OCD51 AME 6005 Thermofluids & Control System · ocd51 university of bolton western international college fze beng (hons) mechanical engineering semester one examination 2015/2016

OCD51

UNIVERSITY OF BOLTON

WESTERN INTERNATIONAL COLLEGE FZE

BENG (HONS) MECHANICAL ENGINEERING

SEMESTER ONE EXAMINATION 2015/2016 ADVANCED THERMOFLUIDS & CONTROL SYSTEM

MODULE NO: AME 6005

Date: Saturday 16 January 2016 Time: 1:00 – 4:00 INSTRUCTIONS TO CANDIDATES: There are 6 questions. Answer 4 questions. All questions carry equal marks. 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 17

Western International College FZE BEng (Hons) Mechanical Engineering Semester 1 Examinations 2015/16 Advanced Thermo fluids & Control System Module No. AME 6005

Q1.

a ) For the laminar viscous flow through a circular pipe, derive an expression for

the velocity distribution and shear stress distribution through it. Also prove the

following:

i) The velocity variation is parabolic

ii) The shear stress variation across the section of the pipe is linear

(10 marks)

b) What power is required per kilometre of a line to overcome the viscous

resistance to the flow of glycerine through a horizontal pipe of diameter 120mm

at the rate of15 litres/s?Take µ =8 poise and kinematic viscosity(ν)= 6 stokes.

(5 marks)

c) An oil of viscosity 0.2Ns/m2 and relative density 0.9 is flowing through a circular

pipe of diameter 65mm and of length 400m.The rate of flow of fluid through the

pipe is 4 litres/s. Determine the following:

i) Pressure drop in a length of 400m

ii) Shear stress at the pipe wall.

(10 marks)

Total 25 marks

Please turn the page

Page 3 of 17


Q2.

a) Water at 25oC flows at a rate of 45 litres/s in a cast iron pipe of 40cm diameter

and 120m 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 = 0.26mm.

(15 marks)

b) The external and internal diameters of a collar bearing are 300mm and 250mm

respectively.Between the collar surface and the bearing, an oil film of thickness

0.25mm and of viscosity 0.9 poise,is maintained.If the shaft is running at 270

r.p.m ,evaluate the following:

i. Torque generated

(5 marks)

ii. Power lost in overcoming the viscous resistance of the oil.

(5marks)

Total 25 marks


Page 4 of 17


Q3.

(a) Steam enters an engine at a pressure of 12MPa absolute and 550oC.

It is exhausted at 2 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)

(b) A closed system contains air at pressure 1.5 bar, temperature 300K and

volume 0.025 m3. This system undergoes a thermodynamic cycle consisting

of the following three processes in series:

Process 1-2: Constant volume heat addition till pressure becomes 4 bar.

Process 2-3: Constant pressure cooling.

Process 3-1: Isothermal heating to initial state

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 Cv =0.718kJ/kgK and R= 287 J/kgK

Total 25 marks

Page 5 of 17



Q4.

(a) An industrial control system shown in Figure Q4 uses a PID controller.

Gc(s) Gp(s) +

-

Input(s) Output(s)

Figure Q4

Where

)1(10)( sKds

KisGc ,

sssGp

6

4)(

2

i. If Ki=0, determine the value of Kd for critical damping.

(4 marks)

ii. With Kd as determined in (i) determine the limiting value of Ki such that

stability is maintained.

(6 marks)

iii. Find the Ki for a parabolic input (Ѳi = ) if GC(s) is a PI controller and the

steady state error is less than 5%. (3 marks)

iv. Design a PID controller by determining Kp and Kd (using the Ki obtained

from (ii) above) to achieve maximum overshoot less than 20 % and settling

time ts less than 4 seconds.

(9 marks)

(b) Analyse how system dynamics is affected by PID parameters Kp, Ki, Kd .

(3 marks)

Page 6 of 17


Total 25 marks


Page 7 of 17


Q5.

(a) Obtain the state space model of a simplified industrial robotic system shown in

Figure.5(a)

Figure .Q5.a

(15 marks)

(b) The state equations for a mechanical system are given below.

Analyse controllability and observability of the system. (10 marks)

Total 25 marks


M1 M2

K1 K2

B1 B2

y1 y2

u

Page 8 of 17


Q6

(a) An industrial manufacturing system controlled by a digital controller is shown in

Figure Q6.

Figure Q6

(i) Discuss the roles of ADC, Digital Computer, and DAC.

(3 marks)

(ii) Illustrate stability criteria for sampled-data control systems.

(3 marks)

(iii) Analyze the stability of the sampled control system shown in Figure.6 (b),

when the sampling time is (i) T=0.5 sec, (ii) T=1 sec.

(19 marks)

Figure Q6.iii

Total 25 marks

END OF QUESTIONS

s( )

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

T. + -

A/D Digital

Computer

D/A Plant

Sensor

i/p o/p

Page 9 of 17



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 10 of 17


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-r

2)

dQ = du + dw

du = Cv dT

dw = pdv

pv = mRT

h = hf + xhfg

Page 11 of 17


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 12 of 17


Page 13 of 17


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

Page 14 of 17


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

Page 15 of 17


Transfer Function for Blocks with feedback loop

G(s) = )()(1

)(

sHsGo

sGo

(for a negative feedback)

Steady-State Errors

)]()(1

1[lim

0s

sGse i

os

ss

(For the closed-loop system with a unity feedback)

Performance measures for second-order systems

Maximum Overshoot in % = exp %100))1(

(2

Settling time ts = n

4

Characteristic equation 1+GH=0

s2+2 n s+ n2=0

Observability Test Matrix = [ CT

: A

T C

T]

Controllability Test Matrix = [ B :

AB]

Page 16 of 17


Laplace Transforms Z Transforms A unit impulse function 1

A unit step function s

1

Exponential Function

A unit ramp function 2

1

s

Page 17 of 17


Table of Laplace, Z transform pairs

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OCD51 AME 6005 Thermofluids & Control System · ocd51 university of bolton western international college fze beng (hons) mechanical engineering semester one examination 2015/2016