tw12 university of bolton school of engineering beng … · tw12 university of bolton school of...

TW12

UNIVERSITY OF BOLTON

SCHOOL OF ENGINEERING

BENG (HONS) IN MECHANICAL ENGINEERING

SEMESTER 2 EXAMINATION 2015/2016

THERMOFLUIDS & CONTROL SYSTEMS

MODULE NO: AME5003

Date: Tuesday 17th May 2016 Time: 10:00- 12:00 noon

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 2015/2016 Thermofluids & Control Systems Module No: AME5003

Q1 a) Describe with the aid of a diagram the principles of operation of Venturi

meter (10 marks)

b) Venturi meter Figure Q1 b is used to establish the flow rate of water in a horizontal Pipeline 50 mm diameter. The throat diameter of the Venturi is 20mm. The pressure drop between the entrance and throat section is 60 mm of mercury. Assuming no losses due to friction and taking the densities of water at 1000 kg m-3 and mercury at 13600 Kg m-3, determine:

i) The velocity of the water in the 50 mm diameter pipeline ii) The volumetric flow rate of water

iii) The mass flow rate of water

Figure Q1b

(15 marks)

Total 25 marks

Q2 a) An orifice of diameter 75 mm discharges water at the rate of 20 litres per

second when the head above the orifice is 90 m. If the jet diameter is 30

mm, determine the value of the coefficients of velocity, contraction and

discharge. (15 marks)

b) Describe with the aid of diagram the principles of operation of the pitot

static tube. (10 marks)

Total 25 marks

Please turn the page

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Q3 a) Air at 1 bar and 300K is compressed till the final volume is one-sixteenth

of the original volume, following a Polytropic process P v 1.25 = constant.

Calculate:

i) The final pressure and temperature of the air

ii) The work done

(10 marks)

b) A reducing right –angled bend lies in a horizontal plane (Figure Q3b),

water enters from the west with a velocity of 3 m/s and a pressure of 30

kPa, and it leaves toward the north. The diameter at the entrance is 500

mm and at the exit it is 400 mm. Neglecting any frictional loss, find the

magnitude and direction of the resultant force on the bend.

(15 marks)

Figure Q3b

Total 25 marks

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Please turn the page

Q4 A simple mechanical system shown in Figure Q4. 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 X1

and X2.

Figure Q4 A Mechanical System

a) Develop the differential equations for the displacements X1 and X2 of the

mechanical system. (8 marks)

b) Determine the Laplace transforms of the differential equations obtained from

Q4(a) above. Assume that the system is subjected to a unit step input and the

initial conditions of the system are zeros (i.e. at time = 0, x, x’, x’’ are all zeros).

(4 marks)

c) Determine the transfer function G(s) = X1(s)/F(s) (8 marks)

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

mechanical system. (5 marks)

Total 25 marks

Q5 a) A DC motor is a first order system. It’s time constant is 0.6 seconds. If the speed

of the DC motor is suddenly increased from being at 50 rpm into 300 rpm,

(i) what will be the speed indicated by the speedometer after 0.5 seconds?

(4 marks)

X2 K2

X1

F

K1

C

M1 M2

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(ii) if the maximum speed of the motor is 1000 rpm and the motor subjects a

unit step input, determine the time t taken for the speed output of the

motor from 0 to reach 75% of its maximum speed value. (6 marks)

Question 5 continued over the page

Question 5 continued

b) Figure Q5 shows a block diagram for a radar control system:

Figure Q5 A Radar Control System

(i) What is the radar control system’s transfer function G(s) = o/i? (5 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

Q6 A production control system has experienced a disturbance D(s), and a gain K has

been inserted into the system as shown in Figure Q6, determine:

Output O +

- - +

Input i

2s

10

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Figure Q6 A Production Control System

Question 6 continued over the page

Question 6 continued

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 step

input, and K = 5. (7 marks)

Total 25 marks

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

of 13


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

of 13


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

of 13


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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

G(s) = 1s

Gss

)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

G(s) = 22

2

0

2 nn

n

ss

b

dtr = 1/2

dtp =

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

(2

ts = n

4

d = n(1-2)

tw12 university of bolton school of engineering beng … · tw12 university of bolton school of...

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