Fluid mechncs by Mcdonald

8/7/2019 Fluid mechncs by Mcdonald

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Scilab Code for

Introduction to Fluid Mechanics

by Fox and McDonald1

Created byEswar Prasad

4th Year StudentB.E. (Mech. Engg.)

National Institute of Technology, Trichy

College Teacher and ReviewerShivraj Deshmukh

Ph.D studentIIT Bombay

29 June 2010

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook companion and scilabcodes written in it can be downloaded from the website www.scilab.in


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Book Details

Authors: Robert W. Fox and Alan T. McDonald

Title: Introduction to Fluid Mechanics

Publisher: John Wiley & Sons

Edition: 5th

Year: 2001

Place: New Delhi

ISBN: 9971-51-355-2

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Contents

List of Scilab Code 4

1 Introduction 101.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2 Scilab Code . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Fundamental Concepts 12

2.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Scilab Code . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Fluid Statics 14


4 Basic Equations in Integral form for a Control Volume 23


5 Introducton to Differential Analysis of Fluid Motion 38


6 Incompressible Inviscid Flow 42

6.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.2 Scilab Code . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7 Dimensional Analysis and Simlitude 49


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8 Internal Incompressible Viscous Flow 55


9 External Incompressible Viscous Flow 66


10 Fluid Machinery 75


11 Introduction to Compressible Flow 95


12 Steady One-Dimensional Compressible Flow 100


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List of Scilab Code

1.01 1.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.01d 1.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 101.02 1.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.02d 1.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 112.02 2.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.02d 2.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 133.01 3.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.01d 3.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 153.03 3.03.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.03d 3.03-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 173.04 3.04.sci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.04d 3.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 183.05 3.05.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.05d 3.05-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 203.06 3.06.sci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.06d 3.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 203.07 3.07.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.07d 3.07-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 214.01 4.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.01d 4.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 244.02 4.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.02d 4.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 254.03 4.03.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.03d 4.03-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.04 4.04.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.04d 4.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 274.05 4.05.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.05d 4.05-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4


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4.06 4.06.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.06d 4.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 284.07 4.07.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.07d 4.07-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 294.08 4.08.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.08d 4.08-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 304.09 4.09.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.09d 4.09-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 304.10 4.10.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.10d 4.10-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 314.11 4.11.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.11d 4.11-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.12 4.12.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.12d 4.12-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 344.14 This is some example . . . . . . . . . . . . . . . . . . . . . 344.14d 4.14-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 354.16 4.16.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.16d 4.16-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 364.17 4.17.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.17d 4.17-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 365.02 5.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.02d 5.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.07 5.07.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.07d 5.07d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.08 5.08.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.08d 5.08-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 405.09 5.09.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.09d 5.09-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 416.01 6.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.01d 6.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 426.02 6.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.02d 6.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 436.03 6.03.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.03d 6.03-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 446.04 6.04.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.04d 6.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 446.05 6.05.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.05d 6.05-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 45

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6.06 6.06.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.06d 6.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 466.08 6.08.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.08d 6.08-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 476.09 6.09.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.09d 6.09-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 487.04 7.04.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497.04d 7.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 507.05 7.05.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507.05d 7.05-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 517.06 7.06.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527.06d 7.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 53

8.01 8.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558.01d 8.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 568.02 8.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568.02d 8.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 578.04 8.04.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578.04d 8.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 578.05 8.05.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588.05d 8.05-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 588.06 8.06.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598.06d 8.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 59

8.07 8.07.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608.07d 8.07-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 608.08 8.08.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608.08d 8.08-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 618.09 8.09.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628.09d 8.09-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 628.10 8.10.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638.10d 8.10-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 638.11 8.11.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648.11d 8.11-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 649.01 9.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

9.01d 9.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 669.04 9.04.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679.04d 9.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 689.05 9.05.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689.05d 9.05-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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9.06 9.06.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

9.06d 9.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 709.07 9.07.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709.07d 9.07-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 709.08 9.08.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719.08d 9.08-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 729.09 9.09.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729.09d 9.09-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . . 7410.01 10.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7510.01d 10.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 7610.02 10.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7610.02d 10.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 77

10.03 10.03.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7710.03d 10.03-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 7810.06 10.06.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7910.06d 10.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 8010.07 10.07.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8110.07d 10.07-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 8110.08 10.08.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8210.08d 10.08-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 8510.11 10.11.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8610.11d 10.11-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 88

10.12 10.12.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9110.12d 10.12-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 9210.14 10.14.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9210.14d 10.14-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 9310.16 10.16.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9310.16d 10.16-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 9411.01 11.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9511.01d 11.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 9611.03 11.03.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9611.03d 11.03-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 9711.04 11.04.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

11.04d 11.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 9912.01 12.01.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10012.01d 12.01-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 10112.02 12.02.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10212.02d 12.02-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 103

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12.03 12.03.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

12.03d 12.03-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 10412.04 12.04.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10412.04d 12.04-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 10512.05 12.05.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10612.05d 12.05-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 10612.06 12.06.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10712.06d 12.06-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 10812.07 12.07.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10812.07d 12.07-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 10912.08 12.08.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11012.08d 12.08-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 111

12.09 12.09.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11112.09d 12.09-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 11312.10 12.10.sce . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11312.10d 12.10-data.sci . . . . . . . . . . . . . . . . . . . . . . . . . 115

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List of Figures

3.1 Output graph of S 3.01 . . . . . . . . . . . . . . . . . . . . . 16

4.1 Output graph of S 4.11 . . . . . . . . . . . . . . . . . . . . . 33

7.1 Output graph of S 7.05 . . . . . . . . . . . . . . . . . . . . . 52

9.1 Output graph of S 9.08 . . . . . . . . . . . . . . . . . . . . . 73

10.1 Output graph of S 10.03 . . . . . . . . . . . . . . . . . . . . 7910.2 Output graph of S 10.07 . . . . . . . . . . . . . . . . . . . . 8310.3 Output graph-1 of S 10.08 . . . . . . . . . . . . . . . . . . . 8610.4 Output graph-2 of S 10.08 . . . . . . . . . . . . . . . . . . . 8710.5 Output graph-1 of S 10.11 . . . . . . . . . . . . . . . . . . . 8910.6 Output graph-2 of S 10.11 . . . . . . . . . . . . . . . . . . . 89

10.7 Output graph-3 of S 10.11 . . . . . . . . . . . . . . . . . . . 9011.1 Output graph of S 11.03 . . . . . . . . . . . . . . . . . . . . 98

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Chapter 1

Introduction

1.1 Discussion

When executing the code from the editor, use the Execute File into Scilabtaband not the Load in Scilabtab

The .sci files of the respective problems contain the input parameters ofthe question

1.2 Scilab Code

Example 1.01 1.01.sce

1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 1 . 0 1 . s c e )2 f i lename=pathname+filesep ()+1.01data . sc i 3 exec ( f i l e na me )4 / / H e a t a d d e d d u r i n g t h e p r o c e s s ( i n k J ) :

5 Q12=mcp (T2T1)6 p r i n t f ( \n\nRESULTS\n\n )7 p r i n t f ( \n\nHea t a dd ed d u r in g t h e p r o c e s s : %f kJ\n\n ,

Q12/1000)

Example 1.01d 1.01-data.sci

1 / / M a s s o f o x y g e n p r e s e n t ( i n k g ) :

2 m=0.95;

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3 / / I n i t i a l t e m p e r a t u r ( i n K ) :

4

T1=300;5 / / F i n a l t e m p e r a t u r e o f o x y g e n ( i n K ) :

6 T2=900;7 / / P r e s s u r e o f o x y g e n ( i n k P a ) :

8 p=150;9 / / S p e c i f i c h e a t a t c o n s t a n t p r e s s u r e ( i n J / k g K ) :

10 c p = 9 0 9 . 4 ;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 1 . 0 2 . s c e )2 f i lename=pathname+filesep ()+1.02data . sc i 3 exec ( f i l e na me )4 / / S p e e d a t w h i c h t h e b a l l h i t s t h e g r o u n d ( i n m / s e c ) :

5 V=sqrt (mg/k(1%e(2k/m(y0 ) ) ) )6 / / T e r m i n a l s p e e d ( i n m / s e c ) :

7 Vt=sqrt (mg/k )8 / / R a t i o o f a c t u a l s p e e d t o t h e t e r m i n a l s p e e d :

9 r=V/Vt ;10 p r i n t f ( \n\nRESULTS\n\n )11 p r i n t f ( \n\nSpeed a t wh ich t he b a l l h i t s he gr oun d : %f

m/sec \n\n ,V)12 p r i n t f ( \n\n Ra ti o o f a c tu a l s pe ed t o t he t e rm i na l s pe ed

: %f\n\n , r )


1 / / M a s s o f b a l l ( i n k g ) :

2 m=0.2;3 / / H e i g h t f o m w h i c h b a l l i s d r o p p e d ( i n m ) :

4 y0=500;5 / / V a l u e o f k :

6 k=2104;7 / / A c c l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

8 g = 9 . 8 1 ;

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Chapter 2

Fundamental Concepts

2.1 Discussion



2.2 Scilab Code


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 2 . 0 2 . s c e )2 f i lename=pathname+filesep ()+2.02data . sc i 3 exec ( f i l e na me )4

5 / / V i s c o s i t y i n u n i t s o f l b f s / f t 2 :

6 u1=u/100/454/32.23 0 . 57 / / K i n e m a t i c v i s c o s i t y ( i n m / s e c 2 ) :

8 v=u1/SG/d ( 0 . 3 0 5 ) 29

/ / S h e a r s t r e s s o n t h e u p p e r p l a t e ( l b f / f t 2 ) :10 tu=u1U/D100011 / / S h e a r s t r e s s o n t h e l o w e r p l a t e ( i n P a )

12 tl=tu 4 . 4 5 / 0 . 3 0 5 213 p r i n t f ( \n\nRESULTS\n\n )

12


14/116

14 p r i n t f ( \n\ n Vi sc os it y i n u ni ts o f l bf s/ f t 2: %1. 8 f

$ l b f s / f t 2\n\n ,u1 )15 p r i n t f ( \n\n K in em a ti c v i s c o s i t y : %1 . 8 f m/ s e c 2\n\n ,v )16 p r i n t f ( \n\n Sh ea r s t r e s on t he u pe er p l a t e : %f l b f / f t

2\n\n , t u )17 p r i n t f ( \n\n Sea r s t r e s s on t he l ow er p l a t e : %f Pa\n\n ,

t l )


1 / / M a s s o f o x y g e n p r e s e n t ( i n k g ) :

2 m=0.95;3 / / I n i t i a l t e m p e r a t u r ( i n K ) :

4 T1=300;5 / / F i n a l t e m p e r a t u r e o f o x y g e n ( i n K ) :

6 T2=900;7 / / P r e s s u r e o f o x y g e n ( i n k P a ) :

8 p=150;9 / / S p e c i f i c h e a t a t c o n s t a n t p r e s s u r e ( i n J / k g K ) :

10 c p = 9 0 9 . 4 ;

13


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Chapter 3

Fluid Statics

3.1 Discussion



When we execute S 3.01, we get Fig. 3.1.

3.2 Scilab Code


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 3 . 0 1 . s c e )2 f i lename=pathname+filesep ()+3.01data . sc i 3 exec ( f i l e na me )4 / / T u b e d i a m e t e r ( i n mm ) :

5 D=1:25;6 D1=D/10007 [m n]= s i z e (D1)8

f o r i =1:n9 / / C h a n g e i n l i q u i d l e v e l f o r w a t e r ( i n mm ) :

10 dhw( i ) =4STw cosd ( thetaw ) /dw/g/D1( i ) ;11 / / C h a n g e i n l i q u i d l e v e l f o r m e r c u r y ( i n mm ) :

12 dhm( i )=4STm cos d ( thetam ) /dm/g /D1( i ) ;

14


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13 end ;14

15 / / P l o t t i n g t u b e d a i m e t e r a n d w a t e r l e v e l :

16 plot (D11000 ,dhw, o )17 / / P l o t t i n g t u b e d a i m e t e r a n d m e r c u r y l e v e l :

18 plot (D1100 0 ,dhm, )19 leg en d ([ Water ; Mercury ]) ;20 x t i t l e ( L i q u i d l e v e l v s Tube d i a m e te r , L i q u i d l e v e l ( i n

mm) , Tube di am et er ( i n mm) )


1 / / S u r f a c e t e n s i o n o f w a t e r ( i n mN / m ) :

2 STw=72.8103;3 / / S u r f a c e T e n s i o n o f m e r c u r y ( i n mN / m ) :

4 STm=37510 3;5 / / C o n t a c t a n g l e f o r w a t e r :

6 thetaw=0;7 / / C O n t a c t a n g l e f o r m e r c u r y :

8 thetam=140;9 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

10 dw=1;11

/ / D e n s i t y o f m e r c u r y ( i n k g / m 3 ) :12 dm=13.6;13 / / A c c e l e r a t i o n d e t o g r a v i t y ( i n m / s e c ) :

14 g = 9 . 8 1 ;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 3 . 0 3 . s c e )2 f i lename=pathname+filesep ()+3.03data . sc i 3 exec ( f i l e na me )

4 / / P r e s s u r e d i f f e r e n c e ( i n l b f / i n 2 ) :5 dp=gd(d1+SGmd2SGod3+SGmd4+d5)/12/1446 p r i n t f ( \n\nRESULTS\n\n )7 p r i n t f ( \n\n P re s su r e d i f f e r e n c e b etw een A and B : %f l b f

/ i n 2\n\n ,dp)

15


17/116

Figure 3.1: Output graph of S 3.01

16


18/116


1 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n f t / s e c 2 ) :

2 g = 3 2 . 2 ;3 / / S p e c i f i c g r a v i t y o f m e r c u r y :

4 SGm=13.6;5 / / S p e c i f i c g r a v i t y o f o i l :

6 SGo=0.88;7 / / S p e c i f i c g r a v i t y o f w a t e r :

8 SGw=1;9 / / D e n s i t y o f w a t e r ( i n s l u g / f t 3 ) :

10 d = 1 . 9 4 ;11 / / H e i g h t s o f l i q u i d i n v a r i o u s t u b e s ( i n i n c h e s ) :

12 d1=10;13 d2=3;14 d3=4;15 d4=5;16 d5=8;

Example 3.04 3.04.sci

1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 3 . 0 4 . s c e )2 f i lename=pathname+filesep ()+3.04data . sc i 3 exec ( f i l e na me )4 / / A s s u m i n g t e m p e r a t u r e v a r i e s l i n e a r l y w i t h a l t i t u d e :

5 / / T e m p e r a t u r e g r a d i e n t ( i n F / f t ) :

6 m=(T1T 2) /( z 2z1 )7 / / V a l u e o f g / ( m R ) :

8 v=g/m/R/32.29 / / P r e s s u r e a t V a i l P a s s ( i n i n c h e s o f H g ) :

10 p12=p1 ((T2+460)/(T1+460))v11 / / P e r c e n t a g e c h a n g e i n d e n s i t y :

12 pc1=(p12/p1(T1+460)/(T2+460)1)10013 / / A s s u m i n g d e n s i t y i s c o n s t a n t :

14 / / P r e s s u r e a t V a i l P a s s ( i n i n c h e s o f H g ) :

15 p22=p1(1( g( z2z 1 ) / ( R32 .2 ) /(T1+460)) )

17


19/116

16 / / P e r c e n t a g e c h a n g e i n d e n s i t y :

17

pc2=0;18 / / A s s u m i n g t e m p e r a t u r e i s c o n s t a n t :

19 / / P r e s s u r e a t V a i l P a s s ( i n i n c h e s o f H g ) :

20 p32=p1%e(g( z2z 1 ) / ( R32 .2 ) /(T2+460))21 / / P e r c e n t a g e c h a n g e i n d e n s i t y :

22 pc3=(p32/p1(T1+460)/(T1+460)1)10023 / / F o r a n a d i a b a t i c a t m o s p h e r e :

24 p42=p1( ( 62+460) /( 80+460) ) ( k /( k1) )25 / / P e r c e n t a g e c h a n g e i n d e n s i t y :

26 pc4=(p42/p1(T1+460)/(T2+460)1)10027 p r i n t f ( \n\nRESULTS\n\n )28 p r i n t f ( \n\n1 ) I f t em pe ra tu re v a r i e s l i n e a r l y with

a l t i t u d e \n\n )29 p r i n t f ( \n\n\ t At mo s ph er i c p r e s s u r e a t V a i l P as s : %f

i n ch e s o f Hg\n\n , p12)30 p r i n t f ( \n\n\ t P e r ce n t a g e c ha ng e i n d e n s i t y wr t D en ver :

%f p e r c e n t\n\n , pc1 )31 p r i n t f ( \n\n2 ) I f d en s it y i s c on st an t\n\n )32 p r i n t f ( \n\n\ t At mo s ph er i c p r e s s u r e a t V a i l P as s : %f


%f p e r c e n t\n\n , pc2 )34 p r i n t f ( \n\n3 ) I f t em pe ra tu re i s c on st a nt \n\n )35 p r i n t f ( \n\n\ t At mo s ph er i c p r e s s u r e a t V a i l P as s : %f


%f p e r c e n t\n\n , pc3 )37 p r i n t f ( \n\n4 ) Fo r an a d i a b a t i c a tm os ph er e\n\n )38 p r i n t f ( \n\n\ t At mo s ph er i c p r e s s u r e a t V a i l P as s : %f


%f p e r c e n t\n\n , pc4 )


1 / / E l e v a t i o n o f D e n v e r ( i n f t ) :

2 z1=5280;

18


20/116

3 / / P r e s s u r e a t D e n v e r ( i n mm o f H g ) :

4

p1=24. 8;5 / / T e m p e r a t u r e a t D e n v e r ( i n F ) :

6 T1=80;7 / / E l e v a t i o n a t V a i l P a s s ( i n f t ) :

8 z2=10600;9 / / T e m p e r a t u r e a t V s i l P a s s ( i n F ) :

10 T2=62;11 / / V a l u e o f R i n f t l b f / l b m R ) :

12 R=53.3;13 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n f t / s e c 2 ) :

14 g = 3 2 . 2 ;15 / / V a l u e o f a d i a b a t i c c o n s t a n t :

16 k = 1 . 4 ;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 3 . 0 5 . s c e )2 f i lename=pathname+filesep ()+3.05data . sc i 3 exec ( f i l e na me )4 / / N e t f o r c e o n t h e g a t e ( i n k N ) :

5 Fr=dgw(DL+L2/2 si nd ( th et a ) )6 / / C e n t r e o f p r e s s u r e :

7 / / C a l c u l a t i o n f o r y c o o r d i n a t e :

8 yc=D/ s i n d ( t h e t a )+L/29 / / A r e a ( i n m 2 ) :

10 A=Lw11 / / M o m e n t o f i n e r t i a o f r e c t a n g u l a r g a t e ( i n m 4 ) :

12 Ixx=wL3/1213 / / y c o o r d i n a t e ( i n m ) :

14 y=yc+Ixx/A/yc15 / / C a l c u l a t i o n f o r x c o o r d i n a t e :

16 Ixy=0

17 xc=w/218 / / x c o o r d i n a t e ( i n m ) :

19 x=xc+Ixy/A/xc20 p r i n t f ( \n\nRESULTS\n\n )21 p r i n t f ( \n\nNet f o r c e on t he g a te : %f kN\n\n , Fr/1000)

19


21/116

22 p r i n t f ( \n\n C oo r di n at e o f c e n t r e o f p r e s s u r e : ( %0 . 1 f , %0

. 1 f )\n\n , x , y )


1 / / L e n g t h o f g a t e ( i n m ) :

2 L=4;3 / / W i d t h o f g a t e ( i n m ) :

4 w=5;5 / / D e p t h o f g a t e u n d e r w a t e r ( i n m ) :

6 D=2;7 / / D e n s i t y o f w a t e r ( i n k g / m 3 :

8 d=999;9 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

10 g = 9 . 8 1 ;11 / / A n g l e o f g a t e w i t h h o r i z o n t a l :

12 t he t a=30;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 3 . 0 6 . s c e )2 f i lename=pathname+filesep ()+3.06data . sc i

3 exec ( f i l e na me )4 / / F o r c e r e q u i r e d t o k e e p t h e d o o r s h u t ( i n l b f ) :

5 function y=f (z) ,y=b/Lp0z+db/L(Lzz 2) , endfunction6 Ft=intg (0 ,L , f )7 p r i n t f ( \n\nRESULTS\n\n )8 p r i n t f ( \n\n Fo rc e r e q u i r e d t o k ep t h e d oo r s h ut : %. 1 f

l b f\n\n , Ft)


1 / / P r e s s u r e a p l l i e d o n t h e d o o r ( i n p s f g ) :

2 p0=100;3 / / L e n g t h o f d o o r ( i n f e e t ) :

4 L=3;5 / / B r e a d t h o f t h e d o o r ( i n f e e t ) :

20


22/116

6 b=2;7

/ / D e n s i t y o f l i q i u i d ( i n l b f / f t 3 ) :8 d=100;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 3 . 0 7 . s c e )2 f i lename=pathname+filesep ()+3.07data . sc i 3 exec ( f i l e na me )4 / / H o r i z o n t a l c o m p o n e n t o f r e s u l t a n t f o r c e ( i n k N ) :

5 Frh=0.5dgwD26 / / L i n e o f a c t i o n o f F r h ( i n m ) :

7 y1=0.5D+wD 3 / 1 2 / ( 0 . 5D)/(wD)8 / / V e r t i c a l c o m p o n e n t o f r e s u l t a n t f o r c e ( i n k N ) :

9 function y=q ( x ) , y=dgw(Dsqrt ( ax ) ) , endfunction10 Frv=intg (0 ,D2/a , q)11 / / L i n e o f a c i o n o f F r v ( i n m ) :

12 function k=f ( x ) , k=dgw/Frvx(Dsqrt ( ax ) ) ,endfunction

13 xa=intg (0 ,D2/a , f )14 / / F o r c e r e q u i r e d t o k e e p t h e g a t e i n e q u i l i b r i u m ( i n k N )

:

15

Fa=1/l ( xa Frv+(Dy1 )Frh)16 p r i n t f ( \n\nRESULTS\n\n )17 p r i n t f ( \n\n Force r e qu i r ed t o keep t he g at e a t

e q u i l i b r i u m : %f kN\n\n ,Fa/100 0)


1 / / W i d t h o f g a t e ( i n m ) :

2 w=5;3 / / D e p t h o f w a t e r ( i n m ) :

4 D=4;

5 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) ;

6 d=999;7 / / A c c e l r a t i o n d e t o g r a v i t y ( i n m / s e c 2 ) :

8 g = 9 . 8 1 ;9 / / V a l u e o f a ( i n m ) :

21


23/116

10 a=4;11

/ / P o i n t w h e r e f o r c e a c t s ( i n m ) :12 l =5;

22


24/116

Chapter 4

Basic Equations in Integral

form for a Control Volume

4.1 Discussion



When we execute S 4.11, we get Fig. 4.1.

4.2 Scilab Code


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 1 . s c e )2 f i lename=pathname+filesep ()+4.01data . sc i 3 exec ( f i l e na me )4 / / I f I = i n t e g r a l o f ( pV . d A ) :

5 / / F o r s y s t e m : I c s = I A 1 + I A 2 + I A 3 + I A 4 .

6

/ / F o r a r e a 17 IA1=dV1A18 / / F o r a r e a 3 : I A 2 = d V 3 A 3 = m 3

9 IA3=m310 / / F o r a r e a 4 : I A 4 =d V 4 A 4 =d Q 4

23


25/116

11 IA4=dQ412

/ / F o r a r e a 2 :13 IA2=IA1IA3IA414 / / V e l o c i t y a t s e c t i o n 2 ( i n f t / s e c ) :

15 V2=IA2/d/A216 / / V 2 i s i n t h e n e g a t i v e y d i r e c t i o n

17 p r i n t f ( \n\nRESULTS\n\n )18 p r i n t f ( \n\n Ve lo ci ty a t s e c ti o n 2 : %. 0 f j f t / s e c \n\n ,

V2)


1 / / A r e a o f 1 ( i n f t 2 ) :

2 A1=0.2;3 / / A r e a o f 2 ( i n f t 2 ) :

4 A2=0.5;5 / / A r e a o f 3 ( i n f t 2 ) :

6 A3=0.4;7 / / A r e a o f 4 ( i n f t 2 ) :

8 A4=0.4;9 / / D e n s i t y o f w a t e r ( i n s l u g / f t 3 ) :

10 d = 1 . 9 4 ;11 / / M a s s f l o w r a t e o u t o f s e c t i o n 3 ( i n s l u g / s e c ) :

12 m3=3.88;13 / / V o l m e f l o w r a t e i n s e c t i o n 4 ( i n f t 3 / s e c ) :

14 Q4=1;15 / / V e l o c i t y a t 1 ( i n f t / s e c ) :

16 V1=10;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 2 . s c e )2 f i lename=pathname+filesep ()+4.02data . sc i

3 exec ( f i l e na me )4 / / I f I = i n t e g r a l o f ( pV . d A ) :

5 / / F o r s y s t e m : I C S = I a b + I b c + I c d + I d a

6 / / B u t I C S = 0

7

24


26/116

8 / / F o r A a b :

9

function p=f (y) ,p=dUwy 0 , endfunction10 IAab=intg (0 , t , f )11

12 / / F o r A c d :

13 function q=g(y) ,q=dUw(2y/ t(y/t ) 2) , endfunction14 IAcd=intg (0 , t , g )15

16 / / M a s s f l o w r a t e a c r o s s s u r f a c e b c ( i n k g / s e c ) :

17 mbc=(IAabIAcd)/100018 p r i n t f ( \n\nRESULTS\n\n )19 p r i n t f ( \n\nMass f l ow r a t e a c r o s s s u r f a c e bc : %. 4 f kg /

s e c \n\n , mbc)


1 / / F l o w v e l o c i t y a h e a d o f t h e p l a t e ( i n m / s e c ) :

2 U=30;3 / / B o u n d a r y l a y e r t c k n e s s a t l o c a t i o n d ( i n mm ) :

4 t=5;5 / / D e n s i t y o f f l u i d a i r ( i n k / m 3 ) :

6 d = 1 . 2 4 ;7

/ / P l a t e w d t h p e r p e n d i c u l a r t o t h e p l a t e ( i n m ) :8 w=0.6;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 3 . s c e )2 f i lename=pathname+filesep ()+4.03data . sc i 3 exec ( f i l e na me )4 / / R a t e o f c h a n g e o f a i r d e n s i t y i n t a n k ( i n ( k g / m 3 ) / s ) :

5 r=dvA/V/1066 p r i n t f ( \n\nRESULTS\n\n )7 p r i n t f ( \n\nRate o f c ha ng e o f a i r d e n s i t y i n t an k : %. 3 f

kg/m3\n\n , r )8 p r i n t f ( \n\nThe d e ns i t y d e c re a s es a s i s i n d i ca t e d b y

t he n e ga t iv e s i g n\n\n )

25


27/116


1 / / V o l u m e o f t a n k ( i n m 3 ) :

2 V=0.05;3 / / P r e s s u r e o f a i r ( I n k P a ) :

4 p=800;5 / / T e m p e r a t u r e o f t a n k ( i n C ) :

6 T=15;7 / / V e l o c i t y o f l e a v i g a i r ( i n m / s e c ) :

8 v=311;9 / / D e n s i t y o f a i r ( i n k g / m 3 ) :

10 d = 6 . 1 3 ;11 / / A r e a o f v a l v e e x i t ( i n mm 2 ) :

12 A=65;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 4 . s c e )2 f i lename=pathname+filesep ()+4.04data . sc i 3 exec ( f i l e na me )4 / / 1 ) C o n t r o l V o l u m e s e l e c t e d s o t h a t a r e a o f l e f t

s u r f a c e i s e q u a l t o t h e a r e a o f t h e r i g h t s u r f a c e

5

u1=15;6 / / F o r c e o f s u p p o r t o n c o n t r o l v o l u m ( i n k N ) :

7 function y=f (A) ,y=u1dV, endfunction8 Rx1=intg (0 ,0 .0 1 , f )9 / / H o r i z o n t a l f o r c e o n s u p p o r t ( i n k N ) :

10 Kx=Rx111 / / 2 ) C o n t r o l v o l u m e s a r e s e l e c t e d d o t h a t t h e a r e a o f

t h e l e f t a n d r i g h t s u r f a c e s a r e e q u i a l t o t h e a r e a

o f t h e p l a t e

12

13 function z=g (A) , z=u1dV, endfunction

14 Fsx=intg ( 0 , 0 . 0 1 , g )15 / / N e t f o r c e o n p l a t e : F x =0 = Bx p a A p + R x

16 / / R x = p a A p + B x

17 / / F r o m t h e a b o v e , i t i s o b t a i n e d t h a t :

18 Rx2=2.25

26


28/116

19 / / H o r i z o n t a l f o r c e o n s u p p o r t ( i n k N ) :

20

Kx2=Rx221 p r i n t f ( \n\nRESULTS\n\n )22 p r i n t f ( \n\n H o r i z o n ta l f o r c e on s u p po r t : %. 3 f kN\n\n ,

Kx/1000)


1 / / V e l o c i t y o f w a t e r l e a v i n g t h e n o z l e ( i n m / s e c ) :

2 V=15;3 / / A r e a o f n o z z l e ( i n m 2 ) :

4 A=0.01;5 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

6 d=999;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 5 . s c e )2 f i lename=pathname+filesep ()+4.05data . sc i 3 exec ( f i l e na me )4 / / W e i g h t o f w a t e r i n t h e t a n k ( i n l b f ) :

5 d1=62. 4;

6 WH2O=d1Ah7 v=5;8 / / T o t a l b o d y f o r c e i n n e g a t i v e y d i r e c t i o n ( l b f ) :

9 function y=f (A) ,y=vd2V1 , endfunction10 F=intg (0 ,A1, f )11 / / F o r c e o f s c a l e o n c o n t r o l v o l u m e ( i n k N ) :

12 Ry=W+WH2OF13 p r i n t f ( \n\nRESULTS\n\n )14 p r i n t f ( \n\n S c a l e R ea di ng : %. 3 f l b f \n\n ,Ry)


1 / / H e i g h t o f t h e c o n t a i n e r ( i n f t ) :

2 l =2;3 / / A r e a o f c r o s s s e c t i o n ( i n f t 2 ) :

27


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4 A=1;5

/ / W e i g h t o f c o n t a i n e r ( i n l b f ) :6 W=5;7 / / W a t e r d e p t h ( i n f t ) :

8 h = 1 . 9 ;9 / / A r e a o f o p e n i n g 1 ( i n f t 2 ) :

10 A1=0.1;11 / / V e l o c i t y a t o p e n i n g 1 ( i n f t / s e c ) :

12 V1=5;13 / / A r e a o f o p e n i n g 2 ( i n f t 2 ) :

14 A2=0.1;15 / / A r e a o f o p e n i n g 1 ( i n f t 2 ) :

16 A3=0.1;17 / / D e n s i t y o f w a t e r ( i n s l u g / f 3 ) :

18 d2=1. 94;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 6 . s c e )2 f i lename=pathname+filesep ()+4.06data . sc i 3 exec ( f i l e na me )4 / / X c o m p o n e n t o f r e a c t i o n f o r c e p e r u n i t w i d t h o f t h e

g a t e ( i n N / m ) :

5 Rxw=(d(V22D2V12D1) )(dg /2(D12D22))6 / / H o r i z o n t a l f o r c e e x e r t e d p e r u n t w i d t h o n t h e g a t e ( i n

N / m ) :

7 Kxw=Rxw8 p r i n t f ( \n\nRESULTS\n\n )9 p r i n t f ( \n\n H o ri z o nt a l f o r c e e x e rt e d p er un t w id th on

the gate : %.3 f kN/m\n\n ,Kxw/1 00 0)


1 / / D i a m e t e r o f c h a n n e l ( i n m ) :

2 D1=1.5;3 / / V e l c i t y o f f l o w i n c h a n n e l ( i n m / s e c ) :

4 V1=0.2;5 / / D i a m e t e r a t s e c t i o n 2 ( i n m ) :

28


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6 D2=0.0563;7

/ / V e l o c i t y a s e c t i o n 2 ( i n m / s e c ) :8 V2=5.33;9 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

10 d=999;11 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

12 g = 9 . 8 1 ;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 7 . s c e )2 f i lename=pathname+filesep ()+4.07data . sc i 3 exec ( f i l e na me )4 / / V e l o c i t y a t s e c t i o n 1 ( i n m / s e c ) :

5 V1=V2A2/A16 / / G a u g e p r e s s u r e ( i n k P a ) :

7 p1g=p1patm8 u1=V1; u2=V2 ;9 / / R e a c t i o n f o r c e c o m p o n e n t i n t h e x d i r e c t i o n ( i n N ) :

10 Rx=p1 gA1u1dV1A111 / / R e a c t i o n f o r c e c o m p o n e n t i n t h e y d i r e c t i o n ( i n N ) :

12 Ry=u2dV2A213 p r i n t f

( \n\nRESULTS\n\n )14 p r i n t f ( \n\n Force t o h ol d elbow a c t in g t o t he l e f t : %. 3

f kN\n\n ,Rx/100 0)15 p r i n t f ( \n\n F or ce t o h o l d e lb ow a c t i n g d ownwards : %. 3 f

N\n\n ,Ry)


1 / / P r e s s u r e a t i n l e t t o t h e e l b o w ( i n N / m 2 ) :

2 p1=2. 21105;3 / / A r e a o f c r o s s s e c t i o n ( i n m 2 ) :

4 A1=0.01;5 / / V e l o c i t y a t s e c t o n 2 ( i n m / s e c ) :

6 V2=16;7 / / A r e a o f c r o s s s e c t i o n o f s e c t i o n 2 ( i n m 2 ) :

8 A2=0.0025;

29


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9 / / A t m o s p h e r i c p r e s s u r e ( i n k P a ) :

10

patm=1.012105;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 8 . s c e )2 f i lename=pathname+filesep ()+4.08data . sc i 3 exec ( f i l e na me )4 / / T e n s i o n r e q u i r e d t o p u l l t h e b e l t ( i n l b f ) :

5 T=Vbelt m/32. 26 p r i n t f ( \n\nRESULTS\n\n )7 p r i n t f ( \n\n Tens ion r e q ui r e d t o p u l l t he b e l t : %. 3 f l b f

\n\n ,T)


1 / / V e l o c i t y o f c o n v e y o r b e l t ( i n f t / s e c ) :

2 Vbelt=3;3 / / V e l o c i t y o f s a n d a l l i n g o n t o b e l t ( i n f t / s e c ) :

4 Vsand=5;5 / / F l o w r a t e ( i n l b m / s e c ) :

6 m=500;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 0 9 . s c e )2 f i lename=pathname+filesep ()+4.09data . sc i 3 exec ( f i l e na me )4 / / M i n i m u m g a u g e p r e s s u r e r e q u i r e d ( i n l b f / i n 2 ) :

5 pg=8/%pi2d/D14Q 2((D1/D2)41) 1446 p r i n t f ( \n\nRESULTS\n\n )7 p r i n t f ( Minimum g au g e p r e s s u r e r e q u i r e d : %. 3 f l b f / i n 2

, p g )


1 / / N o z z l e i n l e t d i a m e t e r ( i n i n c h e s s ) :

30


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2 D1=3;3

/ / N o z z l e e x i t d i a m e t e r ( i n i n c h e s ) :4 D2=1;5 / / D e s i r e d v o l u m e f l o w r a t e ( i n f t 3 / s e c ) :

6 Q=0.7;7 / / D e n s i t y o f w a t e r ( i n s l u g / f t 3 ) :

8 d = 1 . 9 4 ;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 1 0 . s c e )2 f i lename=pathname+filesep ()+4.10data . sc i 3 exec ( f i l e na me )4 u1=VU5 u2=(VU) c osd ( t he t a )6 v2=(VU) sin d ( the ta )7 V1=VU8 V2=V19 / / X c o m p o n e n t o f m o m e n t e q u a t i o n ( i n N ) :

10 function y=f (A) ,y=u1(dV1) , endfunction11 function z=g (A) , z=u2dV2 , endfunction12 Rx=intg ( 0 ,A, f )+intg (0 ,A, g )13

14 / / Y c o m p o n e n t o f m o m e n t e q u a t i o n ( i n N ) :

15 function a=h (A) , a=v2dV1 , endfunction16 Ry=intg (0 ,A,h ) / / T h i s i s a f t e r n e g l e c t i n g w e i g h t o f

v a n e a n d t h e w a t e r .

17 p r i n t f ( \n\nRESULTS\n\n )18 p r i n t f ( \n\n Net f o r c e o n t h e v an e : %. 3 f i +%. 2 f j kN\n\n

,Rx/1000,Ry/1000)


1 / / V a n e t u r n i n g a n g l e :

2 t he t a=60;3 / / S p e e d o f v a n e ( i n m / s e c ) :

4 U=10;5 / / A r e a o f n o z z l e ( i n m 2 ) :

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6 A=0.003;7

/ / F l o w v e l o c i t y o f w a t e r ( i n m / s e c ) :8 V=30;9 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

10 d=999;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 1 1 . s c e )2 f i lename=pathname+filesep ()+4.11data . sc i 3 exec ( f i l e na me )4 / / E v a l u a t i n g t h e v a l u e o f V b :

5 Vb=V(1cosd ( the ta ) )dA/M6 / / V a l u e o f U / V f o r v a r i o u s v a l u e s o f t

7 t =0:2 0;8 [m n]= s i z e ( t )9 f o r i =1:n10 U V( i )=Vb t ( i ) /(1+Vb t ( i ) ) ;11 end

12

13 / / P l o t t i n g U / V v s t :

14 plot ( t , U V )15

x t i t l e ( U/V vs t , t ( in se c ) , U/V )


1 / / M a s s o f v a n e a n d c a r t ( i n k g ) :

2 M=75;3 / / T u r n i n g a n g l e o f v a n e :

4 t he t a=60;5 / / S p e e d o f w a t e r l e a v i n g n o z z l e h o r i z o n t a l l y ( i n m / s e c ) :

6 V=35;7 / / E x i t a r e a o f n o z z l e ( i n m ) :

8 A=0.003;9 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

10 d=999;

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33


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1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 1 2 . s c e )2 f i lename=pathname+filesep ()+4.12data . sc i 3 exec ( f i l e na me )4 / / A c c e l e r a t i o n o f r o c k e t a t t = 0 ( i n m / s e c 2 ) :

5 Veme/M0g6 / / V e l o c i t y o f r o c k e t a t t = 1 0 ( i n m / s e c ) :

7 function y=f ( t ) , y=Veme/(M0me t )g , endfunction8 Vcv=intg (0 , t , f )9 p r i n t f ( \n\nRESULTS\n\n )10 p r i n t f ( \n\n V e lo c i ty o f r o c k et a t t = 10: %. 1 f m/ s e c \n\n

,Vcv)


1 / / I n i t i a l m a s s o f t h r o c k e t ( i n k g ) :

2 M0=400;3 / / R a t e o f f u e l c o n s u m p t i o n ( i n k g / s e c ) :

4 me=5;5 / / E x h a u s t v e l o c i t y ( i n m / s e c ) :

6 Ve=3500;7 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

8 g = 9 . 8 1 ;9 / / T i m e a f t e r w h i c h v e l o c i t y i s t o b e c a l c u l a t e d ( i n s e c )

:

10 t=10;



4 / / A r e a o f j e t ( i n mm 2 ) :

5 Ajet=%pi/4D26 / / J e t s p e e d r e l a t i v e t o t h e n o z z l e ( i n m / s e c ) :

7 Vr el=Q/2/ Aj et 106/60/10008 / / V a l u e o f w R i n m / s e c :

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9 wR=wR2%pi/60/100010

/ / F r i c t i o n t o r q u e a t p i v o t ( i n Nm ) :11 Tf=R( V r e lc o s d ( a l p h a )wR) dQ/1000/60/100012 p r i n t f ( \n\nRESULTS\n\n )13 p r i n t f ( \n\n Je t s pe ed r e l a t i v e t o e ac h n o z z l e : %. 2 f m/

s e c \n\n , Vr el )14 p r i n t f ( \n\ n F r i c t i o n t o rq u e a t p i v ot : %. 5 f Nm\n\n , Tf)


1 / / I n l e t g a u g e p r e s s u r e ( i n k P a ) :

2 p=20;3 / / V o l u m e f l o w r a t e o f w a t e r t h r o u g h t h e s p r i n k l e r ( i n l /

m i n ) :

4 Q=7.5;5 / / S p e e d o f r o t s t i o n o f s p r i n k l e r ( i n r p m ) :

6 w=30;7 / / D i a m e t e r o f j e t f s p r i n k l e ( i n mm ) :

8 D=4;9 / / R a d i u s o f s p r i n k l e r ( i n mm ) :

10 R=150;11 / / S u p p l y p r e s s u r e t o s p r i n k l e r ( i n k P a ) :

12

p=20;13 / / A n g l e a t w h i c h j e t i s s p r a y e d w r t h o r i z o n t a l :

14 al pha=30;15 / / D e n s i t y o f w a t e r ( i n k g / m ) :

16 d=999;



4 / / V e l o c i t y a t e x i t ( i n f t / s e c ) :

5 V2=mR(T2+460)/A2/p2/1446 / / A s p o w e r i n p u t i s t o CV , Ws = 6 0 0

7 / / R a t e o f h e a t t r a n s f e r ( i n B t u / s e c ) :

8 Q=Ws550/778+mcp (T2T1)+mV 22/2/32. 2/778

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9 p r i n t f ( \n\nRESULTS\n\n )10

p r i n t f ( \n\nRate o f h ea t t r a n s f e r : %. 3 f Btu / s e c\n\n ,Q)


1 / / P r e s s u r e a t e n t r y ( i n p s i a ) :

2 p1=14. 7;3 / / T e m p e r a t u r e a t e n t r y ( i n F ) :

4 T1=70;5 / / P r e s s u r e a t e x i t ( i n p s i a ) :

6 p2=50;7 / / T e m p r a t u r e a e x i t ( i n F ) :

8 T2=100;9 / / C r o s s s e c t i o n a l a r e a o f t h e p i p e a t e x i t ( i n f t 2 ) :

10 A2=1;11 / / M a s s f l o w r a t e ( i n l b f / s e c ) :

12 m=20;13 / / P o w e r i n p u t t o t h e c o m p r e s s o r ( i n h p ) :

14 Ws=600;15 / / V a l u e o f c p ( i n B t u / l b m R ) :

16 c p = 0 . 2 4 ;17 / / V a l u e o f g a s c o n s t a n t ( i n f t l b f / ( l b m R ) )

18

R=53.3;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 4 . 1 7 . s c e )2 f i lename=pathname+filesep ()+4.17data . sc i 3 exec ( f i l e na me )4 / / D e n s i t y o f t a n k ( i n k g / m 3 ) :

5 d=(p1+patm ) /R/T6 / / M a s s f l o w r a t e o f a i r i n t o t h e t a n k ( i n k g / s e c ) :

7 m=dVcv r/R/T1000

8 p r i n t f ( \n\nRESULTS\n\n )9 p r i n t f ( \n\nMass f lo w r a t e o f a i r i n t o t he ta nk : %. 3 f g

/ s e c \n\n ,m)


36


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1 / / V o l u m e o f t a k ( i n m 3 ) :

2

V=0.1;3 / / T e m p e r a t u r e o f l i n e a n d t a n k ( i n K ) :

4 T=293;5 / / I n i t i a l t a n k g a u g e p r e s s u r e ( i n N / m 2 ) :

6 p1=1105;7 / / A b s o l u t e l i n e p r e s s u r e ( i n N / m 2 ) :

8 p=2106;9 / / R a t e o f r i s e o f t e m p e r a t u r e a f t e r o p e n i n g o f t h e

v a l v e ( i n C / s e c ) :

10 r =0.0 5;11 / / A t m o s p h e r i c p r e s s u r e ( i n N / m 2 ) :

12 patm=1.01105;13 / / G a s C o n s t a n t ( i n Nm / ( k g K ) ) :

14 R=287;15 / / V a l u e o f c v ( i n Nm / k g K ) :

16 cv=717;

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Chapter 5

Introducton to Differential

Analysis of Fluid Motion

5.1 Discussion



5.2 Scilab Code


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 5 . 0 2 . s c e )2 f i lename=pathname+filesep ()+5.02data . sc i 3 exec ( f i l e na me )4 / / R a t e o f c h a n g e o f d e n s i t y w i t h t i m e ( i n k g / m 3 s ) :

5 r=dV/L6 p r i n t f ( \n\nRESULTS\n\n )7

p r i n t f ( \n\nRa te o f c ha ng e o f d e n s i t y w it h t im e : %. 1 f kg/m3s\n\n , r )


38


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1 / / D i s t a n c e f p i s t o n f r o m c l o s e d e n d o f t h e c y l i n d e r a t

t h e g i v e i n s t a n t ( i n m ) :2 L=0. 15;3 / / D e n s i t y o f g a s ( i n k g / m 3 ) :

4 d=18;5 / / V e l o c i t y o f p i s t o n ( i n m / s e c ) :

6 V=12;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 5 . 0 7 . s c e )2 f i lename=pathname+filesep ()+5.07data . sc i 3 exec ( f i l e na me )4 / / A t p o i n t b , u = 3 mm / s e c

5 u=3;6 / / D i s p l a c e m e t o f b ( i n mm ) :

7 xb=u t8 / / R a t e o f a n g u l a r d e f o r m a t i o n ( i n s 1 ) :

9 def=U/h10 / / R a t e o f r o t a t i o n ( i n s 1 ) :

11 r o t =0.5U/h12 p r i n t f ( \n\nRSULTS\n\n )13

p r i n t f ( \n\nRa te o f a n g u la r d e f or m a ti o n : %. 1 f / s e c \n\n, def )14 p r i n t f ( \n\nRate o f r o t a t i o n : %. 1 f / s e c \n\n , ro t )

Example 5.07d 5.07d

1 / / V a l u e o f ( i n mm / s e c ) :

2 U=4;3 / / V a l u e o f h ( i n mm ) :

4 h=4;5 / / T me a t w h i c h t o f i n d p o s i t i o n ( i n s e c ) :

6 t =1.5 ;


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1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 5 . 0 8 . s c e )2

f i lename=pathname+filesep ()+5.08data . sc i 3 exec ( f i l e na me )4 / / V a l u e o f T :

5 T=log ( 3/2) /A6 x 0 = 1 : 2 ;7 y 0 = 1 : 2 ;8 f o r i =1:29 f o r j =1:210 / / F o r X c o o r d i n a t e :

11 X( i ) ( j )=x0 ( i ) %e(AT)12 / / F o r Y c o o r d i n a t e :

13 Y( i ) ( j )=y0 ( j ) %e(AT)14 end

15 end

16 plot (X,Y)17 / / R a t e s o f l i n e a r d e f o r m a t i o n i n X d i r e c t i o n :

18 Ax=0.3;19 / / R a t e o f l i n e a r d e f o r m a t i o n i n t h e y d i r e c t i o n :

20 Ay=0.3;21 / / R a t e o f v o l u m e d i l a t i o n ( s 1 ) :

22 v=AA23 / / A r e a o f a b c d :

24 A1=1;25 / / A r e a o f a b c d :

26 A2=(33/2)(4/32/3)27 p r i n t f ( \n\nRESULTS\n\n )28 p r i n t f ( \n\nRates o f l i n e a r d ef or ma ti on i n X and Y

d i r e c t i o n : %. 1 f / s , %. 1 f / s\n\n ,Ax, Ay)29 p r i n t f ( \n\nRate o f volume d i l a t i o n : %. 0 f / s e c \n\n ,v )30 p r i n t f ( \n\nAr ea of abc d and a , b , c , d :%. 1 f m2 , %. 1 f m\

n\n ,A1, A2)


1 / / V a l u e o f A ( i n s e c 1 ) :

2 A=0.3;

40


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1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 5 . 0 9 . s c e )2 f i lename=pathname+filesep ()+5.09data . sc i 3 exec ( f i l e na me )4 / / V o l u m e f l o w r a t e ( i n m 3 / s e c ) :

5 Q=dg si nd ( th et a )b( h / 1 0 0 0 ) 31000/u/36 p r i n t f ( RESULTS )7 p r i n t f ( \n\nVolume f l ow r at e : %. 4 f m3/s e c \n\n ,Q)


1 / / T h i c k n e s s o f w a t e r f i l m ( i n mm ) :

2 h=1;3 / / W i d t h o f s u r f a c e ( i n m ) :

4 b=1;5 / / A n g l e o f i n c l i n a t i o n o f s u r f a c e :

6 t he t a=15;7 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

8 d=999;9 / / A c c e l e r a t i o n d u t o g r a v i t y ( i n m / s e c 2 ) :

10 g = 9 . 8 1 ;11

/ / V i s c o s i t y ( k g /m s ) :12 u=103;

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Chapter 6

Incompressible Inviscid Flow

6.1 Discussion



6.2 Scilab Code


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 1 . s c e )2 f i lename=pathname+filesep ()+06.01data . sc i 3 exec ( f i l e na me )4 / / V e l o c i t y o f f l o w ( i n m / s e c ) :

5 V=sqrt (dw/ log ( ( r+w) / r )g/dap/1000)6 / / V o l u m e f l o w r a t e ( i n m 3 / s e c ) :

7 Q=V( dw)8 p r i n t f ( \n\nRESULTS\n\n )9

p r i n t f ( \n\nVolume f l ow r at e : %. 3 f m3/s e c \n\n ,Q)


1 / / D e p t h o f t h e d u c t ( i n m ) :

42


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2 d = 0 . 3 ;3

/ / W i d t h o f t h e d u c t ( i n m ) :4 w=0.1;5 / / I n n e r r a d i u s o f t h e b e n d ( i n m ) :

6 r =0.2 5;7 / / P r e s s u r e d i f f e r e n c e b e t w e e n t h e t a p s ( i n mm o f H g ) :

8 p=40;9 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

10 dw=999;11 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

12 g = 9 . 8 ;13 / / D e n s i t y o f a i r ( i n k g / m 3 ) :

14 da=1. 23;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 2 . s c e )2 f i lename=pathname+filesep ()+06.02data . sc i 3 exec ( f i l e na me )4 / / V e l o c i t y o f f l o w ( i n m / s e c ) :

5 V=sqrt (2dwgp/1000SG/da)6 p r i n t f ( \n\nRESULTS\n\n )7 p r i n t f

( \n\n V e l o c i t y o f f l o w : %. 3 f m/ s e c \n\n ,V)


1 / / P r e s s u r e d i f e r e n c e ( i n mm o f m e c u r y ) :

2 p=30;3 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

4 dw=1000;5 / / A c e l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

6 g = 9 . 8 1 ;7 / / D e n s i t y o f a i r ( i n k g / m 3 ) :

8 da=1. 23;9 / / S p e c i f i c g r a v i t y o f m e r c u r y :

10 SG=13.6;


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1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 3 . s c e )2

f i lename=pathname+filesep ()+06.03data . sc i 3 exec ( f i l e na me )4 / / V e l o c i t y o f f l w a t t h e i n l e t ( i n m / s e c ) :

5 V1=Ae/AiV26 / / G a u g e p r e s s u r e r e q u i r e d a t t h e i n l e t ( i n k P a ) :

7 p=0.5da (V22V12)8 p r i n t f ( \n\nRESULTS\n\n )9 p r i n t f ( \n\nGauge p r s s u r e r e q u i r e d a t t he i n l e t : %. 3 f

kPa\n\n ,p /1000)


1 / / A r e a o f n o z z l e a t i n p u t ( i n m 2 ) :

2 A i = 0 . 1 ;3 / / A r e a o f n o z z l e a t e x i t ( i n m 2 ) :

4 Ae=0.02;5 / / O u t l e t v e l o c i t y o f f l o w ( i n m / s e c ) :

6 V2=50;7 / / D e n s i t y o f a i r ( i n k g / m 3 ) :

8 da=1. 23;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 4 . s c e )2 f i lename=pathname+filesep ()+06.04data . sc i 3 exec ( f i l e na me )4 / / S p e e d o f w a t e r a t e x i t ( i n m / s e c ) :

5 V2=sqrt ( 2gz )6 / / P r e s s u r e a t p o i n t A i n t h e f l o w ( k P a ) :

7 pA=p1+dg(0 l ) 0. 5dV228 p r i n t f ( \n\nRESULTS\n\n )9 p r i n t f ( \n\n Sp eed o f w at er a t e x i t : %. 3 f m/ s e c \n\n ,V2)10 p r i n t f ( \n\n P re s su r e a t p o i nt A i n t he f l ow : %3f kPa\n\

n ,pA/1 000 )


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1 / / L e n g t h o f t u b e a b o v e s u r f a c e ( i n m ) :

2

l =1;3 / / D e p t h o f e x i t b e l o w w a t e r s u r f a c e ( i n m ) :

4 z=7;5 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

6 g = 9 . 8 1 ;7 / / D e n s i t y o f w a t e r ( i n k g / m 3 ) :

8 d=999;9 / / A t m o s p h e r i c p r e s s u r e ( i n N / m 2 ) :

10 p1=1. 01105;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 5 . s c e )2 f i lename=pathname+filesep ()+06.05data . sc i 3 exec ( f i l e na me )4 / / V e l o c i t y o f f l o w a t t h e e x i t ( i n f t / s e c ) :

5 V2=sqrt ( 2g(DuDd/12))6 / / V o l u m e f l o w r a t e / w i d t h ( f t 2 / s e c ) :

7 Q=V2Dd/128 p r i n t f ( \n\nRESULTS\n\n )9 p r i n t f ( \n\n V el o ci ty o f f lo w a t t he e x i t : %. 3 f f t / s e c \n

\n ,V2)10 p r i n t f ( \n\nVolume f l o w r a t e / w i dt h : %. 3 f f t 2/ s e c \n\n ,

Q)


1 / / D e p t h o f w a t e r a t t h e u p s t r e a m ( o n f e e t ) :

2 Du=1.5;3 / / D e p t h o f w a t e r a t t h e v e n a c o n t r a c t a d o w n s t r e a m f r o m

t h e g a t e ( i n i n c h e s ) :

4 Dd=2;5 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n f t / s e c 2 ) :

6 g = 3 2 . 2 ;


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1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 6 . s c e )2

f i lename=pathname+filesep ()+06.06data . sc i 3 exec ( f i l e na me )4 / / P r e s s u r e o f a i r a t 1 0 0 0 m ( i n N / m 2 ) :

5 p=P1pa6 / / D e n s i t y o f a i r a t 1 0 0 0 m ( i n k g / m 3 ) :

7 d=D1da8 / / S t a g n a t i o n p r e s s u r e a t A ( i n k P a ) :

9 p0A=p+0.5d(V1000/3600) 210 / / S t a t i c p r e s s u r e a t B ( i n k P a ) :

11 pB=p+d/ 2( (V1000/3600)2Vb2)12 p r i n t f ( \n\nRESULTS\n\n )13 p r i n t f ( \n\n S t ag n a ti o n p r e s s u r e a t A : %. 3 f kPa\n\n ,p0A

/1000)14 p r i n t f ( \n\ n S t a t i c p r e s s u r e a t B : %. 3 f kPa\n\n ,pB

/1000)


1 / / S p e e d o f p l a n e ( i n k m / h r ) :

2 V=150;3 / / S p e e d a t p o i n t B r e l a t i v e t o t h e w i n g ( i n m / s e c ) :

4

Vb=60;5 / / D e n s i t y o f a i r ( i n k g / m 3 ) :

6 da=1. 23;7 / / A t m o s p h e r i s p r e s s u r e ( i n N / m 2 ) :

8 pa=1. 01105;9 / / A t 1 0 0 0 m ,

10 / / p / p S L :

11 P1=0.8870;12 / / d / d S L :

13 D1=0.9075;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 8 . s c e )2 f i lename=pathname+filesep ()+06.08data . sc i 3 exec ( f i l e na me )

46


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4 / / V e l o c i t y o f f l o w a t e x i t ( i n f t / s e c ) :

5

V4=sqrt ( 2g( z3 0) )6 / / M a s s f l o w r a t e o f w a t e r ( i n s l u g / s e c ) :

7 m=dV4A4/1448 / / R i s e i n t e m p e r a t u r e b e t w e e n p o i n t s 1 a n d 2 ( i n R ) :

9 T=Q3413/3600/m/32.210 p r i n t f ( \n\nRESULTS\n\n )11 p r i n t f ( \n\n Ri se i n t em pe ra tu re b etw een p o i n t s 1 and 2 :

%. 3 f R\n\n ,T)


1 / / A r e a o f c r o s s s e c t i o n o f t h e n o z z l e ( i n i n 2 ) :

2 A4=0.864;3 / / C a p a c i t y o f h e a t e r ( i n kW ) :

4 Q=105 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n f t / s e c 2 ) :

6 g = 3 2 . 2 ;7 / / W a t e r l e v e l i n r e s e r v o i r a b o v e d a t u m l i n e ( i n f t ) :

8 z3=10;9 / / D e n s i t y o f w a t e r ( I n s l u g / f t 3 ) :

10 d = 1 . 9 4 ;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 0 6 . 0 9 . s c e )2 f i lename=pathname+filesep ()+06.09data . sc i 3 exec ( f i l e na me )4 t=0:55 / / V a l u e o f s q r t ( 2 g h ) :

6 x=sqrt (2gh )7 / / V a l u e o f 1 / 2 L s q r t ( 2 g h ) :

8 y=1/2/Lx

9 [m n]= s i z e ( t )10 i =1:n ;11 / / V e l o c i t y ( i n m / s e c ) :

12 V2=xtanh ( y t ( i ) )13 plot ( t ,V2) ;

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14 x t i t l e ( S t r e a m l i n e f l o w f ro m 1 t o 2 , Time ( i n s ) , V2 (

in m/ se c ) )


1 / / D e p t h t o w h i c h w a t e r i s f i l l e d ( i n m ) :

2 h=3;3 / / L e n g t h o f p i p e ( i n m ) :

4 L=6;5 / / D i a m e t e r o f p i p e ( i n mm ) :

6 D=150;7 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n m / s e c 2 ) :

8 g = 9 . 8 1 ;

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Chapter 7

Dimensional Analysis and

Simlitude

7.1 Discussion


When we execute S 7.05, we get Fig. 7.1.The .sci files of the respective problems contain the input parameters of

the question

7.2 Scilab Code


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 7 . 0 4 . s c e )2 f i lename=pathname+filesep ()+7.04data . sc i 3 exec ( f i l e na me )4 / / V e l o c i t y o f p r o t o t y p e i n f t / s e c

5 Vp1=Vp6080/36006

/ / R e y n o l d s n u m b e r o f p r o t o t y p e :7 Rep=Vp1Dp/vp8 / / R e p = R e m

9 / / T h e r e f o r e :

10 Rem=Rep ;

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11 / / V e l o c i t y o f a i r f o r w i n d t u n n e l ( i n f t / s e c ) :

12

Vm=Remvm/(Dm/12)13 / / D r a g f o r c e o n p r o t o t y p e ( i n l b f ) :

14 Fp=Fm(dp/dm) (Vp1/Vm) 2(Dp/(Dm/1 2) ) 215 p r i n t f ( \n\nRESULTS\n\n )16 p r i n t f ( \n\n Te st s pe ed i n a i r : %. 3 f f t / s e c \n\n ,Vm)17 p r i n t f ( \n\nDrag f o r c e on p r ot o ty p e : %. 3 f l b f \n\n ,Fp)


1 / / D i a m e t e r o f t h e p r o t o t y p e ( i n f t ) :

2 Dp=1;3 / / S p e e d o f t o w i n g o f p r o t o t y p e ( i n k n o t s ) :

4 Vp=5;5 / / D i a m e t e r o f m o d e l ( i n i n c h e s ) :

6 Dm=6;7 / / D r a g f o r m o d e l a t t e s t c o n d i t i o n ( i n l b f ) :

8 Fm=5.58;9 / / D e n s i t y o f s e a w a t e r a t 5 C f o r p r o t o t y p e ( i n s l u g / f t

3 ) :

10 dp=1. 99;11 / / K i n e m a t i c v i s c o s i t y a t 5 C f o r p r o t o t y p e ( i n f t 2 / s e c )

:

12 vp=1.69105;13 / / D e n s i t y o f a i r a t S TP f o r m o d e l ( i n s l u g / f t 3 ) :

14 dm=0.00238;15 / / K i n e m a t i c v i s c o s i t y o f a i r a t S TP f o r m o d e l ( i n f t 2 /

s e c ) :

16 vm=1.57104;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 7 . 0 5 . s c e )

2 f i lename=pathname+filesep ()+7.05data . sc i 3 exec ( f i l e na me )4 / / W i d t h o f t h e m o d e l ( i n m ) :

5 wm=Swp0 . 3 0 4 86 / / A r e a o f m o d e l ( i n m 2 ) :

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53/116


9 / / A i r s p e e d i n w i n d t u n n e l ( i n m / s e c ) :

10 V=[18 2 1. 8 26 3 0. 1 35 3 8. 5 4 0. 9 4 4. 1 4 6 . 7 ] ;11 / / D r a g f o r c e ( i n N ) :

12 Fd =[ 3. 1 4 .4 1 6 .0 9 7 .9 7 1 0. 7 1 2. 9 1 4. 7 1 6. 9 1 8 . 9 ] ;13 / / K i n e m a t i c v i s c o s i t y ( i n m 2 / s e c ) :

14 v=1.46105;15 / / D e n s i t y o f a i r ( i n k g / m 3 ) :

16 d = 1 . 2 3 ;17 / / S p e e d o f p r o t o t y p e ( i n k m / h r ) : \

18 Vp=100;

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1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 7 . 0 6 . s c e )2 f i lename=pathname+filesep ()+7.06data . sc i 3 exec ( f i l e na me )4 / / T h e s a m e p u m p i s u s e d f o r b o t h t h e c o n d i t i o n s . H e n c e :

5 D2=D1 ;6 / / T h e s a m e w a t e r i s u s e d f o r b o t h t h e c o n d i t i o n s . H e n c e

:

7 d2=d1 ;8 / / F l o w r a t e a t c o n d i t i o n 2 ( i n g p m ) :

9 Q2=Q1N2/N1(D2/D1)310 / / H e a d a t c o n d i t i o n 1 ( i n f t ) :

11 H1=(N1sqrt (Q1)/Nscu1) (4/3)12 / / H e a d a t c o n d i t i o n 1 ( i n f t ) :

13 H2=H1(N2/N1) 2(D2/D1)214 / / P u m p o u t p u t p o w e r a t c o n d i t i o n 1 ( i n h p ) :

15 P1=d1gQ1H 1/7. 48/60/55016 / / P u m p o u t p u t p o w e r a t c o n d i t i o n 2 ( i n h p ) :

17 P2=P1( d2/d1) (N2/N1) 3(D2/D1)518 / / R e q u i r e d i n p u t p o w e r ( i n h p ) :

19 Pin=P2/Effp20 / / S p e c i f i c s p e e d a t c o n d i t i o n 2 :

21 Nscu2=N2sqrt (Q2)/H2(3/4)22 p r i n t f ( \n\nRESULTS\n\n\n )23 p r i n t f ( \n\nVolume f l o w r a t e a t c o n d i t i o n 2 : %. 3 f gpm\n

\n\n ,Q2)24 p r i n t f ( \n\nHead a t c o n d i t i o n : %. 3 f f t \n\n\n ,H2)25 p r i n t f ( \n\nPump o u tp u t p ow er a t c o n d i t i o n : %. 3 f hp\n\n

\n ,P2)26 p r i n t f ( \n\nR e qui r e d i nput pow er : %. 3 f hp\n\n\n , P in )27 p r i n t f ( \n\ n S p e c i f i c s pe ed a t c o n di t i o n 2 : %. 3 f \n\n\n ,

Nscu2)


1 / / E f f i c i n c o f p u m p :

2 Effp =0.8 ;

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3 / / D e s i g n s p e c i f i c s p e e d ( i n r p m ) :

4

Nscu1=2000;5 / / I m p e l l e r d i a m e t e r ( i n i n c h e s ) :

6 D1=8;7 / / O p e r t i o n s p e d a t e s i g n p o i n t f l o w c o n d i t i o n ( i n r p m ) :

8 N1=1170;9 / / F l o w r a t e a t d e s i g n p o i n t f l o w c o n d i t i o n ( i n g p m ) :

10 Q1=300;11 / / D e n s i t y o f w a t e r ( i n s l u g / f t 3 ) :

12 d1=1. 94;13 / / A c c e l e r a t i o n d u e t o g r a v i t y ( i n f t 2 / s e c ) :

14 g = 3 2 . 2 ;15 / / W o r k i n g s p e e d 2 ( i n r p m ) :

16 N2=1750;

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Chapter 8

Internal Incompressible Viscous

Flow

8.1 Discussion



8.2 Scilab Code


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 8 . 0 1 . s c e )2 f i lename=pathname+filesep ()+8.01data . sc i 3 exec ( f i l e na me )4 / / L e a k a g e f l o w r a t e ( i n mm 3 / s e c ) :

5 Q=%pi/12Da 3( p1p2 ) 103/u/L6 / / V e l o c i t y o f f l o w ( i n m / s e c ) :

7

V=Q/%pi /D/a /1 00 08 / / S p e c i f i c g r a v i t y o f S AE 1 0 W o i l :

9 SG=0.92;10 / / R e y n o l d s N u m b e r :

11 Re=SGdwVa/u/1000

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12 / / A s R e < 1 4 0 0 , f l o w i s l a m i n a r .

13

p r i n t f ( \n\nRESULTS\n\n )14 p r i n t f ( \n\nLeak age f l ow r at e : %. 3 f mm3/s e c \n\n ,Q)


1 / / O p e r a t i o n p r e s s u r e o f h y d r a u l i c s y s t e m ( i n k P a ) :

2 p1=20000;3 / / O p e r a t i o n t e m p e r a t u r e o f h y d r a u l i c s y s t e m ( i n C ) :

4 T=55;5 / / P i s t o n d i a m e t e r ( i n mm ) :

6 D=25;7 / / V i s c o s i t y o f S A E 1 0 W a t 5 5 C ( i n k g / ( m s ) :

8 u = 0 . 0 1 8 ;9 / / M e a n r a d i a l c l e a r a n c e o f a c y l i n d e r ( i n mm ) :

10 a = 0 . 0 0 5 ;11 / / G a u g e p r e s s u r e o n l o w e r p r e s s u r e s i d e o f p i s t o n ( i n

k P a ) :

12 p2=1000;13 / / L e n t h o f p i s t o n ( i n mm ) :

14 L=15;15 / / D e n i t y o f w a t e r ( i n k g / m 3 ) :

16

dw=1000;


1 pa thn am e= g e t a b s o l u t e f i l e p a t h ( 8 . 0 2 . s c e )2 f i lename=pathname+filesep ()+8.02data . sc i 3 exec ( f i l e na me )4 / / S h e a r s t r e s ( i n l b f / f t 2 ) :

5 Tyx=uN2%pi/60D/2/( a/2)6 / / T o r q e ( i n i n c h e s l b f ) :

7 T=%pi/2TyxD2L/144

8 / / P o w e r d i s s i p a t e d i n t h e b e a r i n g ( i n h p ) :

9 P=TN/602%pi/12/55010 / / R e y n o l d s n u m b e r :

11 Re=SGpN2%pi/601 . 5 a/2/u/14412 p r i n t f ( \n\nRESULTS\n\n )

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13 p r i n t f ( \n\nTorque : %.3 f inc hesl b f\n\n ,T)14

p r i n t f ( \n\nPower d i s s i p a t e d i n t he b e a ri n g : %. 3 f hp\n\n ,P)


1 / / t e m p e r a t u r e f o o p e r a t i o n ( i n F ) :

2 T=210;3 / / D i a m e t e r o f t e b e a r i n g ( i n i n c h e s ) :

4 D=3;5 / / D i a m e t r a l c l e a r a n c e ( i n i n c h e s ) :

6 a = 0 . 0 0 2 5 ;7 / / L e n g t h o f s h a f t ( i n i n h e s ) :

8 L=1. 25;9 / / S p e e d o f r o t a t i o n o f t h e s h a f t ( i n r p m ) :

10 N=3600;11 / / V i s c o s i t y o f t h e o i l ( i n l b f s / f t 2 ) :

12 u=2.01104;13 / / S p e c i f i c g r a v i t y o f S A E 1 0 W :

14 SG=0.92;15 / / D e n s i t y o f w a t e r ( i n s l u g / f t

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