Measurements of density in flowing air by means of the double-slit interferometer

(1)

Publisher’s version / Version de l'éditeur:

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la

première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.

Questions? Contact the NRC Publications Archive team at

PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

Technical Translation (National Research Council of Canada), 1947-10-01

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

https://nrc-publications.canada.ca/eng/copyright

NRC Publications Archive Record / Notice des Archives des publications du CNRC :

https://nrc-publications.canada.ca/eng/view/object/?id=a9eed062-2459-41a5-960d-37e6341dff08 https://publications-cnrc.canada.ca/fra/voir/objet/?id=a9eed062-2459-41a5-960d-37e6341dff08

NRC Publications Archive

Archives des publications du CNRC

For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.

https://doi.org/10.4224/20331542

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

Measurements of density in flowing air by means of the double-slit

interferometer

(2)

R e f S e r Q21 ~ 2 t

4

no. TT-37 BLDG * I

IXC

PUB COPY NO. ' "

NATIONAL

RESEARCH

COUNCIL

OF

CANADA

DIVISION OF MECHANICAL ENGINEERING

TECHNICAL TRANSLATION NO.

TT

-

37

MEASUREMENTS

OF DENSITY IN FLOWING AIR

BY

MEANS

OF

THE

DOUBLE

-

SLIT

INTERFEROMETER

(

DICHTEMESSUNG MIT HlLFE DES DOPPELSPALT

-

INTERFEROMETERS

)

BY

KLAUS OSWATITSCH

OTTAWA

(3)

N A T I O N A L RESZARCH LABORATORIZS Ottawa, Canada Pages

-

1 7 F i g ,

-

3 TECFITJICAL THAFSLATION D i v i s i o n o f Mechanical E n g i n e e r i n g Tech, Trans, TT-37 Date- k October, 1947 F i l e - 12-R4-22

T i t l e : Dichtemessung m i t H i l f e des Doppelspalt- I n t e r f e r o m e t e r s ,

By: K l ~ u s O s w a t i t s c h

Reference : ~VVB/~l3/1285. Repopt o f the K a i s e r Wilhelm I n s t i t u t e f o r Flow Research, a t t i n g e n , September 28, 1940,

S u b j e c t : Measurements of d e n s i t y i n flowing a i r by means o f t h e d o u b l e - . s l i t i n t e r f e r o m e t e r , Submitted by: WoFo Campbell T r a n s l a t e d by:

Head, H , A , G , Nathan Aerodynamics S e c t i o n Approved by: J , H , P a r k i n D i r e c t o r , The p r e s e n t r e p o r t b e g i n s w i t h a d e s c r i p t i o n of t h e d o u b l e - s l i t i n t e r f e r o m e t e r and a d e r i v a t i o n of t h e i n t e r f e r o m e t e r formula, Following t h a t t h e a p p l i c a t i o n of t h e i n t e r f e r o m e t e r t o measurements of d e n s i t y i n flows i s d i s c u s s e d and the formula i s m o d i f i e d f o r t h i s p a r t i c u l a r purpose, A c a l i b r a t i o n of t h e i n t e r f e r o m e t e r i s e s s e n t i a l ,

The p o s s i b l e s o u r c e s of e r r o r a r e p a r t i c u l a r l y s t r e s s e d , The formulae g i v e n i n t h i s r e p o p t a r e a p p l i c a b l e t o a l l i n t e r f e r o m e t e r s . I n c o n c l u s i o n measurements of d e n s i t y i n a Lava1 nozzle a r e d i s c u s s e d . These aneasuremgnts p e r m i t an i n s i g h t i n t o the accuracy of the measuring method,

(4)

Page ( f i )

Tech, Trans. TT-37

TABLE OF CONTENTS

Pages O p e r a t i o n o f t h e I n t e r f e r o m e t e r

Measurements o f D e n s i t y i n Nozzles and Tunne 1 s

S o u r c e s o f E r r o r and C o r r e c t i o n s

a ) D e f l e c t i o n o f t h e L a b o r a t o r y F l o o r b ) D e n s i t y V a r i a t i o n s o f t h e A i r i n t h e

L a b o r a t o r y

@ ) I n f l u e n c e o f t h e Boundary Layer Along t h e Walls o f t h e Tunnel

d ) Change i n O p t i c a l D e n s i t y o f t h e Glass

Due t o C o o l i n g o f t h e Flow

e ) Dependpace of t h e O p t i c a l D e n s i t y o f

A i r on Y a t e r Vapour Content and Water C o n t e n t f ) R e f r a c t i o n o f L i g h t Rays Measurements o f D e n s i t y i n a Lava1 Nozzle

a )

D e s c r i p t i o n o f t h e P r o c e d u r e i n Making a Measurement

b ) R e s u l t s and Accuracy o f Measurement Summary

(5)

Page

-

1 Tech, Trans,

TT-33

OPERATION OF T H 3 INTERFEROMETSR I n t e r f e r e n c e o f l i g h t i s g e n e r a l l y produced by l i g h t from a luminous p o i n t a r r i v f n g a t a p o i n t , s a y a s c r e e n o r a m i s c r o s c o p e , by two p a t h s , t h e l e n g t h s of which d i f f e r by a few wave-lengths of t h e l i g h t , An i n t e r f e r e n c e image r e s u l t s , and p o i n t s i n t h e image p l a n e a p p e a r e i t h e r b r i g h t o r d a r k , depending on v h e t h e r the l e n g t h s of t h e two p a t h s by which t h e l i g h t t r a v e l s t o t h e image p l a n e d i f f e r by a n even o r odd m u l t i p l e of h a l f t h e wave-length of t h e

l i g h t , I t i s i m p o r t a n t h e r e t h a t l i g h t of u n i f o r m phase, i , e , , s o - c a l l e d c o h e r e n t l i g h t , t r a v e l s from t h e luminous p o i n t i n t h e d i r e c t i o n of t h e ' two l i g h t , p a t h s o The i n t e r -

f e r e n c e a p p a r a t u s a r e g e n e r a l l y d i s t i n g u i s h e d by t h e manner i n which s e p a r a t i o n of t h e l i g h t r a y s which a r e t o cause i n t e r f e r e n c e i s produced,

The problem i s p r o b a b l y s o l v e d most e a s i l y i n a d o u b l e - s l i t i n t e r f e r o m e t e r ( ~ i ~ ,

1 1 ,

The l i g h t from an a r c l i g h t B i s p r o j e c t e d on a s l i g h t l y opened p r e c i s i o n s l i t PS by means of a con- d e n s e r

K O

The p r e c i s i o n s l i t produces a beam of c o h e r e n t l i g h t due t o d i f f r a c t i o n , The p r e c i s i o n s l i t i s imaged i n t h e microscope M by means of t h e l e n s

L o

A t t h e l e n s L a double s l i t DS i s i n t r o d u c e d i n t o t h e l i g h t p a t h , Both openings of t h e double s l i t a r e p a r a l l e l t o t h e p r e c i s i o n s l i t , The l i g h t can e n t e r the microscope o n l y by two p a t h s and produces t h e r e a system of s t r i p s p a r a l l e l t o t h e pre- c i s i o n s l i t , I f w h i t e l i g h t i s u s e d , i , e , , l i g h t of d i f - f e r e n t wave-lengths, then t h e p o i n t s of g r e a t e s t l i g h t i n - t e r - s i t y f o r d i f f e r e n t wave-lengths, i n g e n e r a l , dg n o t co- i n c i d e , Only a t t h e p o i n t t o which t h e l i g h t t r a v e l s on p a t h s of e q u a l l e n g t h , i , e o , t h e maximum of l i g h t i n t e n s i t y

of z e r o o r d e r , does no i n t e r f e r e n c e o c c u r , hence, an abso- l u t e l y w h i t e s t r i p , This i s bounded b y two d a r k s t r i p s w i t h v a r i c o l o u r e d e d g e s , The subsequent maxima and minima of l i g h t i n t e n s i t y a r e more v a r i e d i n c o l o u r and l e s s marked and can be e a s i l y d i s t i n g u i s h e d from t h e p r f n c i p a l maximum, by t h e s e f a c t s a l o n e ,

The double s l i t may b e r e p l a c e d b y two h o l e s , t h e c o n n e c t i n g l i n e of which i s normal t o t h e p r e c i s i o n s l i t ,

The

openings of t h e double s l i t depend on t h e one hand o n l y on t h e shape g i v e n t o t h e l i g h t r a y , which i s s e n t through t h e a i r t o be i n v e s t i g a t e d and, on t h e o t h e r hand, on t h e q u a n t i t y of l i g h t r e q u i r e d i n t h e microscope, The l e n s L

can a l s o b e r e p l a c e d b y a s u i t a b l e concave m i r r o r , However,

i t i s n o t recommended t h a t the microscope be r e p l a c e d b y a p h o t o g r a p h i c p l a t e ,

(6)

Page

-

2

Tech, T r a n s , TT-37

The mounting o f t h e a p p a r a t u s i s e x t r e m e l y s i m p l e , The double s l i t i s removed t e m p o r a r i l y and c a r e i s t a k e n t h a t a c l e a r image of t h e p r e c i s i o n s l i t r e s u l t s .in t h e m i c r o s c o p e , Only then i s t h e d o u b l e s l i t i n s e r t e d , The c o r r e c t o p e n i n g o f t h e p r e c i s i o n s l i t p r o d u c e s , t h e r e u p o n , a n i n t e r f e r e n c e image, The m i c r o s c o p e must be p r o t e c t e d from d i s t u r b i n g s t r a y l i g h t a s f a r a s p o s s i b l e ,

F o r t h e e q u a l i t y of t h e two l i g h t p a t h s i t i s n o t , o f c o u r s e , g e o m e t r i c a l l e n g t h which i s d e c i s i v e , b u t t h e

time r e q u i r e d b y t h e l i g h t t o t r a v e l from t h e p r e c i s i o n s l i t

t o t h e image p o i n t , The t i m e , however, depends on t h e speed o f l i g h t , i , e , , on t h e r e f r a c t i v i t y o f t h e media t r a v e r s e d by t h e l i g h t , I f t h e two l i g h t r a y s a r e s e n t t h r o u g h two

chambers o f d i f f e r e n t r e f r a c t i v i t y t h e n d i s p l a c e m e n t o f t h e i n t e r f e r e n c e image w i l l r e s u l t , S i n c e t h e r e l a t i o n between o p t i c a l d e n s i t y and mass d e n s i t y o f a body i s known, t h e

p o s s i b i l i t y o f a measurement o f d e n s i t y from t h e d i s p l a c e m e n t o f t h e i n t e r f e r e n c e image i s g i v e n ,

Next we s h a l l d e a l w i t h t h e d i s t a n c e of t h e i n d i v i d u a l maxima of l i g h t i n t e n s i t y i n t h e i n t e r f e r e n c e image, i , e , , t h e s o - c a l l e d width o f s t r i p , The m i c r o s c o p e f s assumed t o be r e p l a c e d by a s i m p l e s c r e e n ,

The s e p a r a t i o n o f t h e g a p s o f t h e d o u b l e s l i t i s d e s i g n a t e d by d ( ~ i ~ , 2 ) , t h e d i s t a n c e of t h e double s l i t from t h e image p l a n e b y

,

t h e w i d t h o f s t r i p by V _{and t h e}

mean wave-lerigth of t h e l i g h t b y F u r t h e r m o r e l e t

With t h e assumption (which c a n always b e made) t h a t d 4 &

,

we may w r i t e :

from which it f o l l o w s t h a t

I f t h e r e f r a c t i v i t y o f a medium r e l a t i v e t o a vacuum i s d e s i g n a t e d by Ni, t h e s p e e d o f l i g h t i n t h i s medium by c i and t h e mass d e n s i t y by pi, t h e n t h e f o l l o w i n g

e q u a t i o n s , which a r e known from t h e t h e o r y o f o p t i c s , h o l d t r u e :

(7)

Page

-

3

Tech, Trans, TT-37

Let t h e r e be two chambers, 1 and 2 , of the l e n g t h b i n t h e immediate v i c i n i t y of the double s l i t , One l i g h t r a y i s

assumed t o pass through each of the two chambers, If the same d e n s i t y p l

=

p2 p r e v a i l s i n b o t h chambers, t h e n the maximum of i g h t i n t e n s i t y should be i n the image p l a n e a t

t h e p o i n t

2 =

0, If

p l

f

p2, then t h e maximum of l i g h t i n - t e n s i t y should be d i s p l a c e d by t h e l e n g t h

&

,

The l i g h t must a r r i v e a t t h e maximum l i g h t i n t e n s i t y through b o t h s l i t s

w i t h i n t h e same time i n t e r v a l , I f c l 4 _{cg, t h e n t h e follow-}

i n g e q u a t i o n i s

t m e :

co i s h e r e the speed of l i g h t i n the a i r of t h e l a b o r a t o r y , Because d

4

1 and hence, a l s o

6%

1 we o b t a i n

With s u f f i c i e n t accuracy we may equate No t o u n i t y

i n

t h i s e q u a t i o n and o b t a i n , then, by means of e q u a t i o n (3)

The d e v i a t i o n from t h e z e r o p o s i t i o n I s hence p r o p o r t i o n a l t o t h e a b s o l u t e d e n s i t y v a r i a t i o n i n t h e two chambers, I t i s a l s o p r o p o r t i o n a l t o t h e l e n g t h of chamber b and t o t h e r a t i o

4,

d I n o r d e r t o o b t a i n d a t a on p2, t h e d e n s i t y p1 must be known, I f t h e d e n s i t y i n chamber 2 i s n o t uniform

throughout, o n l y t h e mean densi t y can be measured, and t h e d e n s i t y d i s t r i b u t i o n must be known i n o r d e r t o g i v e t h e den- s i t y a t each i n d i v i d u a l p o i n t , The s e n s i t i v i t y of t h e pro- c e s s i n c r e a s e s with t h e l e n g t h of chamber b ,

I t

a l s o i n -

(8)

Pag.;t

-

4

Tech, Trans, T T - 3 7

I

c r e a s e s w i t h t h e i n c r s a s e of t h e r a t i o

g

,

b u t n o t t o t h e sar,ie s x t e t i t , s i n c e i - l ; must be taken i n t o a c c o u n t t h a t t h e width of s t r i p i n c r e a s e s a t t h e same time, which i s d e t - r i r n e n t a l t o the a c c u r a c y of r e a d i n

_d:

.

N e v e r t h e l e s s , one

should at,ter.lpt. t o make t h e r a t i o

3

a s l a r g e a s p o s s i b l e ; hence, t o keep d t o a minimum and t o remove the image p l a n e

flaom t h e double s l i t as f a r a s p o s s i b l e , i , e , , t o u s e a l e n s of l o n g f o c a l l e n g t h , s i n c e w i t h l e n s e s of s h o r t f o c a l l e n g t h :;nd l ar:;a image d i s tarlce t h e l i g h t i n t e n s i t y o f t h e image i s to6 s m a l l ,

PI

R;;~;AST-~~<T;IL'IT:NTS

OF D5US

I T Y I N NOZZLZS AXD TUNNELS 0

I n o r d e r t o measure t h e d e n s i t y i n n o z z l e s and tunrlels, t h e I n t e r f e r o m e t e r must be mounted i n s u c h a ruarlrler t h a t t h e flow i n f i g u r e 2 i s v i s u a l i z e d as normal t o

t l l e p l s n s of t h e drawing, Two s i d e v ? a l l s o f t h e t u n n e l must be of' g l a s s , a t l e a s t a t t h e p o i n t s wherg t h e l i g h t r a y

t.rsvo12ses t h e t u n n e l , C r y s t a l g l a s s f r e e frorn s t ~ f a a i s e r ~ ~ i r e l y ~ d e q u a t e f o r t h i s p u r p o s e " I n t h i s manner t h e

r;.,ea~i t-ierlsity I s measured on a s t r a i g h t l i n e i n a c r o s s - s e c t i o n a l p l a n e of t h e t u n n e l *

The l i m i t i n g e f f e c t of' t h e d i s t a n c e between

tkl? t;wo l i g h t r a y s proves t o be tlie s o l e d i f f i c u l t y i n u s i n g

t:41e dou.hl.e-slf t i n t e r f e r o m e t e r , However, t h i s l i m i t i n g

eff'e;:.! i s n:?tl $00 s e v e r e , a s w i l l be shown when d i s c u s s i n g

th;. e<:.t:.uracy o f mea.surement ( c o n c l u s i o n of S e c t i o n I V b')

I n general., v~1:at i s of i n t e r e s t a r e t h e d e n s i t y f i e l d s i n

% h e v i c i n f t y of any body i n t r o d u c e d i n t o

the

flow, e , g , , d e n s i t y f i g l d s i n the v i c i n i t y of an a e r o f o i l , boundary SJ~ayel-s a l c n g p l . a t e s c e t c , I n . a l l t h e s e c a s e s the t e s t

b ' s d i e s can be u s e d s i m u l t a n e o u s l y a s comparison chambers by c . o r i s t ~ ~ ~ c t f n p ; therri hollow and by p a - s s i n g t h e l i g h t r a y 1

t i-!.rl 0 1 2 ~ Y L [;hem,

I n o r d e r n o t t o l e t t h e d e v i a t i o n

6

i n c r e a s e t ~ o niuch, it i s recormended t h a t t h e a n t i c i p a t e d approximate d e r i s i t y where t h e measurement i s t o be t a k e n be reproduced i n t;he .;o:;~r:~~.rison chamber and t h e d e v i a t i o n from t h i s an- t i c i p a t e d d e n s f t y o n l y be measured by means of t h e i n t e r - f e r ~ r : ~ e t.er..

Turning now t o t h e d e r i v a t i o n of the d e n s i t y forrnula f o r the a p p l i c a t i o n of t h e i n t e r f e r o m e t e r and keep- int; i n rr,ind t h a t i n t h e r e a d i n g by t h e microscope a

n l f ' i c a t i o n factola o c c u r s i n a d d i t i o n t o t h e q u a n t i t y

(9)

Page

-

5

Tech , T r a n s , TT-37

The f a c t o r A i s t o b e s u b s e q u e n t l y d e t e r m i n e d b y c a l i b r a t i o n , When b e g i n n i n g t o work w i t h t h e i n t e r f e r o m e t e r ,

i t i s m o s t l i k e l y t h a t t h e d e n s i t i e s i n t h e r a n g e o f measurement and i n t h e comparison chamber a r e n o t e q u a l , The com- p a r i s o n d e n s i t y must be d e t e r m i n e d by measurement o f t h e p r e s s u r e p and t h e a b s o l u t e t e m p e r a t u r e

T,

If,

w f ! t h a i r a t r e s t i n t h e t u n n e l , a l l q u a n t i t i e s a r e d e s i g n a t e d b y t h e s u b s c r i p t o, t h e n t h e r e i s a d i s p l a c e m e i ~ t o f s t r i p i n t h e m i c r o s c o p e e v e n b e f o r e i n t r o d u c i n g t h e f l o w Here, R i s t h e a b s o l u t e g a s c o n s t a n t a n d m t h e m o l e c u l a r w e i g h t of t h e a i r , If i n t h e comparison chamber t h e p r e s s u r e t o be a n t i c i p a t e d i s now e s t a b l i s h e d

(wheeh

can be c a l c u l a t e d

from t h e d e t e r m i n a t i o n o f t h e p r e s s u r e p l and t h e temper- a t u r e

%

i n t h e c o m p a r i s o n chamber] and i f t h e

flow

i n t h e t u n n e l i s s t a r t e d t h e n a . d e f l e c t i o n i s o b t a i n e d i n t h e m i c r o s c o p e 2

Only t h e d i f f e r e n c e

5- 6,

c a n b e r e a d i n t h e m i c r o s c o p e . From t h e two e q u a t i o n s above

If t h e v a r i a b l e s d e n o t i n g t h e s t a t e of t h e a i r i n t h e l a b o r a t o r y a r e d e n o t e d by t h e s u b s c r i p t o a l o n e t h e . f o r m u l a ( 5 a ) i s o b t a i n e d f o r t h e f r e q u e n t l y i n v o l v e d v a l u e

82

Po 0 T h i s f o r m d l a i s g e n e r a l l y s i m p l i f i e d b y t h e f a c t t h a t some o f t h e q u a n t i t i e s o c c u r r i n g a r e e q u a l , Above a l l , i n most

(10)

Page

-

6

Tech, T r a n s , TT=.3?

The c a l i b r a t i o n o f t h e i n t e r f e r o m e t e r can b e c a r r i e d o u t i n s u c h a manner t h a t t h e v a l u e s a t t h e s e c o n d p o i n t o f nieasurement a r e l e f t unchanged and v a r i o u s d e n s i t i e s a r e p r o d u c e d i n t h e comparison chamber, The c a l i b r a t i o n

v a l u e s aye d e n o t e d by t h e s u p e r s c r i p t

E,

Then: I f c a r e i s t a k e n t h a t t h e d e f l e c t i o n s

S

-

do n o t become t o o l a r g e i n t h e m e a s u r s m e n t s , t h e n t h e l a s % term o f e q u a t i o n ( 5 ) f s s m a l l as compared w i t h t h e f i r s t t e r m o n t h e r i g h t hand s i d e o f t h e e q u a t i o n , so t h a t , when c a l i b r a t i n g i t i s s u f f i c i e n t l y a c c u r a t e t o w r i t e

I t i s qui?-,e sufficient i f t h e v a l u e

-

i s o b t a i n e d a s a mean Po A

v a l u e of about f i v e c a l i b r a t i o n v a l u e s , I t i s o f cou s e most f a v o u r a b l e f o r c a l i b r a t i n g t o work w i t h d e f l e c t i o n s

cfE

-

8:

ns l a r g e a s p o s s i b l e ,

SOUACZS OF ERROH AND CORRECTIONS,

--=- I f a m i c r o s c o p e o f 50 d i a m e t e r s m a g n i f i c a t i o n i s u s e d i t i s s t i l l p o s s i b l e t o o b s e r v e d i s p l a c e m e n t o f s t r i p s of 0,002 c e n t i m e t r e r e a s o n a b l y w e l l , S i n c e , a s a r u l e , t h e a p p a r a t u s w i l l have a l e n g t h o f s e v e r a l m e t r e s , v i b r a t i o n s o r e l a s t i c d e f l e c t i o n s o f t h e f l o o r may e a s i l y f a l s i f y t h e measurements, P e r c e p t i b l e v i b r a t i o n s o f t h e f l o o r g e n e r a l l y make measursments ~ m p o s s i b l e , T Care m u s t be t a k e n t h a t a l l p e r s o n s who a r e n e a r t h e i n t e r f e r o m e t e r dur-J

m e a s u ~ e m e n t r e m a i n i n one p l a c e from t h e t i m e o f r e a d i n g u n t i l t h e r e a d i n g o f

&

.

(11)

Page

-

7

Tech, Trans, TT-37 b ) D e n s i t y V a r i a t i o n s of the A i r i n the Laboratory,

The i n t e r f e r o m e t e r i s of course very s e n s i t i v e t o t h e s e v a r i a t i o n s ,

In

g e n e r a l , dens1 t y v a r i a t i o n s e a s i l y a r i s e from thermal convection, The mere presence of a p e r s o n i n t h e v i c i n i t y of t h e double s l i t can cause o s c i l l a t i o n s of the i n t e r f e r e n c e image, It i s t h e r e f o r e a d v i s a b l e , even though n o t a b s o l u t e l y n e c e s s a r y , t o conduct t h e l i g h t r a y s through a t u b e , p a r t i c u l a r l y where they a r e a t some d i s t a n c e from each o t h e r ,

c ) I n f l u e n c e of t)h Tunnel.

Boundary l a y e r s which may f a l s i f y the measurements of d e n s i t y o r i g i n a t e along t h e g l a s s w a l l s bounding

t h e flow. The o r d e r of magnitude of t h e r e s u l t a n t e r r o r

w i l l be e s t i m a t e d ,

L e t

T2

be t h e temperature of t h e flow, It

i s

s u f f i c i e n t f o r t h e e s t i m a t i o n t o assume t h a t t h e g l a s s w a l l s have the s t a g n a t i o n temperature T2 of t h e flow, L e t t h e d e n s i t y of the flow be p2 and along t h e g l a s s w a l l s

P;

=

P2

.

I f

6'

i s a measure f o r t h e t h i c k n e s s of the T2

boundary l a y e r and i f l i n e a r i n c r e a s e of t h e a i r d e n s i t y i n t h e boundary l a y e r i s assumed, then t h e mean d e n s i t y of t h e _-

1

boundary l a y e r i s - ( p i

+

p Z ) The mean d e n s i t y of t h e a i r

2

along the l i g h t ray f a then

Hence t h e e r r o r i n t h e measurement of d e n s i t y caused by t h e boundary l a y e r i s of t h e o r d e r of magnitude:

3 ) ~ r a n s l a t o r ~ s Note: The l a t t e r p o r t i o n of t h i s e q u z t i o n appears i n c o r r e c t l y i n the o r i g i n a l document and should r e a d

(12)

Page ' - e;

Tech,, Trans T T - 3 7

ivlier3 LI, as usual r e p r e s e n t s t h e Mach number, I n o r d e r t o be abbe tao escirnate t h e e p r o r , i t i s e s s e n t i a l t o o b t a i n by some means tht: t h i c k n e s s of b o u n d a ~ y l a y e r

i x O

The er3rol- i i v i l l b e of irrpolttancc o n l y i n l o n g narrow t u n n e l s and

w i t h h i g h Eiach rlurnkers,

d l

-

Clmnge l r l O p t i c a l Densf t y of t h e Glass Due t o Coolinq c=.f the Flow,

---= -

Tne g l a s s w a l l s undergo a change

in

t e m p e r a t u r e

due to the a f k flowfng p a s t them, The change i n t e m p e r a t u r e r e s u l t s i n a change of mass d e n s i t y and c o n s e q u e n t l y of t h e o p t i c s 1 d e n s i t y o f t h e Q a s s , The e r r o r t h u s r e s u l t i n g i s

g i v e n

below

, ~ i t h c ~ u t c a l c u l a t i o n f o r a c a s e which o c c u r s f r e q u e n t 1 y o

It i s assumed t h a t t h e t e m p e r a t u r e of t h e

glass remains unchaniged 8.t t h e p o i n t of p a s s a g e o f bight. pay

"

r c A t t1.1e p o i n t of passage of l i g h t r a y 2 a l i n e a r tempera-

t u r c g r a d i e n t i s assumed. t o a r i s e due t o t h e flow, The d i f -

f'zrsrice i n tiemperature between t h e o u t s i d e and i n s i d e of .the {;lass 3s assumed to b e t e n p e r c e n t of t h e d i f f e r e n c e of t.ernperat- re

A T

between .the o u t e r w a l l s f t h e g l a s s and t h a t

of

%he flow, L e t t h e r a t i o s f t h e t h i c k n e s s of t h e two g2;lasszs t c t h e l e n g t h of t h e l i g h t p a t h i n t h e f l o w i n g a i r , i , e , , t o t h e w i d t h o f t h e t u n n e l , be 1:5,

Let

tl?e ~ ~ e f r n c t i v t . ! index o f t h e g l a s s be N

=

1 , 5 0 , t h e t~ernpzrature c o e f f i c i e n t of L i n e a r e:x,onnsion of t h e g l a s s I3

=

0 0 8

loa5

c , g o s , u n i t s , sa cf t h e e r r o r i n t h e d e n s i t y r a t i o ,

a

PoD c x ~ i s e d 139 t ? ; . ~ : expansion of t h e g l a s s be

&ae

Po

It I s k).roved tE!us t h a t the e r r o r can be t o o h f g h t o b e per-

cifssiijle f o r ar!. exact" e a l c u l & t i o n , It i s p r o p o r t i o n a l t o

t.l-:e la a t i o o f t h e th.ickness of g l a s s t o t h e width o f t h e

t u n n e l and t~ tiie c o e f f i c i e n t o f expansion of t h e g l a s s a s

(13)

Page

-

9

Tech, Trans, TT-37 can be reduced by s e l e c t i n g a g l a s s a s t h i n a s p o s s i b l e and w i t h a low temperature c o e f f i c i e n t o f expansion, On account of t h e complicated c o n d i t i o n s o f h e a t conduction i n t h e

g l a s s , i t w i l l be p r e f e r a b l e i n t h e i n d i v i d u a l c a s e t o determine e x p e r i m e n t a l l y t h e e r r o r d e s c r i b e d above by comparing t h e r e s u l t s o b t a i n e d a f t e r v a r i o u s d u r a t i o n s o f flow, A

d u r a t i o n of flow so b r i e f t h a t s t e a d y c o n d i t i o n s

canna6

de- velop i n t h e g l a s s must b e used a s a s t a r t , Another p o s s i b i l i t y

f o r d e t e r m i n i n g t h e e r r o r i s t o observe t h e d e f l e c t i o n

go

f o r v a r i o u s c o o l i n g s of t h e g l a s s

,

The e r r o r can a l s o b e avoided i f con i d e r a b l e c o o l i n g of t h e g l a s s i s p e r m i t t e d . The r e a d i n g of

8

must i n t h a t case be c a r r i e d o u t immediately a f t e r t h e r e a 8 i n g o f

hence w i t h cooled g l a s s w a l l s , I n t h i s manner t h e e r r o r was s u c c e s s f u l l y e l i m i n a t e d i n t h e measurements g i v e n below,

It i s important i n t h i s c a s e t o determine what t e m p e r a t u r e can be a s c r i b e d t o the a i r i n t h e t u n n e l immediately a f t e r c e s s a t i o n of the flow,

e ) Dependence of t h e O p t i c a l D e n s i t y of A i r on Water Vapour Content and Water Content,

Regarding t h e e f f e c t o f water vapour, r e f e r - ence i s made t o t h e formula i n K o h l r a u s c h ~ s Lehrbuch d e r P r a k t f s c h e n Physik, 1 6 t h E d i t i o n , page 2 6 9 , r h i c h i n t h e p r e s e n t n o t a t i o n $s e x p r e s s e d a s

i n which

NL

i s t h e r e f r a c t i v e index of d r y a i r ,

N2

t h e r e - f r a c t i v e index of t h e a i r c o n t a i n i n g water vapour which flows I n t h e t u n n e l and e t h e p a r t i a l p r e s s u r e of t h e water vapour,

The d i f f e r e n c e I n t h e v a l u e of

N2

-

P

(which i s d e c i s i v e f o r t h e measurement of d e n s i t y ) between d r y a i r and t h a t s a t u r a t e d with water vapour a t 20°C and 760 mm, H g

p r e s s u r e i s 9.0 o Accordingly, f o r a v a l u e o f

NL

=

1,000273 t h i s d i f f e r e n c e i s 0,003 o f t h e v a l u e of

N2

-

1,

The water vapour c o n t e n t o f the a i r a f f e c t s a c c u r a t e d e n s i t y measurements o n l y a t temperatures above t h o s e of normal room temperature and a t h i g h humidity of t h e a i r . I n t h i s case t h e water vapour c o n t e n t of t h e compari- s o n chamber would have t o be taken i n t o account,

(14)

Page

-

1P

Tech, Trsans, TT-37

9x1 o r d e r t o s s t f m a t e t h e i n f l u e n c e of w a t e ~ d r c p l e t s e x i s t i r i g I n t h e a i r on t h e o p t i c a l d e n s i t y o f t h e

air.- l t would be i m p o r t a n t t o know t h e s i z e of t h e w a t e r

clro~)$et,s. Hcwevsr, a s a p u l e , i t w i l l be unknown, T h e r e f o r e two extreme c a s e s

will

be e s c i m a t e d , I n t h e f i r s t c a s e i t

1 s assumed t h a t t h e d i a m e t e r o f t h e w a t e r d r o p l e t i s s m a l l as cornpared w f th t h e wave-,length of t h e l i g h t , I n t h e second c a s e l t I s assumed t h a t 618 t h e w a t e r i s c o n c e n t r a t e d f n one P a y e ~ , The v e i o c i t i e s i n w a t e r i n the t w o c a s e s a r e assumed

t s be ?qua1 a r d l i k e w i s e t h e v e l o c i t i e s I n a i r , FOP t h e f i r s t

c a s a t h e L o r e n t z Lorenr law, by which t h e s p e c i f i c r e f r a c t i o n

of a m o l e c u l a r m i x t u r e s q u a l s t h e sum o f t h e s p e c i f i c r e f r a c - t , i o r ~ c r f t h a ~ n d i v f d u a l m i x t u r e components, i s u s e d , I f t h e mass 2s d e s i g n a t e d b y G , w i t h W a s s u b s c r i p t f o r w a t e r and L f o r a f s , t h e n :;he s p e c i f i c r e f r a c t i o n a c c o r d i n g t o Lorentz- ~2 , Lorenz is

%

0 @ and t h e n ~ 2 , 2 P

From t h i s e q u a t i o n a f t e r some t r a n s f o r m a t i o n s and s i m p l f -

ff c a t i o n s

The secand e s t i m a t i o n w i l l now be d e a l t w i t h , L e t t h e volume

o f t h e a i r be

Vg

.-

--

L

'

the volume o f t h e w a t e r

VW

=

9

?old

Pw

%he voluune c P t h e m l x t u r e

V2

=

VL

+

VWo

If

t h e l e n g t h o f t h e

L i g l , t p a t h i n w a t e r 1 s d e n o t e d by

lL

and

dw,

t h e n

4 = JL%

and, a s s o c i a t , l n g a mean velocf t y

c2

w i t h t h e l i g h t when

p a s s i n g t h r o u p g the w a t e r and a i r l a y e r s , the f o l l o w i n g c a n

be wsff t e n

Hc\wever, s l n c e

e2

:

iL

:

ew

=

V2

:

VL

Vw,,

a c c o r d i n g t o e q u a t i o n (2)

(15)

Page 11

Tech, T r a n s , TT-37 Then a f t e r some t r a n s f o r m a t i o n s and s i m p l f f f c a t i o n s ,

The t e r m r e p r e s e n t i n g t h e e r r o r c a u s e d by t h e p r e s e n c e o f w a t e r d i f f e r s

i n

t h e two e q u a t f o n s m e r e l y b y t h e f a c t o r

3

N+

=

0.927, f o r a r e f r a c t i v e i n d e x o f w a t e r NW

=

1,33. 2 N W 9 2

With a g i v e n mean e r r o r i n measurement t h i s f a c t o r i s w f t h o u t s i g n i f i c a n c e , S i n c e p r a c t i c a l l y t h e same r e s u l t was o b t a i n e d f o r b o t h e x t r e m e c a s e s , i t may b e assumed t h a t t h e e r r o r

i n

t h e d e n s i t y measurement, c a u s e d b y t h e p r e s e n c e of w a t e r , i s , i r r e s p e c t i v e o f t h e s i z e o f t h e w a t e r p a r t i c l e , Assuming t h a t a l l t h e w a t e r v a p o u r of s a t u r a t e d a i r a t 20°C and 760 mm, H g a t m o s p h e r i c p r e s s u r e i s condensed b y a d i a b a t i c e x p a n s i o n , an e r r o r o f a l m o s t two p e r c e n t i s o b t a i n e d f o r G ~ / G ~

=

O o O K

f)

R e f r a c t i o n o f L i g h t Raysc I f t h e r e i s a c o n s i d e r a b l e d e n s i t y g r a d i e n t i n t h e f l o w , t h e n t h e l i g h t r a y 2 w i l l u n d e r g o a change o f

d i r e c t i o n due t o r e f r a c t i o n , T h i s change c a n b e e a s i l y ca$- c u l a t e d ; however, t h e r e i s g e n e r a l l y a n a d d i t i o n a l change of d i r e c t i o n due t o a g r a d i e n t o f t h e o p t i c a l d e n a f t y i n t h e g l a s s , T h i s change o f d i r e c t i o n i s i n most c a s e s o p p o s i t e and c a n n o t be c a l c u l a t e d on a c c o u n t o f t h e c o m p l i c a t e d c'on- d i t i o n s of h e a t c o n d u c t i o n i n t h e g l a s s , The e x p e r i m e n t , however, shows t h a t t h e r e f r a c t i o n e v e n w i t h a d e n s i t y g r a - d i e n t o f

3~

&

=

0,s 0

.lom3

c o g , s . u n i t s i s s t i l l s o s l i g h t t h a t t h e i n t e r f e r e n c e image i s i m p a i r e d by i t b u t n o t d e s t r o y e d ,

(16)

Page

.-.

12

Tech,

Trans,

TT-37

a] D o s c ~ i p t l o n o f t h M a k x g Measuremen t o

The a u t h o r used t h e d o u b l e - s l i t i n t e r f e r o m e t e r f o r rneasurements of' d e n s i t y i n a Lava1 n o z z l e , The c r o s s - s e c t i o n of t h e n o z z l e is shown i n f i g u r e 3

in

f u l l

scale^^,

The w i d t h of t h e n o z z l e was b

=

5 cm, t h r o u g h o u t , The arrow IndLcates t h e d i r e c t i o n of t h e flow, ' h e l a b o r a t o r y a i r was draivn through %he n o z z l e i n t o a vacuunl t a n k , U,p.s+;keam from

t h e n o z z l e t h e r e inrere d e v i c e s f o r t h e p r o d u c t i o n o f a3-r of d i f f e r e n t h u m i d i t i e s which w i l l n o t be d e s c r i b e d h e r e , Down.-

s t r a e m from t h e n o z z l e t h e r e was a q u i c k - c l o s i n g s t o p c o c k , O n e h a l f o f a symmetrical n o z z l e was u s e d ana I . t s curved w a l l

was a d j u s t a b l e , The comparison chamber i s deno+.ed by

P,,

It was h e a t . - i n s u l a t e d a g a i n s t r a p i d changes i n t e m p e r a t u r e from

t.he o u t s i d e by a layer: of h a r d r u b b e r o B y means of a p r e s s u r e h o l e i t w8.s p o s s i b l e to produce v a r i o u s d e n s i t i e s i n t h e

colnpai-isctn char~lber and t o measure the p r e s s u r e p r e v a i l f n g

there, A thermocouple was i n t r o d u c e d i n t o t h e chamber f o r m e a s ~ i r i n g t h e t t = m p e r a t u ~ e , A second p r e s s u r e h o l e mads i t

p o s s i b l e t o measure the s t a t i c p r e s s u r e a t p o i n t 3 , A second t~hermacoup1.e was i n t r o d u c e d n e a r t h i s p o i n t i n t o t h e curved ''cheek of tkie nozzlet' ( m s e n b a c k e ) i n o r d e r t o d e t e m f n e a t t h i s p o i n t t41e t m p e r a t u r e e x i s t i n g i n t h e cheek, The

arrangement. des cri.bed made i t possibl.e t o measure p r e s s u r e

and cie3sit.y a t any p a i n t of t h e n o z z l e by means o f one cornc. p ~ r f 3 ~ ~ chainber and one p r e s s u r e h o l e by s h i f t i n g t h e curved

c k i e ~ k of t h e n 0 z z 9 . e ~ Heading by means of a v e r n i e r permit- t e d t h e determina.tior: of d i s p l a c e m e n t s o f t h e cheek of Q,Ql

c e r l t i r n e b ~ e

.

The doub1.e s l i t c o n s i s t e d of two s q u a r e h o l e s with s3.des approxirnate1.y 0,18 c e n t i r n e t ~ e , The c e n t ~ e s of tihe t.wo h o l e s w e r e a p p r c x i m a t e l y 0,9 c e n t i m e t r e a p a p t , The double s l l t fsshowrl i n t h e f i g u r e by d o t t e d l i n e s , Care w a s t a k e n t h a t the l f n e j o f n f n g h o l e 2 of t h e double s l i t ,

l ~ i t l i the

hole

f o r the s t a t i c p r e s s u r e was e x a c t l y normal t o t h e p l a n e cf!eek of the n o z z l e , how eve^, t h i s by no m e a n s g ~ a r ~ a ; ~ t . e e s measurements of d e n s i t y and p r e s s u r e a t

the same p o i n t , On %he c o n t r a r y , i t sho:va t h a t f o r e x a c t meas?lrernt>nt;s i.n s u c h a s h o r t n o z z l e D c o n s t a n t v a l u e s o f

:i.ensFt.y and p r e s s u r e o v t h e c r o s s - s e c t i o n cannot be ~

assurfled, POP t h e measurements a c u r v a t u r e c o r r e c t i o n : , based on t h e assumption t h a t the s t r e a m l i n e s d e c r e a s e d l i n e a r l y from t h e curved t o the p l a n e cheek o f ' t h e n o z z l e , w a s f n t p o - ducsd f'or t h e d e t e m f n a t i o n of t h e mean d e n s i t y and mean

I e s s u r e , _---,._=- _-_-_-_- This c a l c u l a t f o n wf 11 n o t be c a r r i e d o u t h e r e s f n c e

-

-1) T r a ? ; s l a t o r Q s Note: The f f g u r e a s shown h a s been e n l a r g e d from m i c r o f i l m and r e - drawn and p r o b a b l y df f f e r s i n size from t h e o r i g i n a l r s f e r r e d t o ,

(17)

Page

-

1 3 Tech, T r a n s , TT-37 i t i s n o t a c a s e of i n t e r f e r o m e t e r c o r r e c t i o n b u t r a t h e r one of t h e e r r o r r e s u l t i n g from t h e a p p l i c a t i o n of t h e one- d i m e n s i o n a l n o z z l e t h e o r y t o s h o r t Lava1 n o z z l e s , An a r c l i g h t of 20 amperes a t 220 v o l t s was used as l i g h t s o u r c e , I t s l i p a t was p r o j e c t e d on a p r e c i s i o n

s l i t by means of a condenser, A l e n s of two m e t r e s f o c a l

length

produced an image of t h e p r e c i s i o n s l i t i n a mfcro- scope o f 50 d i a m e t e r s m a g n i f i c a t i o n , The d i s t a n c e between double s l i t and microscope was a p p r o x i m a t e l y s i x . l e t r e s o A s c a l e having 50 d i v i s i o n s was i n the o c u l a r of tne microscope; one d i v i s i o n t h e r e b y c o r r e s p o n d i n g t o 1/50 m i l l i m e t r e

,

The d i s t a n c e between two maxima of l i g h t i n t e n s i t y amounted t o approximately 1 9 d i v i s i o n s , a s can b e e a s i l y c a l c u l a t e d from formula ( I ) , With t h i s l a r g e width of s t p i p

i t

would n o t be e a s y t o r e a d w i t h accuracy t h e c e n t r e of a maximum of l i g h t i n t e n s i t y , The edges of t h e f i r s t two maxima of l i g h t i n -

t e n s i t y , however, showed a marked t r a n s i t i o n from a d e f i n i t e r e d t o a d e f i n i t e b l u e which was p a r t i c u l a r l y c h a r a c t e r i s t i c ,

A t t h i s p o i n t t h e r e a d i n g s were taken, This can be done d i r e c t l y , s i n c e , with a change i n d e n s i t y , t h e e n t i ~ e system o f s t r i p s shows a uniform d i s p l a c e m e n t ,

I t was p o s s i b l e t o r e a d one d i v i s i o n with

a c c u r a c y o which appeared i n t h e measurement due

t o t h e ready::

:rfrT

and

go

t h e r e f o r e amounted t o n o t more

t h a n one d i v i s i o n , i , e , , approximately

-

1 f & = 5 , 7 0

loa5

em,

20°

and No

-

1

=

2.9

l o n 4 $

t h i s r e s u l t s a c c o r d i n g t o formula ( 4 ) i n an i n a c c u r a c y of t h e d e n s i t y v a l u e s

By comparison with t h i s , the t e m p e r a t u r e and p r e s s u r e read- i n g s may b e c o n s i d e r e d completely a c c u r a t e , It i s obvious t h a t t h e p e r c e n t a g e e r r o r i n t h e deteqxnination of

g

i n - c r e a s e s f o r s m a l l e r d e n s i t y r a t i o s Po

The comparison chamber was on the one hand connected with a c o m p a r a t i v e l y l a r g e g l a s s s p h e r e and on t h e o t h e r hand w i t h t h e o u t e r a i r b y a three-way cock, The

volume of t h e g l a s s s p h e r e was l a r g e compared with t h a t o f t h e chamber, A mercury manometer was connected t o t h e g l a s s s p h e r e o B y means of a w a t e r - j e t vacuum pump t h e d e n s i t y

d e s i r e d i n t h e chamber could be p ~ o d u c e d in t h e s p h e r e , This d e n s i t y underwent o n l y a s l i g h t change when the chamber was connected w i t h t h e g l a s s s p h e r e ,

(18)

Page

-

14

Tech, T r a n s , TT-37

Durl-ng t h e r e n d i n g of

go

t h e chamber was con- n e c t e d w i t h t h e o u t s i d e air, Hence, plo

=

po

=

pZo was t o be s u b s t i t u t e d i n , sqi.xation ( 5 a 1 , Furthermore, i t became

evideizt t h a t w i t h the f l ~ i l r b r o u g h t t o a s t a n d s t i l l , t h e a i r between t h e cheeks of t h e n o z z l e assumed t h e t e m p e ~ a t u ~ e of

t h e s e w i t h i n one second, I t was p o s s i b l e t o d e m o n s t r a t e t h i s b y mornerlt,ariby s w i t c h i n g the flow on and o f f , I n t h i s way a i r or" t h e t..eraperature To came between t h e cheeks, A

s m a l l deflection, whfch became e v i d e n t i n t h e microscope,

d i s a p p e a ~ ed ;dtT-lin one aecond, The t e m p e r a t u r e T20, t h e r e f o r e , was t o b e eq-uat.ed t o t h e ternperature measured i n t h e cheek of

t h e n o z z l e a t p o i n t 3 ,

Measurel~ient was c a r r i e d o u t i n t h e f o l l o w i n g manner, Each day on ~ J ' r ~ i c h measurements were t a k e n , t h e i n t e r -

f e r o m s t e r was, flr?lst o f a l l g c a l i b r a t e d by a d j u s t m e n t o f v a r i o u s d e n s i t i e s i n the comparison chamber and b y r e a d i n g

t h e a p p ~ o p r i a t e d e f l e c t i o n s , There was no df f f i c u l t y i n o b t a i n i n g s u f f i c i e n t a c c u r a c y when c a l i b r a t i n g ,

For t h e measurement i t s e l f two p e r s o n s were

always r e q u i r e d , one f o r r e a d i n g the d e f l e c t i o n s i n t h e m i c ~ o - scope and t h e o t h e r one f o r o p e r a t i n g t h e manometers and

r e a d i n g t h e galvanometers of t h e two thermocouples, F i r s t , t h e a r c l f g h t was s w i t c h e d on and t h e curved cheek of t h e n o z z l e was screwed t o t h e p o i n t d e s i r e d , The a i r d e n s i t y

a1iticipat;ed d u r i n ~ t h e rncasurement was o b t a i n e d i n t h e g l a s s s p h e r e by e v a c u a t i o n , Then everyone g o t t o t h e p l a c e a s s i g n e d t o him and was n o t permitted t o l e a v e

i t

b e f o r e t h e c o n c l u s f o n

o f t h o me a s l ~ r e n l e n t , I n t h e b e g i n n i n g t h e comparison chamber was connected t o r-hs o u t s i d e a i r i n o r d e r t o make s u r e o f t h e q u a l i t y of the i t l t e r f e r e n c e image i n t h e microscope, Follow- i n g t h a t , t h e flow was swftched on by means of t h e quick- a c t i n g cock and t h e c o r n p o ~ i s o n chamber a t t h e same time con-

n6cted t o t h e glass s p h e r e o I n t h e microscope the i n t e ~ f e r e n c e image was g e r l e r a l l y d i s p l a c e d by s e v e r a l d i v i s i o n s a n d m a ~ ~ r a t h e r i n d i s t i n c t , Durfng t h e f i r s t seconds a n o t h e r d i s p l a c e m e n t of

t h e image by s e v e r a l d i v i s i o n s o c c u r r e d due t o c o o l i n g of t h e g l a s s , A f t e r t h e n t e r f e r e n c e image had become s t a t i o n a r y , t h e d i s p l a c e m e n t

$

was r e a d i n t h e microscope and, a t t h e same time, t h e mel-cury manometers were b l o c k e d by means o f g l a s s cocks, Immediately a f t e r t h a t , t h e flow was b r o u g h t t o a s t a n d s t i l l by c l o s i n g t h e q u i c k - a c t i n g cock and t h e comparison o h m b e r was a t t h e same time connected t o t h e o u t s i d e a i r , 'rNhilst one o f the a t t e n d a n t s s p e e d i l y r e a d t h e d e f l e c t i o n

&

i n t h e microscope, the o t h e r one watched t h e d e f l e c t i o n s o? t h e two galvanometers, A f t e r r e c o r d i n g t h e s e ,

(19)

Page

-

1 5

Tech, Trans, TT-37 With some p r a c t i c e t h i s manner of r e a d i n g was e a s i l y c a r r i e d o u t , Importance u s t be a t t a c h e d t o q u i c k s u c c e s s i o n of t h e two r e a d i n g s $and Jo i n o r d e r t o p r e v e n t t o o l a r g e changes i n t h e o p t i c a l e e n s i t y of t h e g l a s s , Speedy r e a d i n g o f t h e galvanometers i s l e s s importarit, s i n c e t h e i r d e f l e c t i o n s do n o t change a s r a p i d l y and t h e e r r o r s caused by them a r e s m a l l e r ,

I f t h e c o o l i n g of t h e g l a s s had n o t been t a k e n i n t o account i n t h e measurement under c o n s f d e r a t i o n , t h e e r r o r a t Mach number

M

= 1 , 6 ' would have amounted t o 3 p e r c e n t o f t h e v a l u e of

,

"0

b ) R e s u l t s and Accuracy of Measurement,

The r e s u l t s of t h e s e measurements a r e given below, P r e s s u r e and d e n s i t y measurements were c a r r i e d o u t a t a temperature of 17OC i n t h e l e - b o r a t o r y with r e l a t i v e h u m f d i t i e s of 0, 4 0 , 75 and 90 p e r c e n t , With d ~ y a d i a b a t i c e x p a n s i o n

of the a i r , t h e d e n s i t y v a l u e s a r e now w e l l s u i t e d f o r t h e an-

a l y s i s of t h e q u a l i t y of t h e i n t e r f e ~ o n e t r i c t e s t procedure, s i n c e d e n s i t y values, which a r e o b t a i n e d by c a l c u l a t i o n f r o m t h e

a

; a t i c p r e s s u r e measurements by assuming a d r y a d i a b a t i c e x p a l s i o n , can be used f o r comparison, I n a r e p o r t t o be p u b l i s h e d s h o r t l y t h e a u t h o r w i l l show t h a t m o i s t a i r a l s o expands i n a d r y a d i a b a t i c manner i n s h o r t n o z z l e s a t

M <

9,

For M

7

l, on t h e o t h e r hand, t h i s can g e n e r a l l y n o t be

claimed, I n t h i s case c o n d e n s a t i o n phenomena a r e encountered, and d e n s i t y measurements of m o i s t a i r i n t h i s r e g i o n a r e t h e r e - f o r e no l o n g e r of i n t e r e s t h e r e , s i n c e t h e r e a r e no p o s s i b i l f t i e s f o r comparisons t o p e r m i t an a n a l y s i s of t h e i r n u a l i t y , The d e n s i t y v a l u e s f o r m o i s t a i r i n t h e r e g i o n

lV

,>.

1,

measured by i n t e r f e r o m e t e r , a r e n o t i n c l u d e d i n the t a v l e below,

In

t h e r e g i o n M L 1, t h e r e i s no d i f f e r e n c e i n t h e r e s u l t s o f d e n s i t y measurements of d r y and m o i s t a i r ( w i t h i n measuring' a c c u r a c y ) ,

The f i g u r e s i n t h e f i r s t column of t h e t a b l e i n d i c a t e d i f f e r e n t p o s i t i o n s o f t h e curved cheek of t h e n o z z l e i n m i l l i m e t r e s , The f i g u r e s i n t h e second column r e p r e s e n t

.the v a l u e s f o r ;;)f m a t h e m a t i c a l l y c a l c u l a t e d from t h e n o z z l e

dimensions by assuming d r y a d i a b a t i c expansion w i t h o u t boundary l a y e r s . The d e n s i t y v a l u e s

(e)

,

o b t a i n e d from s t a t i c

Po ad

p r e s s u r e measurements by assuming d r y a d i a b a t i c expansf on, a r e compiled i n column 3 , The d i f f e r e n c e between t h e s e two

(20)

P a g e

-

15 Tech. Trans. TT-37 v a l u e s i s a t t r i b u t e d t o t h e p r e s e n c e o f a boundary l a y e r , Colurrins 4-7 g i v e tk:s v a l u e s f o r v a r i o u s r e l a t i v e d e n s i t i e s

_-

a s o b t a i n e d by i n t e r f e r o m e t e r , T h e i ~ mean v a l u e

L=

is g i v e n P o

i n column 8, The mean e r r o r f o r each i n d i v i d u a l n o z z l e p o s i t i o n

A E

i s sholTm i n column 9 and t h e mean e r r o r f o r

Po

t h z f i r s t s e v e n n o z z l e p o s i t i o n s i n column 1 0 , F i n a l l y t h e a p p r o p r i a t e Mach numbers a r e g i v e n i n column 11, Each of t h e d a t a g i v e n was o b t a i n e d b y one i n d i v i d u a l measurement, t a k i n g i n t o a c c o u n t t h e c u r v a t u r e c o r r e c t i o n mentioned. above, I t was s'iown i n s z c t i o n 3 ( a and d ) how t h e e r r o r s a and d car1 b e a v o i d e d , A c c o r d i n g t o t h e f o m i u l a s g i v e n above, t h e o t h e r e r r o r s a r e s m a l l e r t h a n t h e i n a c c u r a c y o f t h e p r e s e n t r e s u l t s Lnle t o u n c e r t a i n t i e s i n t h s m i c r o s c o p e r e a d i n g ,

T h e

ewer

i n nzcasx~rement i s tlslus d e f i n i t e l y w i t h i n t h e l i m i t s which were t o b e e x p e c t e d i n a c c o r d a n c e w i t h t h e e s t i m a t i o n i n S e c t i o n

IVa,

(21)

Page ' 2 l ?

Tech, T ~ a n s , TT-37 The L a v a l n o z z l e

,,

employed i n t h e measurements =

i s f a v o u r a b l e f o r t h e a p p l i c a t f on o f t h e i n t e r f e r o m e t e r i n a s

-

much a s i t was p o s s i b l e t o k e e p t h e d o u b l e s l i t d i s t a n c e d q u i t e s m a l l . On t h e o t h e r hand t h e L a v a l n o z z l e i s e x t r e m e l y u n f a v o u r a b l e a s to l e n g t h of t h e l i g h t r a y b

-

5 cm, i n t h e a i r t o b e i n v e s t i g a t e d , I t 1s t h e r e f o r e p o s s i b l e t o o p e r a t e w i t h t h e same a c c u r a c y a s h e r e i n a t u n n e l of 50 c e n t i m e t r e s w i d t h w i t h a d i s t a n c e of l i g h t r a y d

-

P O

cm, I n somewhat l e s s a c c u r a t e measurements t h e t e m p e r a t u r e measurements may,

as a r u l e , b e o m i t t e d , p a r t i c u l a r l y when o p e r a t i n g w i t h lVIach n u ~ b e r s M

(

1, The d o u b l e - s l i t i n t e r f e r o m e t e r i s h e n c e a r e l a t i v e l y s irnple and a c c u r a t e a i d f o r t h e d e t e r m i n a t i o n o f d e n s i t y i n f l o w , V SUMMARY I n t h e d o u b l e - s l i t i n t e r f e r o n i e t e r t h e d e n s i t y i s measured from t h e d i s p l a c e n z e n t s of a n i n t e r f e ~ e n c e image, T h i s image o r i g i n a t e s froni i n t e r f e r e n c e o f two l i g h t r a y s conducted p a r a l l e l t o e a c h o t h e r ; one o f ivhich i s c o n d u c t e d t h r o u g h t h e a i r t o be i n v e s t i g a t e d and t h e o t h e r one t h r o u g h a i r w i t h d e n s i t y known, The a c c u r a c y o f t h e m e a s u r i n g pro- c e d u r e depends on t h e d i s t a n c e between t h e two l i g h t r a y s , The e r r o r i n measurement i s g e n e r a l l y v e r y s l i g h t , I n t h e example o f measurements of d e n s i t y i n a L a v a l n o z z l e , q u o t e d

i n t h i s r e p o r t , t h e mean e r r o r amounts t o l e s s t h a n two p e r t h o u s a n d , The i n s t r u m e n t i s p a r t i c u l a r l y s u i t a b l e f o r p o i n t - b y - p o i n t measurements of t w o - d i m e n s i o n a l d e n s i t y f i e l d s i n t h e v i c i n i t y of t e s t p i e c e s , I t Is w r t h m e n t i o n i n g t h a t t h e d o u b l e - s l i t i n t e r f e r o m e t e r can be o b t a i n e d a t Pow c o s t and i s e a s y t o mount,

(22)

F ! C I . 2 , 3 TECt-I: P A N S TT-37 C PS

I$:+--

--

- - -

-

- 4

- - - -

--:-ors

_{- -}

I-

-

- - L

F i g . 1: D o u b l e - ~ 1 l t i n t e r f e r o m e t e r . 1 2

8

c:r 0 L -

-

- - - a - - -

- -

d - - - - - - - - _ _ - - - - - - - - i - -

qi

1 - - -

-4

1 F i g , 2 : A r r a n g e m e n t o f t h e chambsrs I n t h e i n t e r f 9 r o r n e t e r .

1 3 ,

/ i F i g . 3: L o n g i t u d i n a l s e c t i o n t h r o u g h n o z z l e a n d chamber,

.