Measurement Systems - E. O. Doebelin and D. N. Manik [PDF]

Citation preview

Scilab Textbook Companion for Measurement Systems by E. O. Doebelin And D. N. Manik1 Created by KRITI SUNEJA B.TECH Electronics Engineering LAXMI NIWAS MITTAL INSTITUTE OF INFORMATION TECHNO College Teacher NA Cross-Checked by



May 18, 2016



1 Funded



by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in



Book Description Title: Measurement Systems Author: E. O. Doebelin And D. N. Manik Publisher: Tata McGraw - Hill Education Edition: 5 Year: 2007 ISBN: 9780070616721



1



Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.



2



Contents List of Scilab Codes



4



2 Generalized Configurations and Functional Descriptions of measuring instruments



5



3 Generalized Performance Characteristics Of Instruments



7



4 Motion and Dimensional Measurement



13



5 Force Torque and Shaft power measurement



24



6 Pressure and sound measurement



29



7 Flow measurement



38



8 TEMPRATURE MEASUREMENT



47



3



List of Scilab Codes Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa



2.1 3.1 3.2 3.5 3.6 3.7 4.1 4.2 4.3 4.4 4.5 4.7 4.8 4.9 4.10 4.11 4.12 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 6.4 6.5 6.6



Error in measurement . . . . . . . . . . . . . . . . Gaussian distribution . . . . . . . . . . . . . . . . Combination of component errors in overall system First order instrument . . . . . . . . . . . . . . . . Step response of first order instrument . . . . . . . Adequate frequency response conditions for first o Resistance strain gage . . . . . . . . . . . . . . . . Rosette . . . . . . . . . . . . . . . . . . . . . . . . Strain gage . . . . . . . . . . . . . . . . . . . . . . Capacitance pick ups . . . . . . . . . . . . . . . . Piezoelectric transducer . . . . . . . . . . . . . . . Seismic vibrations . . . . . . . . . . . . . . . . . . Seismic velocity pick ups . . . . . . . . . . . . . . Piezoelectric transducer . . . . . . . . . . . . . . . Seismic pick ups . . . . . . . . . . . . . . . . . . . Accelerometers . . . . . . . . . . . . . . . . . . . . Strain gage . . . . . . . . . . . . . . . . . . . . . . Load cell . . . . . . . . . . . . . . . . . . . . . . . Load cell . . . . . . . . . . . . . . . . . . . . . . . Load cell . . . . . . . . . . . . . . . . . . . . . . . Piezoelectric transducer . . . . . . . . . . . . . . . Torque measurement on rotating shaft . . . . . . . manometers . . . . . . . . . . . . . . . . . . . . . . manometers . . . . . . . . . . . . . . . . . . . . . . elastic transducers . . . . . . . . . . . . . . . . . . design of pressure transducers . . . . . . . . . . . . pressure gage . . . . . . . . . . . . . . . . . . . . . high pressure measurement . . . . . . . . . . . . . 4



. . . . . . . . . . . . . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . . . . . . . . . . . . .



5 7 8 10 10 11 13 14 15 16 16 17 18 19 20 22 22 24 25 26 26 27 29 30 30 31 33 34



Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa



6.7 6.8 6.9 6.10 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 8.1 8.2 8.3 8.4 8.5



Mc Leod gage . . . . . . . . Knudsen gage . . . . . . . . . sound measurement . . . . . sound measurement . . . . . Flow measurement . . . . . . Anemometers . . . . . . . . . Gross volume flow rate . . . . Gross volume flow rate . . . . Gross volume flow rate . . . . sonic nozzle . . . . . . . . . . venturi . . . . . . . . . . . . constant pressure drop . . . . thermocouple . . . . . . . . . thermocouple and thermopile electrical resistance sensors . thermistors . . . . . . . . . . pyrometers . . . . . . . . . .



5



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



. . . . . . . . . . . . . . . . .



35 35 36 36 38 39 39 41 42 43 44 45 47 48 49 50 51



Chapter 2 Generalized Configurations and Functional Descriptions of measuring instruments



Scilab code Exa 2.1 Error in measurement 1



// C h a p t e r 2 G e n e r a l i z e d C o n f i g u r a t i o n s and Functional D e s c r i p t i o n s of measuring instruments // C a p t i o n E r r o r i n measurement // Ex 1 p a r t 2 // p a g e 22 disp ( ” t s =0.1 ” ) disp ( ” p s =2.5 ” ) disp ( ”dT=20” )



2 3 4 5 6 7 8 ts =0.1 9 ps =2.5 10 11 12 13



// ( ’ e n t e r t h e t e m p e r a t u r e s e n s i t i v i t y = : ’ ) // ( ’ e n t e r t h e p r e s s u r e s e n s i t i v i t y ( i n u n i t s /MPa) = : ’ ) dT =20 // ( ’ e n t e r t h e t e m p e r a t u r e c h a n g e d u r i n g p r e s s u r e measurement = : ’ ) P =120 // ( ’ e n t e r t h e p r e s s u r e t o be m e a s u r e d ( i n MPa) = : ’ ) error =( ts * dT ) /( ps * P ) ; printf ( ’ t h e e r r o r i n measurement i s %fd p e r c e n t \n ’ , 6



error )



7



Chapter 3 Generalized Performance Characteristics Of Instruments



Scilab code Exa 3.1 Gaussian distribution 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18



// C h a p t e r 3 G e n e r a l i z e d P e r f o r m a n c e C h a r a c t e r i s t i c s Of I n s t r u m e n t s // C a p t i o n : G a u s s i a n D i s t r i b u t i o n // Example 1 clc ; close ; disp ( ”me=7” ) disp ( ” s t d d e v =0.5 ” ) disp ( ” x = 6 ” ) disp ( ” y= 7 . 5 ” ) me =7 ; stddev =0.5; x = 6 // ( ’ e n t e r t h e l o w e r l i m i t o f t h e r a n g e = : ’ ) y = 7.5 // ( ’ e n t e r t h e u p p e r l i m i t o f t h e r a n g e = : ’ ) n = 200 // ( ’ e n t e r t h e number o f s a m p l e s = : ’ ) disp ( ” u s i n g k =a b s ( ( x−me ) / ( ( 2 ˆ 0 . 5 ) ∗ s t d d e v ) ) ; ” ) k = abs (( x - me ) /((2^0.5) * stddev ) ) ; printf ( ’ V a l u e o f e t a 1 i s %1 . 2 f \n ’ ,k )



8



19 p = abs (( y - me ) /((2^0.5) * stddev ) ) ; 20 printf ( ’ V a l u e o f e t a 2 i s %1 . 2 f \n ’ ,p ) 21 // U s i n g t h e g a u s s i a n p r o b a b i l i t y e r r o r



22 23 24 25 26



function table , f i n d the e r r o r f u n c t i o n corresponding to t h e v a l u e o f k and p //LET IT BE s s = 0.95 // ( ’ e n t e r t h e e r r o r f u n c t i o n c o r r e s p o n d i n g to k value =: ’) F ( x ) =(1/2) +(1/2* s ) ; // P r o b a b i l i t y o f h a v i n g l e n g t h s l e s s than x l = 0.68 // ( ’ e n t e r t h e e r r o r f u n c t i o n corresponding to p value =: ’) F ( y ) =(1/2) +(1/2* l ) ; // P r o b a b i l i t y o f h a v i n g l e n g t h s l e s s than y



27 28



printf ( ’ p r o b a b i l i t y o f h a v i n g l e n g t h l e s s t h a n 6 cm i s %1 . 3 f ’ ,F ( x ) ) ; 29 printf ( ’ p r o b a b i l i t y o f h a v i n g l e n g t h l e s s t h a n 6 7 . 5 cm i s %1 . 3 f ’ ,F ( y ) ) ; 30 31 P ( x ) = abs ( F ( y ) -F ( x ) ) ; 32 printf ( ”Number o f s a m p l e s i n t h e g i v e n l e n g t h r a n g e=



”) 33 m =( n * P ( x ) ) ; 34 disp ( m ) ;



Scilab code Exa 3.2 Combination of component errors in overall system 1 2 3 4 5



// C a p t i o n : C o m b i n a t i o n o f component e r r o r s i n o v e r a l l system −a c c u r a c y c a l c u l a t i o n s // e x a m p l e 2 // p a g e 62 clc ; // C o n s i d e r an e x p e r i m e n t f o r m e a s u r i n g , by means o f a dynamometer , t h e a v e r a g e power t r a n s m i t t e d by a 9



6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37



rotating sheft disp ( ”R=1202 ” ) disp ( ”F=45” ) disp ( ”L = 0 . 3 9 7 ” ) disp ( ” t =60” ) R =1202 // ( ’ E n t e r t h e r e v o l u t i o n s o f s h a f t d u r i n g time t =: ’) F =45 // ( ’ E n t e r t h e f o r c e a t end o f t o r q u e arm = : ’ ) L =0.397 // ( ’ E n t e r t h e l e n g t h o f t o r q u e arm = : ’ ) t =60 // ( ’ E n t e r t h e t i m e l e n g t h o f run = : ’ ) W =(2* %pi * R * F * L ) / t ; // Computing v a r i o u s p a r t i a l d e r v a t i v e s dWF =(2* %pi * R * L ) / t ; disp ( dWF ) //dWF r e p r e s e n t s dW/dF dWR =(2* %pi * F * L ) / t ; dWL =(2* %pi * F * R ) / t ; dWt = -(2* %pi * R * F * L ) /( t ^2) ; // L e t f , r , l and t r e p r e s e n t t h e u n c e r t a i n t i e s disp ( ” f =0.18 ” ) disp ( ” r =1 ” ) disp ( ” l = 0 . 0 0 1 2 7 ” ) disp ( ” t =0.5 ” ) disp ( ”Ea=(dWF∗ f ) +(dWR∗ r ) +(dWL∗ l )+a b s (dWt∗ t ) ; ” ) f =0.18 // ( ’ E n t e r t h e u n c e r t a i n t y i n f o r c e = : ’ ) r =1 // ( ’ E n t e r t h e u n c e r t a i n t y i n t h e no o f r e v o l u t i o n s =: ’) l =0.00127 // ( ’ E n t e r t h e u n c e r t a i n t y i n t h e l e n g t h =: ’) t =0.5 // ( ’ E n t e r t h e u n c e r t a i n t y i n t h e t i m e l e n g t h o f run = : ’ ) Ea =( dWF * f ) +( dWR * r ) +( dWL * l ) + abs ( dWt * t ) ; // absolute error printf ( ” The a b s o l u t e e r r o r i s ” ) disp ( Ea ) ; //To f i n d t o t a l u n c e r t a i n t y U =((( dWF * f ) ^2) +( dWR * r ) ^2+( dWL * l ) ^2+ abs ( dWt * t ) ^2) ^0.5 printf ( ” T o t a l u n c e r t a i n t y i s ” ) disp ( U ) 10



Scilab code Exa 3.5 First order instrument 1 2 3 4 5 6 7 8



// C h a p t e r 3 G e n e r a l i z e d P e r f o r m a n c e C h a r a c t e r i s t i c s Of I n s t r u m e n t s // C a p t i o n : F i r s t o r d e r i n s t r u m e n t // Example 5 // Page no . 96 d =.004 // ( ’ E n t e r t h e d i a m e t e r o f t h e d i a m e t e r o f the sphere in meters =: ’) p =13600 // ( ’ E n t e r t h e d e n s i t y o f t h e l i q u i d i n g l a s s bulb =: ’) c =150 // ( ’ E n t e r t h e s p e c i f i c h e a t o f l i q u i d ( i n j / kg d e g r e e c e n t i g r a d e ) = : ’ ) U =40 // ( ’ E n t e r t h e h e a t t r a n s f e r c o e f f i c i e n t i n W/m ˆ2− d e g r e e c e n t i g r a d e = : ’ )



9 10 Vb =( %pi * d * d * d ) /6; // Volume o f s p h e r e 11 Ab = %pi * d * d ; // S u r f a c e a r e a o f s p h e r e 12 timconstant =( p * c * Vb *1000) /( U * Ab ) ; // t i m e c o n s t a n t 13 disp ( timconstant )



Scilab code Exa 3.6 Step response of first order instrument 1 // C a p t i o n : S t e p r e s p o n s e o f 2 // Example 6 3 // p a g e 100 4 clc ; 5 // Given : I n a i r , p r o b e d r y



f i r s t order systems



timeconstant ( tc )



=30 s 6



//



In water



tc



=5 s 11



7



//



I n a i r , p r o b e wet



tc



=20 s 8 // f o r t