chee2003 st

'

m THE UNIVERSITY ~OF QUEENSLAND ~ AUSTRAL IA

VENUE:

SEAT NUMBER:

STUDENT NUMBER:

STUDENT NAME:

I J l -T -J I I I]

Family Name

First Name

FINAL EXAMINATION

St Lucia Campus

PERUSAL TIME

WRITING TIME

EXAMINER

Semester Two 2011

CHEE2003 Fluid and Particle Mechanics

10 mins. During perusal, write on the blank paper provided

2:30 Hours

Lianzhou Wang I jason Stokes

This examination paper has 14 pages (not including the title page) and is printed Double-Sided

THIS EXAMINATION PAPER MUST NOT BE REMOVED FROM THE EXAMINATION ROOM

Exam Type: Open Book - Unrestricted Materials Examiner's use ONLY

Question Mark

Permitted Materials: Calculator -Yes- Casio FX82 series or UQ approved (labelled)

Dictionary -Yes- Any unmarked paper dictionary is permitted

Other -

-No electronic aids are permitted (e.g. laptops, phones)

Answer: (Where All Questions in Writing booklet students should write answers)

Other Instructions: Part A Questions 1 - 3 Part B Questions 4 - 6

Total Number of Questions: (for the 6 whole examination)

Total Number of 120 total marks Marks TOTAL

L__ _ _______

Students must comply with the General Award Rules 1A.5 and 1A.7 which outline the responsibilities of students during an examination .

I

CHEE2003: Fluid & Particle Mechanics- Final Exam, Semester Two, 2011

PART A

Question 1. (20 marks, each part is worth 2 or 4 marks) Please clearly state your answer in the writing booklet.

(1-i) The Mach number (Ma = V/c) is a very important dimensionless parameter in fluid mechanics. It is considered to be (2 marks):

(a) Static Pressure divided by the Dynamic Pressure (b) Inertia force divided by viscous force (c) Speed of an object relative to the speed of sound in a Fluid (d) Gas flow velocity divided by viscous force (e) Inertia force divided by the speed of sound

(1-ii) Shown below are rheological measurements for 3 unknown fluids. You are about to present the results to your manager but you realize that you have mislabelled the samples in your notes. Which viscosity values correspond to which fluid. Subscripts indicate the fluid label. (2 marks)

_......._ co

0... ._ C/) C/) Q) 1.... .......

(/) 1....

co Q)

..c (/)

(a) )..!A= 0.003 Pas, ).lB = 3 Pas, ).lc = 0.8 Pas (b) )..!A= 3.0 Pas, ).ls = 0.003 Pas, llc = 0.8 Pas (c) )..!A = 0.8 Pas, ).lB = 0.003 Pas, ).lc = 3.0 Pas (d) )..!A = 0.003 Pas, ).ls = 0.8 Pas, ).lc = 3.0 Pas (e) you don't have enough information to say which fluid is which

3500 .-----~----~----~----~------~----.

3000

2500

2000

1500

1000

500

0 0 200 400 600 800 1000 1200

Shear Rate (s-1)

Page 1 of 14


(1-iii) Where is the control valve best located for a liquid positive displacement pump: (2 marks) (a) Delivery side. A valve on the suction side could cause areas of low pressure and formation of gas bubbles that could damage the pump. (b) Suction side. Due to high pressure produced by the pump, closing a valve at the outlet will cause severe damage or even pipe rupture. (c) Suction side. Backflow and cavitation can occur if placed on the delivery side. (d) Delivery side. A pressure relief valve is needed due to the high pressure delivered. (e) No control valves required. Pumps operate at a constant speed.

suction -,-------;> delivery

--~· Pump

(1-iv) Shown below are rheological measurements for 4 unknown fluids. As before, you once again failed to label them correctly in your notes. Which constitutive model for the non-Newtonian fluids below belongs to which fluid (subscripts on the stress term indicate the fluid label. All numbers are in SI units)? (2 marks)

ro 0....

(/) (/)

~ U5 '-ro

' Q) ..c (j)

( ) 0 5 . 0·7 20 0 1 . 0 '7 0 01 . 1.5 a TD = · Y ; TF; = + · Y ; Tc = · Y

(b) rD =O.Olfu rE =0.Sf07 ; rF =20+0.1f07

(c) TD =20+0.1f 07 TE =0.0lf15 ; r 0 =0.5f 07

(d) rE = O.Sf 07 rF = O.Olf 15 ; r 0 = 20+0.1f07

(e) Not enough information is provided to say which fluid is which.

100 ' IS. I • I f::.fS.

t:.ts. • Fluid D e t:.ts. 0 Fluid E e

6t:.ts.

80 -1 I "" Fluid F e 6

ts. 1::. Fluid G e

6t:.ts.

• t:.ts. ts.

• t:.ts. ts. 60

• t:.ts. • t:.ts.

ts. • t:.ts.

• t:.ts. 40 • t:.ts.

• t:.ts.

~ 20

0 ~~~~~~~~~~~~~~~~~~ 0 200 400 600 800 1000

Shear Rate (s-1)

Newtonian fluid:

r = O.lf

Power Law fluid (shear thinning):

r = 0.5fo.7

Power Law fluid (shear thickening):

r = O.Olfu

Herschei-Bulkley fluid (yield stress):

r=20+0.ly 0·7

Page 2 of 14


(1-v) Your friends seek your clever advice on pressure. They send you a 2-D map (below) of a dive through a cave network, where the white region is the atmosphere and light-shaded region is water. They have already measured the gauge pressure (P) at locations of A and B (i.e. P A and P8 ) in the lake. However, they are worried that once they enter the caves at point C and beyond point D, that the pressure will increase due to the narrowness of the cave system and thus putting their lives at risk. What do you suggest to them, assuming the map is accurate: (2 marks)

(a) You have no idea, except PB > P A and PG >PH. (b) It could be a problem: PB > P A, PE > PB and PG > PE (c) It could be a problem: PE = PG, PF = P0 , but Po> P A and PE > PB (d) It should be fine: P A= PB, Pc = PE and PH= PG (e) It should be fine: PB = PE = PG

Ael

(1-vi) What are the dimensions ofF orce (dimensions of mass, length and time are M, L & T respectively) ? (2 marks)

(a) MLIT (b) M/TL2

(c) ML2/T3

(d) MLIT2

(e) L

(1-vii) For a pyramid-like crystal of base length 1.0 mm and height 1.0 mm, what is the sphericity (\II) of this crystal? (Hint: the volume of the pyramid= 1/3 x area of the base x height) (4 marks)

(a) 0.64 (b) 0.69 (c) 0.72 (d) 0.76 (e) 0.82

Height

~,/ '>Base

Pyramid

Page 3 of 14


(1 -vi ii) A raindrop of 4 mm equ ivalent diameter sphere falls freely in the sky (Pair = 1.2 kg/m3, 11 air = 1.8 x 10-5 Pa.s). The maximum falling speed of the raindrop is closest to? (4 marks)

(a) 0.78 m/s (b) 2.6 m/s (c) 5.2 m/s (d) 7.8 m/s (e) 10 m/s

Question 2 (20 marks)

Part marks can be given for incorrect answers if reasonable working is shown. Each part is worth the same number of 4 marks. Clearly state your answer in the writing booklet.

(2-i) For a particle settling with a Richardson-Zaki coefficient, n, of2.6, the voidage at which the particle settling flux is maximized is closest to :

(a) E = 0 (b) E = 0.28 (c) E = 0.72 (d) E = 0.88 (e) E = 1

(2-ii) A manometer is used to measure the pressure of a gas in a tank. The fluid used has a specific gravity of 0.85 , and the manometer column height is 55cm, as shown. If the local atmospheric pressure is 96 kPa, what is nearest to the absolute pressure within the tank.

(a) 100.6kPa (b) 5395 Pa (c) 4582 Pa (d) 101.4 kPa (e) 96 kPa

P=?

SG = Cl./s5

Palm= 96 kPa

-i h =55 em

' j _

Page 4 of 14


(2-iii) What is the nearest Reynolds number for a fluid of viscosity 0.062 Pas and specific gravity of 1.17 in fully developed flow through a 0.25 m radius pipe at a volumetric flow rate of 3,000 m3/hour.

(a) 100000 (b) 10000 (c) 1000 (d) 100 (e) 10

(2-iv) A tapered pipe gradually increases in diameter from 0.081 m to 0.25 m. If the volumetric flow rate is 67.25 kg/hour of a fluid with specific gravity of 1.1, what value is closest to the outlet velocity?

(a) 0.1 m/s (b) 1 m/s (c) 10 m/s (d) 100 m/s (e) 1000 m/s

(2-v) Assuming that a Centrelink bus has a size of 3 m x 2.5 m x 15 m moving with a drag coefficient Cd of 8.6, what's the closest power required to account for air resistance during a steady motion of 60 km per hour on level ground?

(a) 60 kW (b) 100 kW (c) 140 kW (d) 180 kW (e) 230 kW

(2-vi) To conduct chemical analysis of an unknown mineral, 2 kg of the mineral sample was ground in the lab and divided into two parts, 1 kg has the equivalent diameter of 2 mm and another 3 mm. The mean diameter of this mixture on a number basis is closest to?

(a) 2.10 mm (b) 2.23 mm (c) 2.32 mm (d) 2.50 mm (e) 2.72 mm

Page 5 of 14


Question 3 (20 marks) Part marks can be given for incorrect answers if reasonable working is shown. Each part is worth the same number of 4 marks. Clearly state your answer in the writing booklet.

(3-i) For a journal bearing of diameter D, length L, radial clearance C, eccentricity E, use the Buckingham Pi theorem to determine a possible functional relationship between the load W (Newtons) that can be supported by the oil film of viscosity fl (Pas) when rotating at a rate of Q s-1

. Note, the unit forD, L, C and E is meters.

(a) W (C E L) f.10D 2 = f D' D' D

(b) W (C E L) f.10LC = f D ' D ' D

(c) pOD 2 = f( QD E !:_J W ~ f.1 'D'C

(d) j.iDLW = !( C E !::__) Q D'D'D

(e) Buckingham pi theorem cannot be used in this instance.

(3-ii) The water in a tank is pressurized by air, and the pressure is measured by a multiple fluid manometer as shown. The tank is located on a mountain at an altitude of 1400 m where the atmospheric pressure is 85.6 kPa. Determine the air pressure in the tank ifh1 = 0.1 m, h2 = 0.2 m and h3 = 0.35 m. Take the densities of water, oil and mercury to be 1000 kg/m3, 850 kg/m3 and 13600 kg/m3 respectively. Indicate what answer below is closest to the value you obtained.

(a) 85.6 kPa (b) 981 kPa (c) 83.14 kPa (d) 52.2 kPa (e) 130 kPa

Air

l

"\

w:ter , - IT hi

~\

.;~, dl l T

-::.- I I I h2 I

.L

Oil

rW2 h,

I 3 .

Page 6 of 14


(3-iii) A Newtonian fluid of viscosity 1.5 mPas and specific gravity of 1.015 is being pumped at an average velocity V in a pipe at an absolute pressure of 131 kPa and at Reynolds number of 1200 to an exit at a tank at atmospheric pressure (101 kPa). If you want to use a Newtonian fluid with a viscosity of 1200 mPas and specific gravity of 1.09 in the same pipe, what is the average velocity relative to V required to achieve the same kinematics in the flow? Choose the answer which is closest.

(a) 0.001342 V (b) 1200 v (c) 750 V (d) 0.745 v (e) V

(3-iv) On UQ Open day, you have been asked to move a type of porous catalyst in a cylindershaped container (cross-section area 0.1 m2) to the Demo site ofHawken Building. You used 12 kg of the catalyst to pack the container to a height of 1 0 em. Given the true or skeletal density of the catalyst is 2800 kg/m3 and the porosity of the catalyst is 20%, the voidage of this packed catalyst is closest to :

(a) 0.40 (b) 0.42 (c) 0.46 (d) 0.52 (e) 0.57

(3-v). You have been asked to design a settling experiment in the chemical engineering lab. You used 45 g of uniformly sized composite spheres (density 1500 kg/m3, diameter 50 11m) in 100 ml of water to form a well-dispersed suspension. Then you filled the suspension into a tube to allow the slurry to settle down, what is the closest value of the settling velocity?

(a) 0.11 mm/s (b) 0.20 mm/s (c) 1.10 mm/s (d) 4.52 mm/s (e) 11.0 mm/s

Page 7 of 14


PARTB


The Mechanical Form of the Energy Equation for pipe flow is often represented by:

( P. -2 J ( p - 2 J ( L )( -2 J [ -2 J 1 v1 2 v2 v "" v -+a -+z +h = -+a -+z + f - - + L...K -pg 1 2 g 1 q pg 2 2 g 2 D . 2 g all minor L 2 g

losses

Filter, K = 12 45• elbow Standard elbow

IN

v2 + exit

You are designing a pipe system to with details of one of your designs shown above. The pipe diameter is constant from the tank outlet (marked "OUT") until the exit point that is open to the atmosphere (marked "exit"). The length of 10 em diameter pipe (relative roughness EID = 0.01) from the tank to filter is 1Om, and from the filter to the jet outlet is 50 m. It passes through 2 x globe valves (one fully open and one half open), and one filter (KL = 12). The fluid has a viscosity of fl = 5 mPas, p = 1005 kg/m3. State and justify any assumptions and show calculations. See charts and tables of information provided.

(a) Assuming turbulent flow, and that the pipe has a constant diameter of 10 em; determine a relationship between the height of fluid in the tank (h) and the velocity of the outlet flow (V 2) and friction factor (f). (5 marks)

(b) If it is desired for the fluid to exits through the 10 em diameter pipe at a velocity of 3.2 m/s, determine the friction factor and then the height of fluid in the tank that is required ?

(5 marks)

(c) If you replace the tank in your design with a centrifugal pump (TACO series, Figure 1) using a 9.5 inch impellor, use your expression in part (a) and friction factor determined in (b) to determine the volumetric flow rate that will be achieved by the pump. Using the pump chart in Figure 1, state what head the pump delivers, as well as its brake horse power and efficiency ? Note: the 9.5 inch impellor characteristic pump curve is also approximated by the following equation: hpump = 29+ 13 5Q - 4405 Q2 when Q has the units m3/s and is expected to range from about 0.01 to 0.1 m3/s (10 Lis= 0.01 m3/s). (6 marks)

(d) Stating your reasoning and/or any calculations, suggest an impellor size and/or pump configuration (e.g. multiple pumps in series) for the TACO series pumps that is needed to efficiently achieve the desired head that you obtained in part (b). How close to the best efficiency point (BEP) will the pump (or pumps) operate? (4 marks)

Page 8 of 14



You have been asked to develop a demonstration packed bed for a School Open Day. You found some sand, a sample of which had the following sieve analysis.

Size Mass

< 100 flm 0 g 100-150 flm 10 g 150-200 f.!m 70 g 200-250 f.!m 10 g > 250 f.!m 10 g

The sand can be considered to be spherical, and has particle density and bulk density of 2500 kg/m3

and 1550 kg/m3, respectively.

The demonstration bed column is 150 mm in diameter, and 8 kg of sand are to be placed into the column.

(a) What pressure drop do you predict through the bed if the flow rate of water (p = 1000 kg/m3, fl = 0.001 Pa.s) is 1 litre/minute? - (8 marks)

(b) Then you wish to change the packed bed to a fluidized bed, please predict the flow rate at the minimum fluidised condition. (6 marks)

(c) Please estimate the voidage of the fluidised bed at the condition ofU = 1.3 Umr (6 marks)

Please clearly state any assumptions that you are using to make your estimate.

Page 9 of 14


Question 6 (20 marks) As a graduate engineer you are placed in charge of operations concerning the flow of gas at a

chemical plant. On your first day, the plant operators highlight some problems and queries they

have been having on the gas pipe. However, you have been warned by your manager that despite

their good nature, the operators will likely put you to the test to see what you know so think

carefully about what they tell you. He encourages you to impress them with quick answers to their

queries to earn their respect. The properties of C02 are: Mw = 44.01; R = 188.9 J/kg.K; Cp = 841.8

J/kg.K; k = 1.40. For an ideal gas: P = pR T, k = Cp/Cv. The speed of sound (c) is given by c2 =

k

kR T. Under isentropic conditions: P2 1 P1 = (T2 IT1 )k=l = (p2 1 p 1 Y . Atmospheric pressure is 101 ,000

Pa. State and justify any assumptions and show calculations.

(a) A pitot tube is being used to monitor the flow rate of C02 in a 10 em diameter pipe at T = 295K.

The pressure readings in the control office show that the static pressure is P static = 150 Pa (gauge)

and the stagnation pressure is Pstagnation = 213 Pa (gauge). For a pitot tube, you recall that the

stagnation pressure is the pressure at the entry point to the pitot tube, while the static pressure is the

pressure in the uninterrupted stream. However, the sneaky operators tell you that the flow is sonic

and that the discharge coefficient arising from the vena contracta effect is Cct= 0.65 and that the

following equation gives the velocity:

v""""' ~ c,J2{;- ;' J Impress the operators by stating and drawing what the type of flow meter this equation is likely to

be for.

Use Bernoulli's equation to derive the actual equation for the velocity determined from pitot tube

measurements in terms of the static and stagnation pressure.

Use your equation to calculate the velocity of the gas in the pipe.

Evaluate and state whether the flow is sub sonic, sonic or supersonic ? (10 marks)

(b) The sneaky operators tell you to be careful near the compressors because they can get to sub

zero temperatures. Calculate the temperature of carbon dioxide after it is compressed isentropically

from room temperature (298K) to 10 atm? (4 marks)

(c) Carbon dioxide is held in a vessel at a pressure of 1400 kPa and 200 °C, with a total weight of

gas being held being 200 kg. Not joking now, the operators tell you that if the pressure relief valve

is triggered when the pressure just exceeds 1400 kPa, 20 kg of C02 is released in exactly 2.35

minutes through a nozzle. To impress them, you say that you can estimate the diameter of the

nozzle. Calculate the area (A) and then the radius of the nozzle required to achieve the mass flow

rate specified by the operators (Recall maximum mass flux occurs when Ma = 1 ).

The operators state they would like to be able to half the initial rate of gas lost when evacuating the

tank, without changing the temperature or pressure in the vessel, or the diameter of the nozzle .

What do you suggest to them? (6 marks)

Page 10 of 14


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Figure 1 - Performance data for a family of centrifugal pumps. SI units for the x-axis (Q in Lis) is at the top and y-axis (Head, m) on the right hand side. Conversions : 1 foot = 0.3048 m; 1 US gallon = 0.0037854 m3; 1 US gal/min =0.0631 litre/s; 1000 litre = 1 m3. .

Page 11 of 14

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""0

'"T1

(})

:::l

.:::s::.

o.>

0 m

..c

X

o.>

0 3 (/

) (J

) 3 (J) en ......

(J)

0.2

0

.4

0.6

0

.8

1.0

'"" --i

~

0 N

0 __,

RTo

( ~ )k

•llk

-1

Qc(

mw

) k

2 C

hoke

mas

s flu

x th

roug

h no

zzle

M

ass

flux

__,


Table 1 -List ofKL values to account for minor losses in pipe flow.

Fittin~ KL Globe valve (fully open) 6 Glove valve (half open) 15 I Return Bend 0.3 Standard elbow 0.3 45° elbow 0.29 I

Pipe exit 1.0

~ L

Square-edged entrance t,,. f:r 0.5

--,_ 0.25

Sudden contraction: 2:1 ~ --,_ 0.46

Sudden contraction: 10:1 ~ ----- 0.02 General contraction (30°) -----

Page 14 of 14

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