Torsion balance as a micromanometer

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Torsion balance as a micromanometer

Reichardt, H.

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R e f S e r 421

~ 2 t 4

no.

TT-84

BLDG IRC PITI3 COPY NO. ,,

NA'TIONAL

RESEARCH

COUNCIL

OF

CANADA

DIVISION OF MECHANICAL ENGINEERING

'TECHNICAL TRANSLATION NO. TT

-

8 4

THE TORSION BALANCE AS A MICROMANOMETER

( DIE TORSIONSWAAGE ALS MIKROMANOMETER )

BY H. REICHARDT

OTTAWA

NATIONAL RESEARCH LABORATORIES Ottawa, Canada T E C H N I C A L TRANSLATI ON D i v i s i o n of Mechanical E n g i n e e r i n g Pages

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P r e f a c e

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2

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Text

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18 F i g u r e s 5 Tech, Trans. TT-84 Date

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13 November, 1948, Lab, Order No,

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54248 Fl.le

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12-R4-22

T i t l e : Die Torsionswaage a l s blikr40manome t e r . By ,O H, R e i c h a r d t

R ~ f e r e n c e : Z e i t s c h r i f t f u r I n s trurnentenkunde, Vol, 55 ( 1 9 3 5 ) , pp, 25-33,

S u b j e c t : THE TORSION BALANCE AS A MICROMANOMETERo

Submit.ted by: VJo F, Campbell, T r a n s l a t e d by: He ad, D o A , S i n c l a i r Aerodynamics L a b o r a t o r g ,

Approved by: J o K O P a r k i n ,

Page ( i f ) Tech, Trans, TT-84 TABLE OF C O N T E N T S Page A , I n t r o d u c t i o n 1 B. Known F l ~ w Manometers 1 C, The P r i n c i p l e of t h e P i s t o n wf t h S i d e Clearance 3

D o General Conditions f o r t h e Applf- c a t i o n and Design of P r e s s u r e

Balances w i t h F r e e l y Moving P i s t o n s 5 1, D e t r i m e n t a l P r e s s u r e Drop 5 2, P e r i o d of O s c i l l a t f o n and Ad-

justment Time c f t h e System 7 3 , E f f e c t of t h e Flow i n t h e S l i t on t h e Turning F4omen.t 1 0 4 , P i s t o n Shapes, S l i t Dimensions 11

E.

D e s c r i p t i o n of a Complete Micro- p r e s s u r e Balance f o r hfleasurements o f P r e s s u r e D i f f e r e n c e s f n Gases 13 Summary 17

Page

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1

Tech, Trans, TT-84 THE TORSION B A L A N C E A S A MICROMANOlVIETER

I N TRO DU C T I ON

The micromanometer d e s c r i b e d i n t h i s n o t e was developed i n connection wfth i n v e s t i g a t i o n s i n t o t h e e f f e c t of h e a t s t r a t i f i c a t i o n on t u r b u l e n c e , I n the course of these in- v e s t i g a t i o n s i t was necessary t o determine t h e p r e s s u r e

g r a d i e n t i n a t u n n e l one metre wide and 0,25 metre h i g h a t v e l o c i t i e s of l e s s than 2 metres per second, The p r e s s u r e d i f f e r e n c e s t o be measured were of the o r d e r of mrn, of water and l e s s , For t h e s e measurements t h e r e f o r e , a mano- meter with a minimum s e n s i t i v i t y of

lon4

mm. of water was r e q u i r e d ,

S i n c e the f a m i l i a r l i q u i d micromanometers do n o t possess such s e n s i t i v i t y a n o t h e r manometric p r i n c i p l e had

t o be employed, A t f i r s t t h e c o n s t r u c t i o n of a flow manometer was considered (Fig. 1 )1), Since the t o r s i o n balance p r i n c i p l e may be a p p l i e d i n t h i s type of manometer, very g r e a t s e n s i -

t i v i t i e s can be a t t a i n e d , ~ e i s z ) , f o r example, has designed a flow manometer u s i n g a t o r s i o n f i b r e of 2P t h i c k n e s s , which possesses a s e n s i t i v i t y of approximately

l o n 7

mm, of water, However, t h e flow manometers have s e r i o u s disadvantages and

t h e r e f o r e have seldom been employed,

I n o r d e r t o avoid some of t h e e s s e n t i a l f a u l t s of the flow manometer the a u t h o r has developed an arrange- ment which, i n p r i n c i p l e , r e p r e s e n t s a t o r s i o n p r e s s u r e balance ( ~ o r s i o n s - ~ r u c k w a a g e ) , A t o r s i o n p r e s s u r e balance with r o t a r y p i s t o n was presented and d e s c r i b e d by t h e a u t h o r a t t h e Aerbodynamics Convention i n Goettingen on t h e 6 June,

1933, The p r e s e n t work g i v e s more d e t a i l e d d a t a concerning

the c a l c u l a t i o n , design and p o s s i b l e a p p l i c a t i o n s of the new i n s t m e n t ,

B,

KN

OVIrN FLOW NIAN OM@

TE

RS

I n the flow manometer ( F i g , 1) a flow i s pro- duced by the p r e s s u r e d i f f e r e n c e which i s t o be measured, p

-

po, This flow s t r i k e s an o b s t a c l e , H, and e x e r t s a

f o r c e on i t , I n the known flow manometers t h i s f o r c e i s m e a s u r e d b y means o f a t o r s i o n balance,

1) This i s t h e type of manometer ap- p a r e n t l y r e f e r r e d t o by Edelmann i n Zei t s c h r , f , Ohrenheilkunde 56,

p , 335, 1908,

2 ) Hefs, Physikal, Z e i t s c h r , 25,

Page

-

2

Techo Trans, TT-84

I f t h e flow v e l o c i t y i s n o t t o o s m a l l t h e f o r c e . a c t i n g on H i s p r o p o r t i o n a l t o t h e impulse g i v e n by t h e flow emerging from t h e blow-pipe, R , L e t

P

-

the f o r c e a c t i n g on the o b s t a c l e A p = p

-

P . ~

-

p r a s s u r e d i f f e r e n c e

4

-

l e n g t h o f blow-pipe r

-

r a d i u s o f blow-pipe

w

-

mean flow v e l o c i t y i n t h e blow-pipe ( P o i s e u i l l e )

k

-

v i s c o s i t y o f t h e flowfng medium p

-

d e n s i t y of t h e f l o w i n g me d i m ,

The f o l l o w i n g t h e n a p p l i e s f o r the "impulse manometerft3):

( F o r t h e p r e s s u r e d i f f e r e n c e s i n u e s t i o n t h e flow i n t h e blow-pipe i s l a m i n a r , ) E q u a t i o n

?

1 ) a p p l i e s t o a f l a t s u r - f a c e , H, which r e c e i v e s t h e e n t i r e impulse,

A t v e r y low flow v e l o c i t i e s t h e f o r c e a c t i n g on H i s determined e s s e n t i a l l y by t h e i n t e r n a l friction o f t h e flowing medium, H then a c t s a s a S t o k e s body o f r e s i s - t a n c e , and t h e f o r c e P i s p r o p o r t i o n a l t o w o r t o A p, An e x a c t mathematical t r e a t m e n t o f the ' r e s i s t a n c e manometer" p r e s e n t s s e r i o u s d i f f i c u l t f e s , and i t i s n e c e s s a r y t o d e t e r - mine t h e s e n s i t i v i t y e x p e r i m e n t a l l y , I n E d e h a n n s flow manometer t h e d e f l e c t i o n s a r e p r o p o r t i o n a l t o Ap f o r A p

<

0,02 mrn, w a t e r ( Z e i t s c h r . f . Ohrenheilkunde 56, p , 348, 1908). F o r A p

>

0,02 m, w a t e r t h e d e f l e c t i o n s i n c r e a s e w i t h t h e p r e s s u r e d i f f e r e n c e more than l i n e a r l y , y e t n o t q u a d r a t i c a l l y , Thus, f o r Ap

<

0,02 mm, water Edelmannqs i n s t r u m e n t a c t s a s a r e s i s t a n c e manometer, whereas a t g r e a t e r p r e s s u r e s (0,02

<

A p

<

0,13 mm, w a t e r ) t h e

~ a n d b u c h d e r Experfmentalphysik, IV,

P a r t 1, p , 542). I n B e t z f s fornlula t h e f a c t o r 4/3 has b e e n omf t t e d by m i s t a k e ,

Page

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3

Tech, Trans, TT-84 HeisC manometer a c t s e n t i r e l y a s a r e s i s t a n c e S i m i l a r l y t h e arrangements d e s c r i b e d b y G e r l a c h and Z $ F g T O r e p r e a e n t r e s i s t a n c e manometers.

Among o t h e r d i s a d v a n t a g e s o f t h e flow mano- m e t e r s i s t h e s e r i o u s one t h a t t h e i r f u n c t i o n i n g depends on

t h e e x i s t e n c e o f a flow, Consequently, very u n d e s i r a b l e p r e s - s u r e g r a d i e n t s o c c u r i n t h e probes and c o n n e c t i n g t u b e s , If e i t h e r t h e p r e s s u r e t a p s o r c o n n e c t i n g t u b e s a r e narrow,

i t

i s p o s s i b l e t h a t o n l y a f r a c t i o n of t h e p r e s s u r e d i f f e r e n c e t o b e measured w i l l l i e a c r o s s t h e manome t e r , To l i m i t t h e d e t r i m e n t a l p r e s s u r e l o s s i t i s n e c e s s a r y t o employ probes and c o n n e c t i n g t u b e s , t h a t a r e a s s h o r t and of a s l a r g e diameter a s p o s s i b l e t o g e t h e r w i t h a very narrow blow-pipec A r e d u c t i o n i n t h e amount o f flow through t h e manometer, how- e v e r , n e c e s s i t a t e s an i n c r e a s e i n t h e s e n s i t i v i t y o f t h e t o r s ion balance.

C 0 THE PRINCIPLE OF

THE

PISTON WITH SIDE CLEARANCE .a,

I n s t e a d o f producing a flow by means o f t h e p r e s s u r e d i f f e r e n c e t o be determined and measuring t h e f o r c e of t h i s flow, i t i s more advantageous, f o r v a r i o u s r e a s o n s

( s e e below), t o measure t h e p r e s s u r e d i f f e r e n c e df r e c t l y o This i s done wf t h t h e a p p a r a t u s shown i n F i g u r e 2 0

The p r e s s u r e d i f f e r e n c e t o be measured a c t s on a p i s t o n which i s s i t u a t e d i n a c y l i n d e r , The d i a m e t e r of t h e p i s t o n i s somewhat s m a l l e r t h a n t h e i n n e r d i a m e t e r o f t h e c y l i n d e r , Hence t h e p f s t o n i s n o t o n l y f r e e t o move i n the d i r e c t i o n o f t h e c y l i n d e r a x i s , b u t a l s o h a s some s i d e c l e a r a n c e , The a n n u l a r s l i t between t h e p i s t o n and t h e

c y l i n d e r i s e n t i r e l y f i l l e d by t h e medium f n which the p r e s - s u r e d i f f e r e n c e i s t o b e measured5). S f n c e t h e r e i s no

packfng be tween t h e p i s t o n and t h e c y l i n d e r , u n c o n t r o l l a b l e f o r c e s , which under c e r t a i n c i r c u m s t a n c e s might be s e v e r a l

_-

a r e avoided, The t e c h n f s c h e phyiik: 10, p, 457, -1929, When t h e a u t h o r gave h f s p a p e r on t h e p r e s s u r e b a l a n c e w i t h a f r e e l y moving p i s t o n a t t h e G o e t t i n g e n Aerodynamics Convention he d i d n o t know t h a t t h e p r o i n c f p l e o f t h e p i s t o n wf t h f r e e p l a y had been u s e d p r e v i o u s l y , I n 1925 Creed and O r l i n g a p p l i e d f o r a p a t e n t on a c o n t r o l a p p a r a t u s w i t h a " f l o a t - i n g p i s t o n t t ( ~ r i t i s h P a t e n t S p e c f - f i c a t f o n 265071; 1927),

Page

-

4

Tech, T r a n s , TT-84

p i s t o n i s a t t a c h e d t o t h e balance arm of a t o r s i o n b a l a n c e , When the f i b r e i s t w i s t e d by an amount s u i t a b l e f o r t h e g i v e n p r e s s u r e d i f f e r e n c e t h e p i s t o n can be k e p t i n a p o s i t i o n where

i t h a s p l a y i n t h e c y l i n d e r w i t h o u t touchfng t h e w a l l , When a r o t a r y p i s t o n i s employed a d i r e c t i n d i c a t i o n can be o b t a i n e d , even f o r l a r g e v a l u e s ( F i g , 5 ) ,

The p r e s s u r e balance shown i n F i g u r e 2 a l s o h a s t h e fundamsntal d i s a d v a n t a g e t h a t t h e p r e s s u r e d i f f e r e n c e , p

-

po, produces a c o n t i n u o u s f l o w which c a u s e s d e t r i m e n t a l p r e s s u r e d r o p s , However t h e amounts f l o w f n g t h r o u g h t h e s l i t can be made r e l a t i v e l y s m a l l , Whereas i n t h e flow manometer t h e amount of flow p a s s i n g through i s i t s e l f t h e measure f o r t h e f o r c e e f f e c t , t h e flow i n t h e s l i t of t h e p r e s s u r e balance Is merely an accompanying phenomenon, which f o r p r a c t i c a l

r e a s o n s i s u n a v o i d a b l e , b u t which h a s no a p p r e c i a b l e i n f l u e n c e on t h e magnitude of t h e f o r c e e f f e c t , Thus, f o r e q u a l s e n s i - t i v i t y and q u a n t i t y of flow, p r e s s u r e b a l a n c e s can be b u i l t much more s t u r d i l y t h a n flow manometers,

I n flow manometers v i s c o s i t y and d e n s i t y p l a y a c o n s i d e r a b l e p a r t , S i n c e t h e s e v a r i a b l e s change w i t h tem- p e r a t u r e ( i n g a s e s v e r y c o n s i d e r a b l y ) t h e t e m p e r a t u r e must

always be t a k e n i n t o account f n measurements made w i t h t h e flow manometer, The d e f l e c t i o n s of t h e p r e s s u r e b a l a n c e , however,

a r e independent o f v i s c o s i t y and d e n s i t y , and f o r a l l p r e s - s u r e r a n g e s and a l l t e m p e r a t u r e s a r e a f u n c t i o n of t h e p r e s - s u r e d i f f e r e n c e a l o n e , It i s p o s s i b l e , indeed, t o o b t a i n

s t r i c t p r o p o r t i o n a l i t y between t h e p r e s s u r e d i f f e r e n c e and t h e d e f l e c t i o n , (Concerning o t h e r p o s s i b l e s c a l e s w i t h p r e s s u r e b a l a n c e s s e e D 41,

With flow manometers p r o p o r t i o n a l s c a l e s a r e p o s s i b l e o n l y f o r v e r y s m a l l Reynolds numbers, i , e , , o n l y f o r very s e n s i t i v e systems, The s e n s i t i v i t y must be determined by c a l i b r a t i o n , i , e , , i t i s n e c e s s a r y ( i n t h e absence of

a n o t h e r manometer f o r comparison) t o connect a n e x a c t l y known s m a l l p r e s s u r e d i f f e r e n c e t o t h e i n s t r u m e n t which i s t o be c a l i b r a t e d and t h e n determine t h e d e f l e c t i o n , With t h e p r e s - s u r e b a l a n c e , however, a c a l i b r a t i o n i n t h i s s e n s e ( p r e s s u r e

c a l i b r a t i o n ) i s n o t needed i f t h e d a t a concerning t h e d i r e c t i o n a l f o r c e of t h e system, t h e p i s t o n c r o s s - s e c t i o n and t h e l e v e r

arm a r e known w i t h s u f f i c i e n t accuracy, I f e i t h e r t h e l e v e r arm o r t h e e f f e c t i v e p i s t o n c r o s s - s e c t i o n cannot be measured w i t h s u f f i c i e n t accuracy ( a s , f o r example, i n t h e c a s e o f t h e

r o t a r y p i s t o n i n s t r u m e n t d e s c r i b e d below i n F i g , 5 ) t h e s e magnitudes may be s u i t a b l y determined from a p r e s s u r e c a l l - b r a t i o n u s i n g a p r e s s u r e b a l a n c e c o n s t r u c t e d

In

accordance w i t h F i g u r e 2 e s p e c i a l l y f o r t h i s purpose, The

Page

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5

Tech, Trans, TT-84 d i r e c t i o n a l f o r c e o f t h e f i b r e i s determined i n t h e u s u a l way from o b s e r v a t i o n of t h e o s c i l l a t i o n time with a known moment of i n e r t i a ,

I n a d d i t i o n t o t h e s e n s i t i v i t y , o t h e r e s s e n - t i a l p r o p e r t i e s of t h e p r e s s u r e b a l a n c e may be determfned by c a l c u l a t i o n ,

Do

GENERAL

CONDITIONS FOR TfIE APPLICATION AND DESIGN OF PRESSURE

BALANCES WITH FREELY MOVING P I S - TONS

1, D e t r i m e n t a l P r e s s u r e D ~ o p

The minimum wfdth o f t h e s l i t i s determined e s s e n t i a l l y by t h e e x t e n t o f t h e f o u l i n g t h a t f r e q u e n t l y o c c u r s , The t e s t s showed t h a t s l i t widths of l e s s t h a n 0 , l mm, a r e u n s u i t a b l e (tklfs width r e l a t e s t o p i s t o n s o p e r a t i n g

i n a i r ) , The s m a l l e s t s l i t w i d t h which p e r m i t s a n u n h i n d e r e d p l a y o f t h e p i s t o n i s thus p r a c t i c a l l y independent, of t h e p i s t o n d i a m e t e r ,

A t g i v e n s l i t wfdth and g i v e n p r e s s u r e d i f - f e r e n c e t h e amount o f flow through t h e s l i t i s determfned by t h e depth o f t h e s l i t and i t s c i r c u m f e r e n c e , L e t Dp,

-

t h e p r e s s u r e d i f f e r e n c e o v e r t h e s l i t d

-

p i s t o n diameter e

-

s l i t width t - . s l i t d e p t h e

-

d i s t a n c e o f c y l i n d e r a x i s from p i s t o n a x i s (0

<

e

<

s ) F

-

v i s c o s i t y o f t h e medium i n which t h e p r e s s u r e d i f f e r e n c e s a r e t o be measured, The flow p e r second through t h e s l i t i s t h e n 6 )

(For t h e p r e s s u r e d i f f e r e n c e s and s l i t w i d t h i n q u e ~ t i o n t h e I f 2r be t h e d i a m e t e r o f t h e c o n n e c t i n g andbuch d e ~ Experiment a l p h y s i k ,

Page

-

6 Tech, Trans, TT-84 t u b e s , t h e flow, Q, r e s u l t s i n t h e f o l l o w i n g p r e s s u r e drop o v e r t h e c o n n e c t i n g l e n g t h

A :

Applying e q u a t i on (2 is t h e n o b t a i n e d ,

Thus t h e d e t r i m e n t a l p r e s s u r e drop A pr depends on t h e a d j u s t m e n t of t h e system, \%en i n e x a c t a d j u s t m e n t

t h e a x e s of p i s t o n and c y l i n d e r c o i n c i d e ( e = 0 ) and t h e b r a c k e t e d e x p r e s s i o n o f e q u a t i o n ( 4 ) becomes e q u a l t o u n i t y , I f the p i s t o n touches the c y l i n d e r w a l l ( 8

=

9 )

,

A pr h a s 2,s tirnos i t s v a l u e f o r e x a c t a d j u s t m e n t ,

The p r e s s u r e d r o p t o be measured i s

Ap, i s i n d i c a t e d by t h e p r e s s u r e b a l a n c e ; App i s determined by e q u a t i o n ( 4 ) , S i n c e & pI, depends on t h e adjustment of t h e p f s t o n i t i s b e s t t o choose t h e d e s f g n p a r m e t e k s ,

L ,

d, s , t and I*, such t h a t bp,, i s v e r y much s m a l l e r t h a n b p g o The

r e a d i n g of the manometer i s t h e n p r a c t i c a l l y independent o f the p o s i t i o n of t h e p f s t o n i n the c y l i n d e r , If t h e c o n d f t i o n

i s s a t i s f i e d the r e a d i n g of the manometer w i l l be too s m a l l by n o t more than 0,5% when the p i s t o n f s n e a r l y t o u c h i n g t h e w a l l , and n o t more t h a n 0,2$ when i t i s i n e x a c t adjustment

( s e e e q u a t i o n (4)10

Considerably more troublesmome t h a n t h e p r e s - s u r e d r o p i n the c o n n e c t i n g t u b e s i s t h e p p e s s u r e d r o p a t t h e pressuke t a p p i n g s , o r i n t h e h o l e s of t h e measuring a p p a r a t u s ( s u c h a s a p i t o t t u b e ) , which a r e connected t o t h e manometer, The p r e s s u r e t a p s a r e u s u a l l y v e r y narrow, Mfcropressure

b a l a n c e s can be used d i r e c t l y w i t h a p p a r a t u s o f t h i s t y p e o n l y i f c o n d i t i o n ( 5 ) i s s a t i s f i e d a t t h e p o i n t o f maximum r e s i s - t m c e 0

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7

Tech, Trans, TT-84

D i s t u r b a n c e s a r i s e i n t h e flow which i s t o be i n v e s t i g a t e d due t o t h e i n f l o w o r o u t f l o w a t t h e t e s t p o i n t s , These d i s t u p b a n c e s must, o f c o u r s e , be k e p t s m a l l , i , e , , t h e flow p e r second i n t h e manometer c o n n e c t i o n s must be s m a l l compared w i t h t h e flow b e i n g i n v e s t i g a t e d ,

It i s b a s i c a l l y p o s s i b l e t o d e c r e a s e t h e s e n s i t i v i t y of a p r e s s u r e b a l a n c e by i n t r o d u c i n g a narrow tube i n t o t h e c o n n e c t i n g tube, By t h i s means a l a r g e r

measuring r a n g e may be a t t a i n e d , j u s t a s t h e measuring range o f a v o l t m e t e r i s i n c r e a s e d by i n t r o d u c i n g a r e s i s t a n c e i n t o the c i r c u i t b e f o r e i t , However, because of t h e dependence of t h e flow p e r second on t h e p o s i t i o n o f t h e p i s t o n i n * t h e c y l i n d e r , t h e p r a c t i c a l u s e of c a p i l l a r i e s connected b e f o r e i t i s v e r y r e s t r i c t e d ,

2 , P e r i o d of O s c i l l a t i o n and Adjustanent Time o f t h e System I n o r d e r t o o b t a i n a small flow v a l u e t h e

p i s t o n c r o s s - s e c t i o n must be made a s s m a l l a s p o s s f b l e , S i n c e t h e f o r c e a c t i n g on t h e system i s p r o p o r t i o n a l t o t h e p i s t o n c r o s s - s e c t i o n , t h e r e d u c t i o n i n t h e s i z e of t h e p i s t o n must be accompanied by an e q u i v a l e n t d e c r e a s e i n t h e d i r e c t i o n a l f o r c e of the system i f t h e s e n s i t i v i t y o f t h e manometer i s t o remain t h e same, Decreasfng t h e d i r e c t i o n a l f o r c e does n o t n e c e s s a r i l y e n t a i l a n i n c r e a s e i n t h e o s c i l l a t i o n p e r i o d o f t h e system s i n c e t h e moment o f i n e r t i a a l s o d e c r e a s e s due t o t h e r e d u c t i o n of t h e p f s t o n dimensions, a

-

angle o f d e f l e c t i o n a t t h e p r e s s u r e d i f f e r e n c e A p a

-

l e v e r aram F

-

p i s t o n s u r f a c e Q

-

moment of i n e r t i a o f t h e system, The p e r i o d o f undamped o s c i l l a t i o n i s t h e n (The a c t u a l angle o f d e f l e c t i o n i s r a t h e r l a r g e r t h a n t h i s a, s i n c e i n a d d i t i o n t o t h e p r e s s u r e f o r c e a c t i n g on F t h e t h r u s t f o r c e s on t h e circumference o f t h e p i s t o n a r e a l s o e f f e c t i v e ;

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s e e n e x t c h a p t e r a ) The moment o f i n e r t i a of t h e system con- s i s t s of the moment o f i n e r t i a o f the p i s t o n , 8k, and a sup- plementary moment o f I n e r t i a , Q Z , made up e s s e n t i a l l y o f t h e moments of t h e b a l a n c e l e v e r , t h e counterweight, and t h e p o i n t e r o r m i r r o r , I f i t be assumed, f o r pupposes o f rough

c a l c u l a t f o n , t h a t t h e mass m o f t h e p i s t o n i s p r o p o r t i o n a l t o the p i s t o n s u r f a c e F, then, n e g l e c t i n g g Z ( a c o n d i t i o n which a p p l i e s e s s e n t f a l l y o n l y f o r s y s tems which do n o t have l o n g p o i n t e r s ) , i t f o l l o w s t h a t

( f

-

d e p t h of p i s t o n , p Q

-

mean densf t y of t h e p i s t o n m a t e r i a l ) ,

For i n s t m m e n t s which have r o t a r y p i s t o n s i t a l s o f o l l o w s from ( 6 a ) t h a t

where a, i s t h e maximum d e f l e c t i o n f o r maximum measured p r e s - s u r e d i f f e r e n c e npmo

Example: For

a,-

1/3(-200); a -1; p V -1;

ap,

--

0,Ol dyne p e r s q , cm,, t h e n To -10 s e c o

Wfth a s c a l e o f 1000 u n i t s the s e n s i t i v i t y o f the measuring a p p a r a t u s would be

l o w 7

mm, o f w a t e r ,

Equations ( 6 ) t o ( 6 b ) s t a t e t h a t f o r m pro- p o r t f o n a l t o F and €Iz -S €3k t h e p e r i o d of o s c i l l a t i o n o f t h e system a t a given s e n s i t i v i t y i s Independent of t h e d i a m e t e r o f the p i s t o n , Thus, w i t h o u t m y i n c r e a s e i n t h e p e r f o d o f o s c i l l a t i o n , t h e amount o f d e t r i m e n t a l flow can be reduced by d e c r e a s i n g t h e diameter o f t h e p i s t o n , The e x t e n t t o which

t h e d i a m e t e r o f t h e p i s t o n may be reduced i s l i m i t e d only by t h e s t i p u l a t i o n t h a t t h e supplementary moment o f i n e r t i a must remain s m a l l compared with t h e moment o f i n e r t f a of the p i s t o n ,

A

s m a l l p i s t o n d i a m e t e r i s a l s o an advantage from t h e p o i n t of view of d e s i g n ( s e e D 4 ) , S i n c e a c o n s i d e r a b l e d e c r e a s e of flow w i t h reduced p i s t o n s i z e o c c u r s o n l y i f the diameter o f t h e p i s t o n i s l a r g e compared w i t h t h e width o f t h e s l i t , and s i n c e s l i t widths of l e s s t h a n 0 , 1 mm, have proved un- s u i t a b l e , i t i s o f no v a l u e t o reduce t h e diameter of t h e p i s - t o n much below 1 mm,

While t h e p i s t o n i s i n motion t h e amount o f

flow through t h e manometer changes, For example, i f t h e p i s - t o n moves i n the d i r e c t i o n of t h e p r e s s u r e d r o p , some gas ( o r f l u i d ) i s f o r c e d o u t o f t h e low p r e s s u r e s e c t i o n , w h i l e

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9

Tech0 Trans, TT-84 an e q u a l amount flows i n t o t h e h i g h p r e s s u r e s e c t i o n , Thus an a d d i t i o n a l flow, o r a n a d d i t i o n a l p r e s s u r e g r a d i e n t , A p Z , a r i s e s , and t h e p r e s s u r e d i f f e r e n c e a c t i n g on t h e p i s t o n i s reduced by t h e amount of t h i e f l o w , I f t h e p i s t o n h a s moved o u t beyond t h e p o s i t i o n o f e q u i l i b r i u m and f a now swinging back, the sf gn o f ApZ has changed, i , e , , t h e e f f e c t i v e p r e s -

s u r e d i f f e r e n c e h a s i n c r e a s e d by t h e amount A p Z o Apz always a c t s i n such a way a s t o d e l a y a t t a i n m e n t o f t h e p o s i t i o n of e q u i l i b r i u m , Hence, due t o t h e d e f l e c t i o n o f the p i s t o n , a supplementary b r a k i n g moment

M Z

=

x/4 d2 a D p z a p p e a r s , MZ may be t h o u g h t of a s t h e r e s u l t o f a supplementary " f r i c t i o n

_--

M dampingw R Z

=*.

Hence

-

d t

S i n c e the . supplementary flow p e r second i s

i t f o l l o w s from ( 7 ) t h a t

The a d j u s t m e n t time i s n o t much greater" t h a n To, provided t h e damping i s a p e r i o d i c , A n o v e r - a p e r i o d i c damping s h o u l d be avoided, i , e , , I n s o f a r a s p o s s i b l e t h e c o n d i t i o n

s h o u l d p r e v a i l ( D

-

d i r e c t i o n a l f o r c e ) , I f c o n d i t i o n ( 9 ) i s p r e s c r i b e d f o r R a s a whole, i t i s even more t o be s o u g h t f o r

Rz 0 S u b s t i t u t i n g R,, from e q u a t i o n (8), and

D

=

x

a d 2 b p _4a I n e q u a t i o n ( 9 ) , t h e n

For r o t a r y p i s t o n i n s t r u m e n t s , i n which t h e supplementary moment of i n e r t i a may be ne l e c t e d , I t a l s o f o l l o w s from

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1 0

Tech, Trans, TT-84

b

3, E f f e c t o f t h e Flow f n t h e S l f t on t h e Turnlng Moment The f o ~ c e s a c t i n g on the p i s t o n i n c l u d e n o t o n l y t h e p r e s s u r e f o r c e , b u t a l s o t h e t h r u s t f o r c e s of t h e flow i n the s l i t , When the width o f t h e s l i t i s s m a l l com- pared w i t h t h e d i a m e t e r o f t h e p i s t o n t h e t h r u s t s t r e s s e s a r e t r a n s m f t t e d t o t h e p i s t o n a t d i s t a n c e s o f t h e p i s t o n from t h e c y l i n d e r w a l l o f y

<

s/2, and a r e t r a n s m i t t e d t o t h e c y l i n d e r

w a l l a t d i s t a n c e s y > s/2 ( F i g , 3 shows t h e v e l o c i t y p r o f i l e i n t h e s l i t when t h e p i s t o n f s i n b a l a n c e ) , The p r e s s u r e f o r c e nd

9

a p ,

upon t h e a r e a , nd

,

o f t h e r i n g around the

2

p i s t o n o f a r e a

9

d2, is thus imparted t o t h e p i s t o n . The p i s t o n s u r f a c e a p p e a r s t o be e n l a r g e d by t h e s l f t flow, and

t h e d i a m e t e r of t h e " e f f e c t i v e p i s t o n supface" i s , i n f a c t made up of t h e d i a m e t e r , d, of t h e p i s t o n , p l u s t h e width

o f t h e s l i t,, s o This a p p l i e s , of c o u r s e , o n l y i f t h e e n t r a n c e l e n g t h , A , o f the flow i n the s l i t ( c ~ e s s s - s e c t i o n o f the s l i t a d j a c e n t t o t h e h i g h p r e s s u r e s p a c e ) i s s m a l l compared w i t h t h e d e p t h of t h e s l i t , t o

The e n t r a n c e l e n g t h , h

,

is approximately

s2

U

0,025 -7 For A

<<

t , i s determined bssfca1l.y by t h e P o f s e u i l l e p r e s s u r e d r o p o Thus t h e c o n d i t i on

must be s a t i s f i e d f f t h e e f f e c t i v e p i s t o n d i a m e t e r i s t o b e made p r a c t i c a l l y e q u a l t o d

+

s o

When t h e Kg-condition i s s a t f s f i e d t h e e q u a t i o n f o r the angle s f d e f l e c t i o n , a , o f the m f c r o p r e s s u r e b a l a n c e becomes

( e

-

moment o f i n e r t i a and T

-

p e r i o d of h a l f an o s c i l l a t i o n

d u r i n g c a l i b r a t i o n ; cr; i s e x p r e s s e d i n degrees and Ap i n rnm,

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11

Tech, Trans, TT-84 There i s a s m a l l e r r o r due t o t h e f a c t t h a t t h e flow, emerging from t h e s l i t c o n t i n u e s t o p a s s a l o n g t h e p i s t o n and s t r i k e s t h e b a l a n c e l e v e r o r o t h e r p a r t s o f t h e system, Thus the system g i v e s an i n d i c a t i o n o f p a r t of t h e impulse of t h e s l i t flow, T o e s t i m a t e t h i s e r r o r the t o t a l impulse o f t h e s l i t flow w i l l b e compared w i t h t h e p r e s s u r e f o r c e on the p i s t o n ,

The f o r c e o f the impulse i s

and t h e r a t i o o f t h e t o t a l f o r c e o f t h e impulse t o t h e p r e s - s u r e f o r c e i s :

I f t h e c o n d i t i o n

i s s a t i s f i e d t h e impulse f o r c e o f t h e s l i t flow i s a t m o s t 0 , 2 p e r c e n t of t h e p r e s s u r e f o r c e on t h e c e n t r e d p i s t o n

( e / s

=

O ) , o r 1.2 p e r c e n t when the p i s t o n almost touches t h e w a l l ( e / s -1). S f n c e o n l y a f r a c t i o n of t h e t o t a l i m - p u l s e i s imparted t o the system t h e e f f e c t of t h e flow

emerging from t h e s l i t when t h e K4-condition i s s a t i s f l e d i s i n any c a s e i n s i g n i f i c a n t ,

A t v e r y s m a l l p r e s s u r e d i f f e r e n c e s where t h e r e i s no impulse and o n l y the v i s c o s i t y of the flow emerging from t h e s l i t remains e f f e c t i v e , t h e e f f e c t , t h e r e f o r e , be- comes even more t r i v i a l , because the p r e s s u r e s p a c e s a r e much wider t h a n t h e s l i t and t h e p r e s s u r e drop a l o n g t h e system o u t s i d e t h e s l i t i s e n t i r e l y unimportarlt compared with t h e p r e s s u r e df f f e r e n c e which i~ t o be measured,

4 , P i s t o n Shapes, S l i t Dimensions

When p i s t o n s and c y l i n d e r s w i t h l i n e a r axes a r e employed ( F i g , 2 ) o n l y s m a l l d e f l e c t i o n s a r e p o s s i b l e . To measure a r e l a t i v e l y l a r g e p r e s s u r e d i f f e r e n c e t h e t o r s i o n

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1 2 Tech, T r a n s , TT-84 f i b r e m u s t be s u b j e c t e d t o a n i n i t i a l s t r e s s s u c h t h a t t h e p i s t o n b a l a n c e s a t t h e p o s i t i o n o r i g i n a l l a t t a i n e d f o r t h e p r e s s u r e d i f f e r e n c e z e r o ( n u l l i n s t r u m e n t A l a r g e r a n g l e o f d e f l e c t i o n , i , e o , a d i r e c t p r e s s u r e r e a d i n g , c a n be o b t a i n e d by two d i f f e r e n t methods : 1) By a s h o r t , s t r a i g h t p i s t o n s i t u a t e d i n a c u r v e d c y l i n d e r ; 2 ) By a c u r v e d p i s t o n ( r o t a r y p i s t o n ) p a s s i n g t h r o u g h a s h o r t , s t r a i g h t c y l i n d e r , The s e c o n d a r r a n g e m e n t i s c o n s i d e r a b l y more s u i t a b l e t h a n t h e f i r s t o n e , f o r t h e f o l l o w i n g r e a s o n s , I t was d e m o n s t r a t e d i n S e c t i o n D 2 t h a t t h e most f a v o u r a b l e p i s t o n d i a m e t e r i s o f t h e o r d e r o f one m i l l i m e t r e , I n o r d e r

t o r e a l i z e a r r a n g e m e n t number one i t would be n e c e s s a r y t o

a t t a c h t h e p i s t o n , i , e , , a s m a l l p i e c e o f w i r e o f a p p r o x i m a t e l y one m i l l i m e t r e i n d i a m e t e r , t o a w i r e o f s m a l l e r d i a m e t e r , t h e " p i s t o n r o d " , b e n t i n t o t h e form o f a n a r c , However, t h i s t h i n n e r , a r c - s h a p e d w l r e , i f p a s s e d t h r o u g h a s h o r t , c y l i n d - r i c a l h o l e r e s u l t s i n a r r a n g e m e n t number two ( F i g , 5 a and b ) ,

This l a t t e r a r r a n g e m e n t , t h e r e f o r e , f o r t h e p a r t i c u l a r d i - m e n s i o n s i n q u e s t i o n , i s much s i m p l e r t h a n number one. S i n c e

i n a r r a n g e m e n t number two t h e s l i t always r e m a i n s i n t h e same p l a c e and i s e a s y t o o b s e r v e i n t h e e n t i r e a s s e m b l y , t h i s a r r a n g e m e n t h a s a f ' u r t h e r d e c i s i v e a d v a n t a g e i n t h a t t h e p o s i t i o n o f t h e p i s t o n i n t h e c y l i n d e r c a n e a s i l y be d e t e r - mined, and t h e a d j u s h e n t c a n be c a r r i e d o u t e f f e c t i v e l y , F u r t h e r m o r e , any f o u l i n g which may o c c u ~ c a n b e d e t e c t e d by l o o k i n g t h r o u g h t h e s l i t , S i n c e w i t h t h e i n s t r u m e n t shown i n F i t h e r o t a r y p i s t o n p a s s e s t h r o u g h a c y l i n d r i c a l h o l e

$uare

c u r v e d o p e n i n g i s more c o m p l i c a t e d and c a n n o t b e o b s e r v e d s o e a s i l y ) , t h e s l i t d e p t h depends on i t s w i d t h , S h o r t , n a r r o w s l i t s a r e o f c o u r s e s u p e r i o r t o d e e p , wide o n e s , s i n c e t h e amount o f f l o w i s p r o p o r t i o n a l t o s 3 / t 0 Moreover, w i t h s h o r t h o l e s i t i s p o s s i b l e t o o b t a i n r e l a t i v e l y n a r r o w s l i t s w i t h o u t e n c o u n t e r i n g any o b s t a c l e t o t h e movement o f t h e p i s t o n , S l i t w i d t h s o f l e s s t h a n a p p r o x i m a t e l y 0 , l mm,, however, need n o t b e c o n s i d e r e d , A s a l r e a d y m e n t i o n e d above, t h e e x a c t , d i r e c t measurement o f s m a l l r o t a r y p i s t o n s e n t a i l s d i f f i c u l t i e s . However, t h e l e v e r arm and t h e e f f e c t i v e c r o s s - s e c t i o n o f a

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a n g l e of d e f l e c t i o n ) can b e a c c u r a t e l y determined by a c a l i - b r a t i o n o f t h e r o t a ~ y p i s t o n i n s t r u m e n t a g a i n s t a n u l l in-

s t r u m e n t ( F i g u r e 2), The dimensions of t h e b a l a n c i n g appa- r a t u s must be l a r g e enough t o p e r m i t a c c u r a t e measurement w i t h i n approximately 0 , l p e r c e n t , Because of t h e g r e a t e r

dimensions, t h e amount o f d e t r i m e n t a l flow i n such a c a l i - b r a t i n g i n s t r u m e n t i s r e l a t i v e l y l a r g e , I t f s t h e r e f o r e n o t

very s u i t a b l e f o r measuring purposes, Furthermore a b a l a n c i n g a p p a r a t u s i s c o n s i d e r a b l y more expensive than a r o t a r y p i s t o n i n s t r w n e n t ( i t r e q u i r e s a second r e a d i n g device and a good t o r s i o n mechanism), and a t the same time t h e s i m p l e r o t a r y p i s t o n i n s t r u m e n t i s much s u p e r i o r t o t h e b a l a n c i n g a p p a r a t u s wf t h r e s p e c t t o o p e r a t i o n and u s e f u l n e s s , Non-linear A p - s c a l e s a r e o b t a i n e d w i t h t h e a i d o f p i s t o n s whose e f f e c t i v e c r o s s - s e c t i o n s o r l e v e r arms v a r y w i t h t h e angle o f d e f l e c t i o n , A p i s t o n w i t h f l a t t e n e d s i d e s i s shown i n F i g u r e 4 , I t s w i d t h i s a f u n c t i o n o f the a n g l e of d e f l e c t i o n , The p i s t o n p a s s e s through a s m a l l s l i t i n t h e w a l l s e p a r a t i n g t h e h i g h - p r e s s u r e space from t h e low- p r e s s u r e s p a c e , The i n c r e a s e d flow i n t h e wide s l i t l i m i t s the a p p l i c a t i o n o f t h i s arrangement, o f c o u r s e , t o c a s e s where s h o r t , wide c o n n e c t i n g tubes can be employed, and where a

f a i ~ l y s t r o n g s h u n t t o t h e main flow i s p e r m i s s i b l e , The s l i t channel must be narrow enough s o t h a t t h e amount o f flow and t h e impulse e f f e c t w i l l s t i l l n o t be e x c e s s i v e when t h e p i s t o n does n o t p e n e t r a t e i n t o t h e c h a m e l , As l o n g a s t h e impulse o f t h e flow i n t h e s l i t p l a y s no e s s e n t i a l p a r t , t h e r e a d i n g of an i n s t r u m e n t such a s t h a t shown i n Ff gure 4 i s of c o u r s e independent of the. amount of flow, which v a r i e s w i t h t h e a n g l e of d e f l e c t i o n ,

A change i n t h e s e n s i t i v i t y of t h e manometer with the p r e s s u r e df f f e r e n c e i s d e s i r a b l e , f o r example, i n

t h e c a s e of dynamic p r e s s u r e measurements f o r the d e t e r - m i n a t i o n of flow v e l o c i t i e s , I f t h e d e f l e c t i o n o f t h e mano- m e t e r i s t o be p r o p o r t i o n a l t o t h e wind v e l o c i t y t h e n t h e width o f p i s t o n a d m i t t e d by t h e s l i t a t any g i v e n i n s t a n t must be i n v e r s e l y p r o p o r t i o n a l t o t h e a n g l e o f d e f l e c t i o n , F i g u r e 4 i l l u s t r a t e s t h i s p a r t i c u l a r c a s e ,

DESCRIPTION OF A COJPLETE MICHOPRESSURE BALANCE FOR MEASURE- hlENTS OF PRESSURE DIFFERENCES I N GASES

E x p l a n a t i o n o f F i g u r e 5: a

-

r o t a r y p i s t o n , b

-

-

c y l i n d r i c a l h o l e i n the w a l l separatTng t h e h i g h and low p r e s s u r e chambers, 5

-

knife-edge p o i n t e r , d

-

m i r r o r ( t h e l e t t e r s i n b r a c k e t s r e l a t e t o t h e case i n wxich t h e system i s removed from t h e housing and s e t up f o r d i r e c t i o n a l f o r c e

Page

-

14 Tech, Trans, TT-84 c a l i b r a t i o n of t h e f i b r e ) , To damp t h e l a t e r a l o s c i l l a t i o n s of t h e system a s m a l l p l a t e i s suspended b e n e a t h t h e m i r r o r and i s immersed i n a v e s s e l c o n t a i n i n g o i l , e

-

m i r r o r s c a l e

-

f

-

t o r s i o n f i b r e

-

g

-

rod w i t h t h e t o r s i o n f i b r e s o l d e r e d i n t o i t s a x i s h

-

adjustment r f n g w i t h sen-

-

a i t i v e l e v e p f o r a d j u s t i n g t h e z e r o p o i n t i

-

s t o p f o r c o r r e c t h e i g h t of

-

t h e suspension,

When t h e r o d ,

J,

h a s been lowered t h e system r e s t s a t t h e lower edge of t h o h o l e , b, and t h e s u p p o r t ,

k,

The p o s i t i o n of t h e p i s t o n i n h o l e b Gay be observed through windows

and

&;

t h e m i r r o r

-

d

is

v i s i b l e through window

4 .

-

n i s a stop-cock, I n t h e i n d i c a t e d p o s i t i o n t h e stop-cock c u t s o f f t h e manometer from t h e p r e s s u r e d i f f e r e n c e and e q u a l i z e s t h e p r e s s u r e s i n t h e high- and low-pressure s p a c e s ,

Rhen t h e manometer i s r e a d y f o r use it i s c l o s e d a t t h e t o p by means of a g l a s s p l a t e , m ( i n F i g u r e 5 thtj p l a t e m h a s been l i f t e d o f f and pushed upp, The p l a t e c o n t a i n s a-hole t h r o u g h which t h e f i b r e p a s s e s and i s joined t o t h e s f d e s and t o t h e p a r t i t i o n by means of a r u b b e r packing, I n o r d e r t o i n s e r t t h e system, o r remove i t , t h e g l a s s p l a t e must be l i f t e d o f f and pushed upwards, I n t h e p o s i t i o n shown

i n F i g u r e 5 t h e p l a t e i s f a s t e n e d t o t h e s u s p e n s i o n device by means of a f o r k ,

2 ,

(which i s p r e v e n t e d from r o t a t i n g about t h e a x i s ,

q,

by means of a p i n ,

g),

The p a r t of t h e f o r k t o t h e r i g h t of t h e a x i s of r o t a t i o n , 9, a s i n d i c a t e d by t h e d o t t e d l i n e s i n F i g u r e 5, s e r v e s t o h o l d t h e system f o r t h e purpose of c a l i b r a t i n g t h e d i r e c t i o n a l f o r c e of t h e f i b r e , During t h i s o p e r a t i o n t h e upper s i d e of t h e system l i e s f a c e down on t h e f o r k , and t h e f i b r e w i t h t h e r o d , (81, hangs be-

low i t , A d i s c w i t h known moment of i n e r t i a i s pushed o v e r t h e r o d , When t h e c a l i b r a t i o n i s f i n i s h e d and t h e system h a s been i n s e r t e d , the f o r k o i s swung back through 90°, t h e g l a s s p l a t e , m_, and t h e shelT,

c,

a r e pushed downward u n t i l t h e g l a s s p l a t e r e s t s on the housing and t h e r u b b e r r i n g ,

g ,

i s f o r c e d i n t o t h e h o l e i n t h e g l a s s p l a t e , A f t e r t h e g l a s s p l a t e h a s been clamped down t h e housing i s a i r - t i g h t ,

Page

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1 5

Tech, Trans, TT-84 The f i r s t r o t a r y p i s t o n s were c o n s t r u c t e d from l i g h t m e t a l , L a t e r t h e y were made from g l a s s t u b e s , The manufacture o f a r o t a r y p i s t o n r e q u i r e s g r e a t c a r e , s i n c e t h e r a d i u s and d i a m e t e r o f t h e p i s t o n must be a c c u r a t e t o s e v e r a l hundredths o f a m i l l i m e t r e , I n a d d i t i o n t h e r o t a r y system

must be w e l l b a l a n c e d , However t h e adjustment of an e f f i c i e n t l y o p e r a t i n g and w e l l c l e a n e d s y s tern p r e s e n t s no d i f f i c u l t i e s ,

The l a t e r a l p o s i t i o n s a r e a d j u s t e d by t u r n i n g 'the foot-screws and the h e i g h t by d i s p l a c e m e n t o f t h e r o d , $,

I n o r d e r t o a v o i d t h e r m a l p p e s s u r e d i f f e r e n c e s the r o t a r y system and the c o n n e c t i n g p i p e s a r e s i t u a t e d i n t h e same h o r i z o n t a l p l a n e , This p l a n e should l i e aa n e a r l y a s p o s s i b l e a t t h e l e v e l o f t h e p r e s s u r e t a p p i n g s s o t h a t the l e a d s may remafn h o r i z o n t a l o v e r t h e i r e n t i r e l e n g t h , Otherwise t h e i n c l i n e d s e c t i o n s o f t h e tubes would have t o be t h e r m a l l y s h i e l d e d s o t h a t t h e same temperature would p r e v a i l i n t h e i n c l i n e d s e c t i o n o f t h e low-pressure l e a d a s i n the c o r r e s p o n d i n g s e c t i o n of t h e h i g h - p r e s s u r e l e a d ,

The manometer i s b e s t r e a d under d i f f u s e

i l l u m i n a t i o n , IBlumfnation by a lamp i n the immediate v i c i - n i t y Is n o t p e r m i s s i b l e , s i n c e thermal c o n v e c t i o n c u r r e n t s

occur due t o h e a t r a d i a t i o n , The system t h e n performs a f l u c t u a t i n g motion, i , e , , I t s z e r o p o s i t i o n changes con- t i n u o u s l y

,

P r i n c i p l e dimensions: Height w i t h normal adjustment

o f t h e f o o t screws

-

32 cm,

Housing

-

7 x B4,5

x

16 em,

Df ameter o f r o t a r y p i s t o n

-

d

-

1,6 mm,

Width o f s l i t

-

s

-

0 , l mm,

Lever arm

-

a = 2 em,

Depth o f s l i t - t = = 2 m , Maximum angle of d e f l e c t f o n

-

% -. BOO0

Outer s c a l e r a d i u s

-

8,2 cm, Length of s c a l e

-

1 4 , 3 cm, Radius of tube s o c k e t s f o r

Page

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16 Tech, T r a n s , TT-84 p o i n t e r r e a d i n g of t h e s y s t e m 0 , l m, w a t e r 0 , 0 1 mm, w a t e r 10-5 mn, w a t e r I f t h e f l o w r e s i s t a r l c e of t h e e n t i r e a r r a n g e - ment c o n s i s t s e s s e n t i a l l y of t h e t u h e r e s i s t a n c e of t h e con- n e c t i n g l e a d s i t f o l l o w s f r o m t h e K 1 - c o n d i t i o n ( 5 ) f o r t h e l e n g t h of t u b e p r o v i d e d t h e w i d t h of t h e t u b e i s e q u a l t o t h e w i d t h of t h e t u b e s o c k e t s , i , e , , 2 r w

1,s

cm, Thus, u n d e r t h e s e circum- s t a n c e s t h e l e n g t h of t h e c o n n e c t i n g l e n d s may t o t a l 1 2 m e t r e s , With a l e a d l e n g t h of 1 0 m e t r e s t h e K z - c o n d i t i o n ( 1 0 ) f o r t h e m e a s u r i n g r a n g e of 0 , l rnm, of w a t e r (-10 dyne p e r s q , cm,) i s a s f o l 7 . 0 ~ ~ :

and f o r t h e measuring 1 ange of 0 , 0 1 mm, of w a t e r

( v i s c o s i t y of a i r p 4 , 7 x 1 0 " ~ ) ~ Thus with a i r a s t h e

medium t h e damping due t o t h e con!pressfve motion of t h e p i s - t o n p l a y s no p a r t w h a t s o e v e r , I n l f q u f d p r e s s u r e b a l a n c e s , however, 1.t may b e c o n s i d e r a b l e ,

With w a t e r a s t h e medium ( P - O G O 1 ) t h e f o l - lowing would a p p l y f o r t h e measuring r a n g e of 0 , 0 1 mm, of w a t e r

and i n an o i l o f I * - 0 , l t h e K2-condition f o r t h e g i v e n de- s i g n s p e c i f i c a t i o n s would n s l o n g e r b e f u l f i l l e d a t a l l , In s u c h a c a s e , t h e r e f o r e , t h e manometer system would be more t h a n a p e r i o d i c a l l y damped due t o t h e compressive m o t i o n of t h e p i s t o n i t s e l f , f o e , , i t t a k e s c o n s f d e r a b l y l o n g e r t h a n

To f o r t h e f i n a l praessupe d i f f e r e n c e , b p s , t o become p r a c - t i c a l l y a d j u s t e d o v e r t h e s l i t ,

Page

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18

Tech, Trans, TT-84

e f f e c t of t h e j e t emerging from t h e s l i t may a l s o be neg- l e c t e d ,

A d e s c r i p t i o n of an a c t u a l p r e s s u r e b a l a n c e with r o t a r y p i s t o n , knife-edge p o i n t e r and m i r r o r s c a l e , which was t e s t e d i n t h e K a i s e r Wilhelm I n s t i t u t e f o r Flow Research, h a s been g i v e n ( s e n s i t i v i t

-

depending on t h e s t r e n g t h of t h e f i b r e employed

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1 0 3 t o 10-5 mm. of w a t e r ) .

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