TW23 UNIVERSITY OF BOLTON
SCHOOL OF ENGINEERING
BENG (HONS) IN MECHANICAL ENGINEERING
SEMESTER 2 EXAMINATION 2016/2017
THERMOFLUIDS & CONTROL SYSTEMS
MODULE NO: AME5003
Date: Tuesday 16 May 2017 Time: 10.00 – 12.00
INSTRUCTIONS TO CANDIDATES: There are SIX questions on this paper.
Answer ANY FOUR questions.
All questions carry equal marks.
Marks for parts of questions are
shown in brackets.
CANDIDATES REQUIRE : Property Tables provided
Formula sheet (attached)
Take density of water as
1000 kg/m3
Page 2 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
Q1 a) Describe with the aid of a diagram the principles of operation of an orifice
plate. (10 marks)
b) Water from a nozzle Figure Q1b fills a 0.5 L glass in 20 seconds . If the
diameter of the jet leaving the nozzle is 1.5 cm .What is the diameter of
the jet when it strikes the water surface in the glass which is positioned
36 cm below the nozzle.
Figure Q1b
(15 marks)
Total 25 marks
Q2 a) A pitot –static is used to measure the velocity of helium in a pipe. The
temperature and pressure are 4∘C and 172 kPa. A water manometer
connected to the pitot – static tube indicates a reading of 5.8 cm.
Determine the helium velocity. Take the density of Helium as 0.3 kg/m3.
(15 marks)
b) Water flows through a hole in the bottom of a large open tank FigureQ2b
with a speed of 8 m/s, determine the depth of water in the tank.
Question 2 continued over the page
Page 3 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
Question 2 continued
Figure Q2b (10 marks)
Total 25 marks
Q3 a) Air at 1000 kPa and 1500K expands in a Polytropic process, n= 1.5, to a
pressure of 200 kPa.
Calculate:
i) The final temperature of the air
ii) The work done
Take R = 0.287 kJ/kg K, use PV = m RT
(10 marks)
b) A 600 mm diameter pipeline shown in Figure Q3b carries water under a
head of 30 m with a velocity of 3 m/s. This water main is fitted with a
horizontal bend which turns the axis of the pipeline through 75O. Calculate
the resultant force on the bend and its angle to the horizontal.
Page 4 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
Question 3 continued over the page
Question 3 continued
Figure Q3b
(15 marks)
Total 25 marks
Q4 Fique Q4 shows a simplified CNC machine system, where K1 and K2 are the
spring stiffness, C is the viscous damping coefficient, and M1 and M2 are the
masses for Mass 1 and Mass 2. The input to the system is the Force F and the
outputs are displacements y1 and y2.
a) Develop the differential equations for the displacements y1 and y2 of the
machine system. (8 marks)
b) Determine the Laplace transforms of the differential equations obtained
from Q4(a) above. Assume the initial conditions of the system are zeros (i.e.
at time = 0, y, y’, y’’ are all zeros). (4 marks)
c) Determine the transfer function G(s) = y2(s)/F(s) (8 marks)
Page 5 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
d) Using the transfer function G(s) obtained from Q4(c) above, draw an open
loop block diagram and a closed loop block diagram (with a feedback H =
H(s)) for this system. (5 marks)
Question 4 continued over the page
Question 4 continued
Figure Q4 A Simplified Machine System
Total 25 marks
Q5 a) Assume that the speed of a vehicle system is a first order system, and its
transfer function is
Input Force F
Mass M1
K1 C
K2
y1
y2 Mass M2
Page 6 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
G(s) = 164
350
s
If the speed of the vehicle is suddenly increased from being at 8 m/s into 20
m/s, what will be the speed indicated by the speedometer after 0.7
seconds? (8 marks)
Question 5 continued over the page
Question 5 continued
b) Figure Q5 shows a block diagram for a manufacturing control system:
Figure Q5 A Manufacturing Control System
(i) What is the manufacturing control system’s transfer function G(s) = Output/Input? (7 marks)
(ii) If a unit step input is applied into the system, determine the system’s
percentage overshoot, rise time, settling time, peak time, natural
frequency, damped frequency, and damping ratio.
(10 marks)
Total 25 marks
+
- Output
- +
Input
0.8s
2
3
Page 7 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
Q6 A central heating control system has experienced a disturbance D(s), and a gain K has been inserted into the system as shown in Figure Q6, determine
a) the whole system’s output X(s) function (8 marks)
b) the range of values of K for the system which will result in stability. You
may use Routh-Array method. (10 marks) c) the steady-state error if the disturbance D(s) = 0, R(s) is a unit ramp
input, and K = 3. (7 marks)
Question 6 continued over the page
Question 6 continued
Figure Q6 A Central Heating System
END OF QUESTIONS
+ Output
X(s)
- +
Input
R(s)
D(s)
K
Page 8 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
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
dv/v
dP- = Modulus Bulk
du/dy =
gsd
4 =h
2g
V +
g
P + Z =
2g
V +
g
P + Z
222
2
211
1
1 - a
a
1 - h 2g
= V
2
1
2
L
1
Page 9 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
W = P (v2 – v1)
V
V PV = W
1
2ln
Q = Cd A √2gh
12 21
g
ghgCV m
.ΔMΔt
ΔMF
F = ρ QV
Re = V L ρ/
dQ = du + dw
du = cu dT
dw = pdv
pv = mRT
h = hf + xhfg
s = sf + xsfg
v = x Vg
hm w - Q...
1 -n
V P - V P =W 2211
Page 10 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
3
2
2
R
RL
LF
n
T
dQds
1
2n12 L
T
TCSS pL
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
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
Page 11 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
g
Khm
2
v2
g
VVkhm
2
2
21
H
L
T
T1
T
QSSSgen )12
geno STSSTUUW 02121 )(
)( 12 VVPWW ou
)()()( 21021021 VVPSSTUUWrev
)()()( 00 oVVPoSSTUU
genToSI
1000
gQHp
RRt60
NT
R
RL
uL2F
t
V
rV
4
2
4
1
2
1
2n
Page 12 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
Page 13 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
Blocks with feedback loop
G(s) = )()(1
)(
sHsGo
sGo
(for a negative feedback)
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)
)](
]1)()[(1
)(1
1[lim
1
10
s
sHsG
sGse i
sss
(if the feedback H(s) ≠ 1)
])1)((1
)([lim
12
2
0d
sss
sGG
sGse
(if the system subjects to a disturbance input)
Laplace Transforms
A unit impulse function 1
A unit step function s
1
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)
Page 14 of 14
School of Engineering BEng (Hons) Mechanical Engineering Semester 2 Examinations 2016/2017 Thermofluids & Control Systems Module No: AME5003
Performance measures for second-order systems
dtr = 1/2
dtp =
P.O. = exp %100))1(
(2
ts = n
4
d = n(1-2)