine the sampled data transfer function for the given
system.
(8 marks)
(b) Analyse the stability of the sampled control system shown for
sampling time T=0.5 sec and T=1 sec.
(14 marks)
(c) Compare and contrast the stability for given sampling time.
(3 marks)
Total 25 marks
Please turn the page
R(s) E(s) E*(s) C(s)
T. + -
Page 6 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
Q5. A closed-loop control system is shown in Figure Q5.
Gc(s) Gp(s) +
-
Input(s) Output(s)
Figure Q5.
Given sKds
KisGc 51015)( &
62
2)(
2
sssGp
Where Kp is proportional gain, Ki is integral gain and Kd is derivative
gain.
(a) If Ki=0, Determine the value of Kd for critical damping.
(8 Marks)
(b) With Kd as determined in (a) ,determine the limiting value of Ki Such
that stability is maintained.
(8 Marks)
(c) Find the Ki for a ramp input if Gc(s) is a PI controller and the steady
state error is less than 0.01.
(9 Marks)
Total 25 marks
Please turn the page
Page 7 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
Q6. (a) Develop the state space model of a simplified industrial robotic system
shown in FigureQ6a.
FigureQ6a. (15 marks) (b) The state equations of a mechanical system are given below.
Analyse controllability and observability of the system. (10 marks)
Total 25 marks
END OF QUESTIONS
M1 M2
K1 K2
B1 B2
y1 y2
u
Page 8 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
FORMULA SHEET
P = F/A
ρ = m/v
m. = ρAV
P = Pg + Patm
P = ρ gh
Q- W = ΔU + ΔPE + ΔKE
W = PdV
P Vn = C
W = P (v2 – v1)
du/dy =
1 -n
V P - V P =W 2211
Page 9 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
V
V PV = W
1
2ln
Q = Cd A √2gh
12 21
g
ghgCV m
.ΔMΔt
ΔMF
F = ρ QV
τ = -(∂p/∂x) r/2
Re = V D ρ/
∆p = (32VL)/D2
U = 1/(4) -(∂p/∂x) (R2-r2)
dQ = du + dw
du = Cv dT
dw = pdv
pv = mRT
h = hf + xhfg
Page 10 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
s = sf + xsfg
v = x Vg
hm w - Q...
3
2
2
R
RL
LF
n
T
dQds
1
2n12 L
T
TCSS pL
2
1L n12
P
PmRSS
f
fg
pLgT
hTCS
273L n
f
pu
f
gf
pLT
TC
T
hfTCS nn L
273L
1
2n
1
2np12
P
PMRL
T
TL MCSS
Page 11 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
sCDFD
2u 2
1
suFL
2
LC 2
1
)( gZPds
dS p
L
pDQ
128
4
gD
L
Rh f
2
v64 2
Re
16f
g2d
fLv4h
2
f
g
Khm
2
v2
g
VVkhm
2
2
21
H
L
T
T1
η= (h1 – h2)/(h1- hf 2)
Page 12 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
T
QSSSgen )12
geno STSSTUUW 02121 )(
)( 12 VVPWW ou
)()()( 21021021 VVPSSTUUWrev
)()()( 00 oVVPoSSTUU
genToSI
F = τ πDL
1000
60
2
4
2
4
1
2
1
2
gQHp
RRt
NT
R
RL
uLF
t
V
rV
n
Blocks with feedback loop
G(s) = )()(1
)(
sHsGo
sGo
(for a negative feedback)
Page 13 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
G(s) = )()(1
)(
sHsGo
sGo
(for a positive feedback)
Steady-State Errors
)]())(1([lim0
ssGse iOs
ss
(for an open-loop system)
)]()(1
1[lim
0s
sGse i
os
ss
(for the closed-loop system with a unity feedback)
Laplace Transforms Z Transforms
A unit impulse function 1
A unit step function s
1
Exponential Function
A unit ramp function 2
1
s
First order Systems
)1( / t
ssO eG (for a unit step input)
)1( / t
ssO eAG (for a step input with size A)
Performance measures for second-order systems
dtp =
Page 14 of 14 University of Bolton Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2016/17 Advanced Thermofluids & Control System Module No. AME6005
P.O. = exp %100))1(
(2
ts = n
4
d = n(1-2)