FM42 - Manual

7232019 FM42 - Manual

httpslidepdfcomreaderfullfm42-manual 111

SOLTEQ983214 FREE AND FORCED VORTEX (MODEL FM 42)

10 INTRODUCTION

This SOLTEQreg Free and Forced Vortex (Model FM has been designed for studentsexperiments to produce and measure free and forced vortices It consists of a clear acryliccylinder where the free vortex is generated by water discharging through an interchangeable

orifice in the base of the cylinder The resulting profile is then measured using a combinedcaliper and depth scale The forced vortex is induced by a paddle rotated by jets of water atthe cylinder base

The profile of the forced vortex is then determined using a series of depth gauges Velocity at anypoint in the free or forced vortices may be measured using the appropriate pitot tube supplied Asecondary flow at the base of the free vortex may be demonstrated by means of dye crystals (notsupplied)

1

7232019 FM42 - Manual



0 $ENERL DESCRIampTION

21 Unt e)l+

The accessory is designed to be positioned on the side channels of the hydraulics benchtop channel

The apparatus consists of a cylindrical vessel having two pairs of diametrically opposedinlet tubes verflow cutouts ensure a constant level in the tan during experiments Asmooth outlet is centrally positioned in the base of the vessel and a set of pushin orificesof various diameters are supplied

The $ampmm diameter inlet tubes which are angled at $amp degrees impart a swirling motionto the liuid entering the vessel and are used as entry tubes for the free vortex experimentThe forced vortex is created by using the mm inlet tubes which are angled at degrees

to the diameter The input from these tubes impinges on a paddle which acts as astirrer+flow straightener The paddle rotates on a stud mounted on a bushed plug insertedin the central orifice

A bridge piece incorporating with measuring needles is used to determine the profile of theforced vortex The needles are set at fixed distances from the side of the tan Thedistances are given below

If the profile of the free vortex is reuired this can be determined by replacing themeasuring needles with a gauge which measures the depth of the vortex at differentdiameters

Velocity heads may be visualied by the insertion of pitot tube in the measuring bridge

22 e)l+ Ve

2

6

1

2

4

3

5

1011

9

7

8

12

7232019 FM42 - Manual



$ -ridge rofile easuring 0auge

1 mm dia 2ole 3 Three 4ay Inlet Valve

amp $ampmm dia 2ole Inlet

5 6urface robe 7 utlet valve

utlet $ itot Tube$$ rifice $ addle

23 Ex-er)ental Ca-alte

i 8xperiment to plot the shape of a free vortex by measurement of surfaceprofile coordinates and thus verity that =vr constant where v is thespeed and r is the radius of the vortex

ii 8xperiment to plot the surface profiles of various forced vortices formedunder different speed conditions

iii Verification of the formula g

r h

2

22ω

= for forced vortices where h is the

height of the surface of the water above the datum point ω is the vortexangular velocity and r is vortex radius

24 S-eccaton

verall 9imensionength ampampmm4idth 1ampmmlteight 1ampmm

6torage 9imension9iameter 3ampmmverflow lteight $7mmrifice 9iameter 7mm $mm $mm 3mm

9istance of =orced Vortexeasuring 0auge fromgteservoir enter 1mm ampmm 5mm mm $$mm

itot Tube ength $ampmm

25 $eneral Rere)ent

4ater supply from ltydraulic -ench

3

7232019 FM42 - Manual



0 SUMMR2 OF T3EOR2

31 Free Cylindricl Vre

4hen a liuid is flowing out of a tan through a hole at the bottom of the tan free vortex is

formed with the number of oscillation depending on the distortion that created the flow Theliuid is moving spirally towards center following current energy per unit mass is assumedto be constant when energy loss by viscosity is neglected If while the mass of water isrotating the central exit hole is plugged the flow of water in the vertical plane ceases andthe motion becomes one of simple rotation in the horiontal plane This is nown as freecylindrical vortex

-ernoullis theorem can be used because the movement is along the flow axis

=++ z g

V

g

p

2

2

ρ onstant

=or horiontal plane the relation becomes

=+ g

V

g

p

2

2

ρ onstant

Integration of the above relation with r gives

01

=+dr

dV

g

V

dr

dp

g ρ ($)

2ext consider a pair of stream line being divided with distance r δ and is in samehoriontal plane and are lined by a fluid tube wide Aδ The centrifugal force of the tube is

balanced by the pressure difference between both ends that is Ar

dr

dp

gr

V r A g δ δ δ δ ρ sdotsdot=sdotsdotsdot

2

dr

dp

gr

gV =

2 ρ

()

ombine ($) and () to produce

0

2

=+dr

dV

g

V

gr

V

0=+

r

V

dr

dV

Integrate above relation to obtain=+ V r lnln onstant

K vr = (onstant)

r

K V = (1)

In free cylinder vortex velocity is inversely proportional to distance from spiral axis

-ernoullis theorem is used to determine surface profile as follow

4

7232019 FM42 - Manual



C z g

V =+

2

2

(onstant) (3)

6ubstitute (1) into (3)

C z gr

K =+

2

2

2

2

2

2 gr

K z C =minus (amp)

That is euation for hyperbolic curve A yx =2 that is symmetry to axis of rotation and is

horiontal to

32 Free Vre

ovement in free vortex is different with free cylindrical vortex because free vortex

contains radial velocity towards center 8uation for such situation can be generated byconsidering the water passes through round segments towards its diameter where energypassing any tube and is ept constant until

=++ z g

V

g

p

2

2

ρ onstant

If A and V is surface area and velocity of a particular position while 1 A and 1

V are surface

area and velocity at distance r from center circle

== 11V A AV onstant

-y taing Kr A =

r

V r V 11=

If z is constant

C gr

V r

g

p=+

2

2

1

2

1

2 ρ

2

2

1

2

1

2 gr

V r C

g

pminus=

ρ ()

Also

C g

V

g

p=+

2

2

11

ρ

there4

2

2

1

2

1

2

11

22 gr

V r

g

V

g

p pminus=

minus

ρ

minus=

minus2

2

1

2

111

2 r

r

g

V

g

p p

ρ (5)

=ree vortex can be said as combination of cylinder vortex and radial flow Velocity is

inversely proportional to radius in every case Angle between flow axis and radius vector atany point is constant and these axis form the spiral pattern

5

7232019 FM42 - Manual



33 Frced Vre

As we now angular velocity is constantr V ω =

Increase in radial pressure is given by

r r

V

dr

dp 22

ρω ρ ==

int int =2

1

2

1

2 p

p

r

r

rdr dp ρω

)(2

1 2

1

2

2

2

12 r r p p minus=minus ρω (7)

-y taing 01 p p = when 0

1 =r and p p =2 when r r =2

2

2

0

2r

g w

g

p p=

minus

ρ

-ecause h g

p = ρ

so

22

2r

g hh o

ω =minus

22

02

r g

hh ω += ()

This is a parabolic euation

6urface profile for forced vortex can be represented by euation

g

r z

2

22Ω=

9istribution of total head can be represented by euation

g

r H

22Ω=

4hereB 6urface profile

Ω Angular velocityr gtadiusg 0ravitylt Total ltead

Angular velocity can be calculated by


C Angular velocityr gtadius

6

7232019 FM42 - Manual



g 0ravity

0 E4ampERIMENTL ampROCEDURES

41 $eneral Start5- amprocedre

$ lace the study bench on the hydraulic bench

6et up the inlet and outlet hose

1 Adjust the stand of the euipment to reach the horiontal position

7

7232019 FM42 - Manual



42 $eneral S6t5don amprocedre

$ lose the valves and switch off the pump

gtemove the orifices paddle and other accessories from the cylindrical vessel

Ex-er)ent 1 Free Vortex

O$eciampe$ To study on surface profile and speed To find a relation between surface profile and speed

rcedre

$ erform the general startup procedures

8

7232019 FM42 - Manual



6elect an orifice with diameter 3mm and place iton the base of cylinder tan

1 lose the output valve and adjust the inlet 1wayvalve to let the water flows into the tan from two pipes with $amp mm diameterThe water can flow out through the orifice

3 6witch on the pump and open the control valveon the hydraulic bench slowly until the tan limit aintain the water level byadjusting the control valve

amp 4hen the water level is stable collect the vortexprofile by measuring the vortex diameter for several planes using the profilemeasuring gauge

ush down the profile measuring gauge until theboth of sharp point touch the water surface

5 gtecord the measured height h (from the top ofthe profile measuring gauge to the bridge) btain the value of a (distancefrom the bridge to the surface of the water level (bottom level of the cutout))

7 Dse the pitot tube to measure the velocity bysining it into the water at the depth of ampmm from the water surface easurethe depth of the pitot tube in the water lt

gtepeat step 1 7 for another three orifice with diameter $mm $mm and7mm respectively

$ lot the coordinates of vortex profile for all diameter of orifice in graph andcalculate the gradient of graph as shown below

E

4here E is the pressure head + depth of the pitot tube$$ lot graph of velocity which is calculated from the pitot tube reading versus theradius of the profile

V (glt) amp

Theoretically the velocity can be calculated by using the following euation

r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())

amprere3ead 9 De-t6o t6e -tot

te7 4 ())

Ex-er)ent Forced Vortex

O$eciampe$ To study on surface profile and angular velocity To find a relation between surface profile and total head

9

7232019 FM42 - Manual


7232019 FM42 - Manual



The orifices paddle and other accessories should be removed from the cylindricalvessel when not in use

11

7232019 FM42 - Manual



0 $ENERL DESCRIampTION

21 Unt e)l+

The accessory is designed to be positioned on the side channels of the hydraulics benchtop channel

The apparatus consists of a cylindrical vessel having two pairs of diametrically opposedinlet tubes verflow cutouts ensure a constant level in the tan during experiments Asmooth outlet is centrally positioned in the base of the vessel and a set of pushin orificesof various diameters are supplied

The $ampmm diameter inlet tubes which are angled at $amp degrees impart a swirling motionto the liuid entering the vessel and are used as entry tubes for the free vortex experimentThe forced vortex is created by using the mm inlet tubes which are angled at degrees

to the diameter The input from these tubes impinges on a paddle which acts as astirrer+flow straightener The paddle rotates on a stud mounted on a bushed plug insertedin the central orifice

A bridge piece incorporating with measuring needles is used to determine the profile of theforced vortex The needles are set at fixed distances from the side of the tan Thedistances are given below

If the profile of the free vortex is reuired this can be determined by replacing themeasuring needles with a gauge which measures the depth of the vortex at differentdiameters

Velocity heads may be visualied by the insertion of pitot tube in the measuring bridge

22 e)l+ Ve

2

6

1

2

4

3

5

1011

9

7

8

12

7232019 FM42 - Manual












r h

2

22ω



24 S-eccaton





25 $eneral Rere)ent


3

7232019 FM42 - Manual



0 SUMMR2 OF T3EOR2





=++ z g

V

g

p

2

2

ρ onstant


=+ g

V

g

p

2

2

ρ onstant


01

=+dr

dV

g

V

dr

dp

g ρ ($)



dr

dp

gr


2

dr

dp

gr

gV =

2 ρ

()


0

2

=+dr

dV

g

V

gr

V

0=+

r

V

dr

dV


K vr = (onstant)

r

K V = (1)



4

7232019 FM42 - Manual



C z g

V =+

2

2

(onstant) (3)


C z gr

K =+

2

2

2

2

2

2 gr

K z C =minus (amp)


horiontal to

32 Free Vre



=++ z g

V

g

p

2

2

ρ onstant


V are surface


== 11V A AV onstant

-y taing Kr A =

r

V r V 11=

If z is constant

C gr

V r

g

p=+

2

2

1

2

1

2 ρ

2

2

1

2

1

2 gr

V r C

g

pminus=

ρ ()

Also

C g

V

g

p=+

2

2

11

ρ

there4

2

2

1

2

1

2

11

22 gr

V r

g

V

g

p pminus=

minus

ρ

minus=

minus2

2

1

2

111

2 r

r

g

V

g

p p

ρ (5)



5

7232019 FM42 - Manual



33 Frced Vre



r r

V

dr

dp 22

ρω ρ ==

int int =2

1

2

1

2 p

p

r

r

rdr dp ρω

)(2

1 2

1

2

2

2




2

2

0

2r

g w

g

p p=

minus

ρ

-ecause h g

p = ρ

so

22

2r

g hh o

ω =minus

22

02

r g

hh ω += ()



g

r z

2

22Ω=


g

r H

22Ω=






6

7232019 FM42 - Manual



g 0ravity






7

7232019 FM42 - Manual








rcedre


8

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual












r h

2

22ω



24 S-eccaton





25 $eneral Rere)ent


3

7232019 FM42 - Manual



0 SUMMR2 OF T3EOR2





=++ z g

V

g

p

2

2

ρ onstant


=+ g

V

g

p

2

2

ρ onstant


01

=+dr

dV

g

V

dr

dp

g ρ ($)



dr

dp

gr


2

dr

dp

gr

gV =

2 ρ

()


0

2

=+dr

dV

g

V

gr

V

0=+

r

V

dr

dV


K vr = (onstant)

r

K V = (1)



4

7232019 FM42 - Manual



C z g

V =+

2

2

(onstant) (3)


C z gr

K =+

2

2

2

2

2

2 gr

K z C =minus (amp)


horiontal to

32 Free Vre



=++ z g

V

g

p

2

2

ρ onstant


V are surface


== 11V A AV onstant

-y taing Kr A =

r

V r V 11=

If z is constant

C gr

V r

g

p=+

2

2

1

2

1

2 ρ

2

2

1

2

1

2 gr

V r C

g

pminus=

ρ ()

Also

C g

V

g

p=+

2

2

11

ρ

there4

2

2

1

2

1

2

11

22 gr

V r

g

V

g

p pminus=

minus

ρ

minus=

minus2

2

1

2

111

2 r

r

g

V

g

p p

ρ (5)



5

7232019 FM42 - Manual



33 Frced Vre



r r

V

dr

dp 22

ρω ρ ==

int int =2

1

2

1

2 p

p

r

r

rdr dp ρω

)(2

1 2

1

2

2

2




2

2

0

2r

g w

g

p p=

minus

ρ

-ecause h g

p = ρ

so

22

2r

g hh o

ω =minus

22

02

r g

hh ω += ()



g

r z

2

22Ω=


g

r H

22Ω=






6

7232019 FM42 - Manual



g 0ravity






7

7232019 FM42 - Manual








rcedre


8

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual



0 SUMMR2 OF T3EOR2





=++ z g

V

g

p

2

2

ρ onstant


=+ g

V

g

p

2

2

ρ onstant


01

=+dr

dV

g

V

dr

dp

g ρ ($)



dr

dp

gr


2

dr

dp

gr

gV =

2 ρ

()


0

2

=+dr

dV

g

V

gr

V

0=+

r

V

dr

dV


K vr = (onstant)

r

K V = (1)



4

7232019 FM42 - Manual



C z g

V =+

2

2

(onstant) (3)


C z gr

K =+

2

2

2

2

2

2 gr

K z C =minus (amp)


horiontal to

32 Free Vre



=++ z g

V

g

p

2

2

ρ onstant


V are surface


== 11V A AV onstant

-y taing Kr A =

r

V r V 11=

If z is constant

C gr

V r

g

p=+

2

2

1

2

1

2 ρ

2

2

1

2

1

2 gr

V r C

g

pminus=

ρ ()

Also

C g

V

g

p=+

2

2

11

ρ

there4

2

2

1

2

1

2

11

22 gr

V r

g

V

g

p pminus=

minus

ρ

minus=

minus2

2

1

2

111

2 r

r

g

V

g

p p

ρ (5)



5

7232019 FM42 - Manual



33 Frced Vre



r r

V

dr

dp 22

ρω ρ ==

int int =2

1

2

1

2 p

p

r

r

rdr dp ρω

)(2

1 2

1

2

2

2




2

2

0

2r

g w

g

p p=

minus

ρ

-ecause h g

p = ρ

so

22

2r

g hh o

ω =minus

22

02

r g

hh ω += ()



g

r z

2

22Ω=


g

r H

22Ω=






6

7232019 FM42 - Manual



g 0ravity






7

7232019 FM42 - Manual








rcedre


8

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual



C z g

V =+

2

2

(onstant) (3)


C z gr

K =+

2

2

2

2

2

2 gr

K z C =minus (amp)


horiontal to

32 Free Vre



=++ z g

V

g

p

2

2

ρ onstant


V are surface


== 11V A AV onstant

-y taing Kr A =

r

V r V 11=

If z is constant

C gr

V r

g

p=+

2

2

1

2

1

2 ρ

2

2

1

2

1

2 gr

V r C

g

pminus=

ρ ()

Also

C g

V

g

p=+

2

2

11

ρ

there4

2

2

1

2

1

2

11

22 gr

V r

g

V

g

p pminus=

minus

ρ

minus=

minus2

2

1

2

111

2 r

r

g

V

g

p p

ρ (5)



5

7232019 FM42 - Manual



33 Frced Vre



r r

V

dr

dp 22

ρω ρ ==

int int =2

1

2

1

2 p

p

r

r

rdr dp ρω

)(2

1 2

1

2

2

2




2

2

0

2r

g w

g

p p=

minus

ρ

-ecause h g

p = ρ

so

22

2r

g hh o

ω =minus

22

02

r g

hh ω += ()



g

r z

2

22Ω=


g

r H

22Ω=






6

7232019 FM42 - Manual



g 0ravity






7

7232019 FM42 - Manual








rcedre


8

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual



33 Frced Vre



r r

V

dr

dp 22

ρω ρ ==

int int =2

1

2

1

2 p

p

r

r

rdr dp ρω

)(2

1 2

1

2

2

2




2

2

0

2r

g w

g

p p=

minus

ρ

-ecause h g

p = ρ

so

22

2r

g hh o

ω =minus

22

02

r g

hh ω += ()



g

r z

2

22Ω=


g

r H

22Ω=






6

7232019 FM42 - Manual



g 0ravity






7

7232019 FM42 - Manual








rcedre


8

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual



g 0ravity






7

7232019 FM42 - Manual








rcedre


8

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual








rcedre


8

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual












E


V (glt) amp


r

K V =

Da)eter atCentre7 D

())

Meared3e86t7 6

())

amptot Te3ead

Derence7

3 ())


te7 4 ())



9

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual


7232019 FM42 - Manual




11

7232019 FM42 - Manual




11

FM42 - Manual

Documents

Transcript of FM42 - Manual