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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

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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

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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.

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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)

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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)



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

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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)



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

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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)



Figure Q6 A Central Heating System

END OF QUESTIONS

+ Output

X(s)

- +

Input

R(s)

D(s)

K

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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

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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

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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

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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

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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)

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Performance measures for second-order systems

dtr = 1/2

dtp =

P.O. = exp %100))1(

(2

ts = n

4

d = n(1-2)

tw23 university of bolton school of engineering beng … · tw23 university of bolton school of...

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