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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

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


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)



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



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


R(s) E(s) E*(s) C(s)

T. + -


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



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


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


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


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


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)


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)


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 =


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

(2

ts = n

4

d = n(1-2)

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