Chapte

Q1.

The sdiamet

75L pushedof 6v cylindetop an

10tp The gcylindeviscosi

Calculapiston

Q2.

The sradius thatvelocitybetweeand thwith vis

Derive requireof the p

er1

schematic ter of mm and m

d upwards 6 m/s. Th

er is 125 md bottom 1 kPa and

gap betweer wall is fity of 0 ate the poupwards.

schematic R , height

t is being y . Ten the cone cavity isscosity .

an expreed to rotateparameters

shows a124.7D

mass 2m with a for

he internalmm and the

surfaces od 100bp een the illed with a0.29 kg/ms

ower requ

shows aH and harotated a

The width ne and thes filled wit

ssion for te the cone s given ab

DEPART

M

a piston w75 mm, 2 kg that isce F at al diameter

e pressuresof the pistkPa respepiston an

a lubricant .

ired to pu

a cone walf cone anat an angu

of the ge cavity is th a lubric

the poweras a funct

ove.

UNIVERS

TMENT OF

MEC3033F

FLU

Wo

with a length

s being a speed r of the s at the ton are

ectively. nd the t with a

ush the

with ngle ular gap y

cant

r P tion

SITY OF C

F MECHAN

F THERM

UID MECH

orked exam

CAPE TOW

NICAL ENG

MOFLUIDS

ANICS

mples

WN

GINEERIN

S II

1

NG

Chapte

Q3.

A thr

2v xi.

ii.

iii.

iv.

Q4.

A thre10v i.

ii.

iii.

iv.

Q5.

The de

and the

Calculain the b

er2

ree-dimens

2 x x xy yCalculate

Calculate

Calculate

Calculate 1,0,0 , 1

ee-dimensi t x x xy

Calculate

5t s. Calculate

at time t Calculate

Calculate 0,1,0 , 1

ensity distri

e gravitatio

ate the mablock defin

sional flo 3y xz z

the speed

the total ac

the rotatio

the volum1,1,0 , 1,1,

onal, uns 2 5xy y t

the speed

the total a

5 s. the rotatio

the volum1,1,0 , 1,1,

ibution in a

onal accele

agnitude ofned by the

ow field m/s.

of a partic

cceleration

n of the flo

me flow rat1 and 1,0

steady flowz m/s.

d of a part

cceleration

n of the flo

me flow rat1 and 0,

a three-dim

eration vec

f the total gorigin and

is des

cle moving

n of a parti

ow at the p

te through0,1 .

w field is

ticle movin

n of a parti

ow at the p

te through1,1 at time

mensional f

ctor by g gravitationa

4x , y

scribed b

through th

cle moving

oint 2,3,1 a flat sur

s describe

ng through

icle moving

oint 10,2, a flat sure 5t s.

flow field is

5.7 8y al force ex2 and z

by the

he point 2g through t

. rface defin

ed by the

h the point

g through t

5 at time rface defin

s given by

8 z m/s2. xerted on th2 .

velocity

2,3,1 . the point 2

ned by the

e velocity

t 10,2,5 the point

5t s. ned by the

2 2x z

he fluid co

2

vector

2,3,1 .

e points

vector

at time

10,2,5

e points

z kg/m3

ntained

Q6.

A two-d

Calcula0.5,3.2

Q7.

A two-d

Find th

Q8.

The bu1 5p

Calcula

dimensiona

ate the ma2 .

dimensiona

he position

ulk densityMPa is giv

ate the den

al pressure

agnitude a

al pressure

,x y whe

y of water ven as 1 nsity 2 at

e field is gi

and directio

e field is gi

ere the pre

is given a1000.4 kg20C, 2p

iven by p on of the

iven by p essure will

as 6.01 g/m3.

15 MPa.

2xy Pa.gradient o

2 23 4x y x be a minim

81 10 N/m

of the pres

6x y Pa. mum.

2 and the

ssure at th

density a

3

he point

at 20C,

Chapte

Q9.

The figwire thwith diaopen towithout1 and 2negligib

Q10.

Calculathe noz

Q11.

A smanozzle pressuthe su

1.2 dischar

Flexiblecoupling

W

er3

gure showshrough its ameter 1Do atmospht friction fro2 is 4 m. Tble.

Calculate point 2. Calculate

ate what thzzle on the

all toy car with a di

re of 10 kPurrounding kg/m3 is trge coeffic

Derive an

Determine

D1=e g

Water

s a cone thcenter wit

30 mm here strikeom below.The height

what the

the mass o

he magnitue strut.

on wheelsameter ofPa. The c

air on tthe densitycient of the

expression

e the termin

=80 mm

V1

hat can slidhout any fand veloci

es the cone The distat difference

diameter

of the cone

ude and d

s weighs f 5.0D mcombined tthe car cy of the sur

nozzle ma

n for the sp

nal velocity

D

V2

de up and dfriction. Aity 1 15v me symmetrance betwee between

of the jet

e.

W

Tvsf

w

irection wi

1.2m kgmm. The total drag acan be carrounding aay be assu

peed of the

y Tu .

2=40 mm

Air

down on aA water jetm/s that isrically andeen points2 and 3 is

will be at

Water flowbend nozzThe nozzlevia a fleshown andfixed strut.cross-sectwith diamerate throug

ll be of the

and is drair is sup

and frictionalculated aair and u iumed to be

e car over

t s

t

ws throughzle in a e is fixed toxible rubbd also to t. The nozional area

eters as indgh the nozz

e resultant

riven by applied at an force fromas 1.2F s the spee

e 0.6dC . time u t .

1

2

3

h the 90 horizontal o the pipe ber couplthe groundzzle has a a along itsdicated. Tzle is 0.01

t force exe

air issuing a constantm the whe

2 22 10 u ed of the ca

.

60

4

degree plane.

system ling as d with a circular

s length The flow

m3/s.

erted by

from a t gauge els and where

ar. The

0

4m

Q12.

Neglecmomen

Q13.

The flodiamet

2

30

ct all lossents exerted

ow rate ofters of the

Derive arequired rfunction ogiven consCalculate required maintain 180 rpm. Calculate speed wiresisting to

2

100

es and deted on the su

f water thtwo outlet

an equatioresisting tof , to stant rotatithe magnresisting

a rotation

what thll be, in orque is ap

z

1

100

ermine theurface of th

rough thenozzles ar

on for torque, as

maintain onal speed

nitude of ttorque

al speed

e rotationrpm, if

pplied.

x

y

100

e magnitudhe tank wh

e sprinkler re 7 mm ea

the a

a d. the to of

nal no

3

3

The pithe flapoint 1points diamet

2 15D the v1 1.5v

all provthe pneglecwater m

de and direre the pip

shown abach.

30

pe fitting st top surfa but open

2 and ers are5 mm and velocity a

m/s. Thevided in mmpipe matted but thmust be tak

ection of ape is fixed t

bove is 0

Q=

shown is face of a to atmosp3. The

e 1 2D 3 15D m

at the ine dimensiom. The wterial mahe weight ken into ac

all the forcto it.

.0012 m3/s

D=7m

=0.0012m3

5

fixed to tank at

phere at e pipe 25 mm,

mm and nlet is ons are eight of ay be

of the ccount.

ces and

s. The

mm

3/s

Q14.

The ba

Q15.

The fig50D

atmosp

3

ackward c

gure shows mm is us

phere. Neg

DetermineDetermine

3

D

r1 =63.5

30

1v

curved cen

s a tank thsed to sypglect all los

e the masse the gaug

D=50mm

Air

mm

trifugal fan

at is open phon watesses.

s flow rate ge pressure

r2 =1

n is rotatin

r

ivop

tv

d

to atmospr from the

of water.e at point 2

1m

147mm

g at 3000rate of

1.2 kg/is 30 as velocity aoutwards. passages

Findthat the avane.

Finddrive the fa

phere at poe tank. Th

2 just insid

0

12

Water

rpm while 0.5v m3/

/m3. The oshown a

t the inle The wid

is 200 mm

d the inletir will ente

d the powan if the eff

oint 0. A phe jet at p

e the pipe.

pumping /s with outlet vane

and the aet 1v is dth of the

m.

t vane aner parallel

wer requfficiency is

pipe with dpoint 3 is o

.

2.5m

6

air at a density e angle

absolute radially e vane

ngle so to the

ired to 60 %.

iameter open to

Q16.

K1=

10m

P

=0.5 K22=3K3=0.25

K4=0.25

200kPa

oil

K5=1.0

Thsho

hea

the coef

andL Detwith

a he

20m

e total heaown is give

ad as Lh sum o

efficients 0.02 , the

d the to150 m.

termine theh density

38.5 10 kead of Mh

ad loss in en in term

Lf KD

of the K , the pipe diam

otal length

e mass flo850 kg

kg/ms if th45.2 m.

the pipe ms of the

2

2vKg

witrespective

friction meter D h of the

ow rate ofg/m3 and v

he pump s

7

system velocity

th K e loss

factor 0.25 m

e pipe

f the oil viscosity

supplies

1

Q17.

The figradius water wflowingouter ddetermthe pipsectionincremand thpositioneach o

Q18.

A pipe

diamet

1 20T measu

50mm numbe

1.0pc

i r[i][mm]

1 02 53 114 165 216 267 328 379 4210 47

gure show100D

with a deng. A pitodiameter o

mine the mpe. For nal area ients with e tip of thned in turn

of these inc

with an inn

ter of 2D C flows red as p

1 250D m er of the a

006 kJ/kgK

DetermineDetermineisothermaDeterminenot isotherCompare flow rates.

dP[i][Pa]112511081090107010461018985942880760

ws a pipe mm throu

nsity of 10t-static tub

of 3.2 mm ass flow rathis the ps divided width dr

he pitot tun at ir at thcrements fo

Tmdthm

Do

ner diamet

75 mm. Ainto the ve

20p kPamm , 0.4 pproaching

K and 0vc e the masse the massl.

e the massrmal. the three

.

with inneugh whic00 kg/m3 ibe with ais used t

ate througpipe crossinto equa

as showube is thehe centre oor 1...i m .he positio

measured ifferential ohe neares

measureme

Determine tn the data

ter of 1D Air with visenturi tube

a. For th

0.75 g flow def

0.718 kJ/kg

flow rate is flow rate

s flow rate

results by

er ch is

an to gh s-al

wn en of .

on of the to the

over the pst 1 Pa. ents taken

the total mprovided.

150 mm is

scosity e and the e venturi

and 2 10fined as R

gK.

if the flow iif the flow

e if the flow

y calculatin

ir

R

tip of thenearest 1

pitot tube cThe table

with 10m mass flow r

s fitted with51.821 10

pressure tube it is50 ReD

1 1ReDv D

is assumedw is assum

w is assum

ng the res

e pitot tub1 mm andcould onlye provides0 .

rate throug

h a venturi 5 kg/ms at difference given tha

61 10 wit. Also gi

d be incommed to be c

med to be

spective er

be could od the p

y be meass the res

gh the pipe

tube with a

1 100p k over the at 0.9dC th the Re

iven for th

mpressible.compressi

compress

rrors in the

8

only be ressure ured to

sults of

e based

a throat

kPa and tube is 995 for

eynolds

he air is

. ble and

ible but

e mass

dr

Chapte

Q19.

A viscoround bradius fluid isatmospdevelobetweenegligib

Derive functioviscosiand b .

Q20.

er4

ous liquid bar under of the soli

s b . Thphere. Thped at th

en the liquble.

a relationn of the rty , grav.

Derive an Derive an

Derive an

Derive an

flows dowthe influend bar is a

he outsidehe flow che point ouid and the

nship for adius r , t

vitational a

expressionexpression

expression

expression

wn the ounce of grav and the

e of the an be assof interese air can

the velocithe fluid dcceleration

n for the stn for the ve

n for the m

n for the vo

utside of avity as shoouter radiliquid is sumed to

st and thebe assum

ity profile ensity , n g and th

A viscous under The thicknof the liquflow can the point the liquid negligible

tatic presselocity prof

maximum s

olume flow

a vertical own. The us of the open to be fully

e friction ed to be

zv as a the fluid

he radii a

s liquid flowthe influe

ness of theuid layer isbe assumeof interesand the

.

ure p as afile xv fhear stres

w rate v f

ws down aence of ge liquid lays open to aed to be fst and the air can be

a function o

z, , , ,g H s max f , , ,f g H

a ramp witravity as

yer is H . Tatmospherfully develoe friction be assumed

of z .

,H . , , , ,g H

,H .

9

h angle shown. The top re. The oped at

between d to be

.

Chapte

Q21.

The figimpelle

er5

gure belower diameter

Make usePI groups Use 20 porelationshiMake use required pdiameter orotational s

w provides tr of 160 mm

e of dimenthat charaoints on tips betweeof the rela

power willof 230 mmspeed of 2

the performm.

nsional anacterize thehe perform

en the PI gationships al be if a

m is used to2700 rpm.

mance cur

nalysis to e pump permance curroups. above to dgeometric

o provide

rves for a s

derive therformancerves to dra

determine wcally similaa water m

specific wa

e relevant . aw up gra

what the par pump

mass flow r

ater pump

non-dime

aphs show

ressure hewith an i

rate of 4.5

10

with an

ensional

wing the

ead and mpeller l/s at a

Q22.

A dam depth o

You ar

You kn

wall with of 10H mre asked to

now that th

Make usegroups. Determinebe to ensu

a length ofm, the ave

o design a

e gravity g

of dimens

e what the ure similari

f 1250L rage veloc150

scale m

g will be an

sional ana

volume floty.

H

m is desigcity of the w

model of th

n importan

alysis to de

ow rate ov

v

gned so thwater over

he dam wa

nt paramete

erive the r

ver the wal

at if water r the wall w

all to study

er in the sc

elevant no

l of the sc

r flows ovewill be 1v

the flow p

caling proc

on-dimensi

cale model

11

er it at a 1.2 m/s.

atterns.

cess.

ional PI

should

Chapte

Q23.

A pipepipes diametand D

1 45L 3 54L

of all ththe hea

2Mh unknoware giv

Take inand de

Q24.

Take inpipes awill be

K=0

K=0

er6

eline consisas sho

ters 1 0D 3 0.076D m.72 m, 4.86 . Thehree pipes ad over th24.66 m. wn secondven. (For w

nto accounetermine th

nto accounare connecbetween t

2

0.5

0.5

sts of threown with0.05 m, 2Dm and tot

2 27.43L e surface is 0.04 e turbine iThe valu

dary loss cwater 1 nt the frict

he power ex

nt the frictiocted to thehe two res

1

ee differenh interna2 0.152 mtal lengths m androughness46 mm andis given asues of thecoefficients

30 kg/m3 a

ional lossextracted fro

onal lossese reservoirservoirs.

6

3

t al m s d s d s e s and 10 es as well om the flui

Ththe

1D

3D

are

31L

s as well ars and det

30.48m

60m

3 kg/ms.)

as all theid via the t

he diametee two 1 0.05 m,3 0.1 m, te 1 2.5

2 mm a60 m, L

s the inlet termine wh

K=0.5

K=0.9

1

e relevant surbine.

ers of the reservoirs

2D the pipe su5 mm, and the p

2 90L m a

and outlet hat the tota

K=0.95

5

secondary

pipes cons shown0.12 m

urface rou

2 1.2 mmpipe lengtand 3 12L

losses whal mass flo

Turbine

2

12

y losses

necting n are

and ghness

m and ths are 0 m.

here the ow rate

Valve

K=6.3

3

Q25.

Neglecflow rat

Q26.

The fig

4 0.D 1 120L

betwee

Neglecof the p

A

30mA

ct all seconte of water

gure show1 m; 1 0 m, 2L en A and D

ct all seconpump to ob

1

ndary losser in each o

ws a pipe 0.002 m, 90 m, 3L

D is AH Hndary lossebtain a tota

100m

1

B

es and detef the three

network w

2 0.001 60 m an

78DH m aes and deteal volume f

B

m

2

J

ermine thee pipes.

with 1 0D 12 m, 3d 4 80L and the pu

ermine whflow rate fr

2

3

70m

3

C

The resethat pipepoininterD rougpipe

2L e magnitud

0.1 m, 2D0.0025 m

m. The dmp efficien

hat the inpuom A to D

Pump

C

figure ervoirs ope

are conns with a ct J. The prnal 250 mm

ghness of lengths 150 m and

de and dire

0.12 m, m and 4difference ncy is 0 ut power reof 0.03v

C

shows en to atmonected viacommon jpipes all hdiameter and a

0.5 mmare 1L

d 3 110L ection of th

3 0.05D 4 0.002 min the tota0.58 .

equirement3 m3/s.

4

13

three osphere a three unction

have an of

surface m. The

80 m, m.

e mass

m and

m; and al head

t will be

D