HEAD LOSES IN HORIZONTAL AND VERTICAL ORIFICEMETER A COMPARATIVE EVALUATION AND ANALYSES WITH APLLICATION OF STATISTICAL METHOD OF DATA RELIABILITY
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ABSTRACT
A comparative investigation was undertaken to determine the head loss coefficients for horizontally mounted and vertically mounted orifices using a Fluid mechanics and Heat transfer trainer developed in Nigeria. Experiments were carried out observing the procedure and the discharge of the flow of water was collected to obtain the volumetric flow rate and also read off the right and left limb of the horizontal and vertical manometers at different set points. The experimental measurements were subjected to further study to determine the head loss using the applied Bernoulli’s equation with addition of pump to the system. A graph of head loss against the kinetic head of water was plotted and the gradient of the graph yield the head loss coefficient (k). It was observed that there was no significant difference between the head loss coefficient for horizontal and vertical orifices. Hypothesis test was done to test the accuracy, precision and the statistical reliability of the head loss coefficient for the horizontal and vertical orifices, however better result was recorded in the horizontal orifice by statistical analysis. This report provides conclusion and recommendation to the challenges experienced.
TABLE OF CONTENT
Title page-----------------------------------------------------------------------i
Certification-------------------------------------------------------------------ii
Approval page----------------------------------------------------------------iii
Dedication--------------------------------------------------------------------iv
Acknowledgment-------------------------------------------------------------v
Abstract-----------------------------------------------------------------------vi
Table of content-------------------------------------------------------------vii
A comparative investigation was undertaken to determine the head loss coefficients for horizontally mounted and vertically mounted orifices using a Fluid mechanics and Heat transfer trainer developed in Nigeria. Experiments were carried out observing the procedure and the discharge of the flow of water was collected to obtain the volumetric flow rate and also read off the right and left limb of the horizontal and vertical manometers at different set points. The experimental measurements were subjected to further study to determine the head loss using the applied Bernoulli’s equation with addition of pump to the system. A graph of head loss against the kinetic head of water was plotted and the gradient of the graph yield the head loss coefficient (k). It was observed that there was no significant difference between the head loss coefficient for horizontal and vertical orifices. Hypothesis test was done to test the accuracy, precision and the statistical reliability of the head loss coefficient for the horizontal and vertical orifices, however better result was recorded in the horizontal orifice by statistical analysis. This report provides conclusion and recommendation to the challenges experienced.
TABLE OF CONTENT
Title page-----------------------------------------------------------------------i
Certification-------------------------------------------------------------------ii
Approval page----------------------------------------------------------------iii
Dedication--------------------------------------------------------------------iv
Acknowledgment-------------------------------------------------------------v
Abstract-----------------------------------------------------------------------vi
Table of content-------------------------------------------------------------vii
CHAPTER ONE
INTRODUCTION
1.1 Background of the study----------------------------------------------1
1.2 Historical developments-----------------------------------------------4
1.3 Significance of the study---------------------------------------------11
1.4 Problem statement----------------------------------------------------14
1.5 Objective of the study------------------------------------------------15
1.6 Scope of the study----------------------------------------------------16
INTRODUCTION
1.1 Background of the study----------------------------------------------1
1.2 Historical developments-----------------------------------------------4
1.3 Significance of the study---------------------------------------------11
1.4 Problem statement----------------------------------------------------14
1.5 Objective of the study------------------------------------------------15
1.6 Scope of the study----------------------------------------------------16
CHAPTER TWO
INTRODUCTION
2.1 Head losses-------------------------------------------------------------17
8
2.2 Types of head loss-----------------------------------------------------20
2.2.1 Major head-----------------------------------------------------------20
2.2.2 Minor head-----------------------------------------------------------20
INTRODUCTION
2.1 Head losses-------------------------------------------------------------17
8
2.2 Types of head loss-----------------------------------------------------20
2.2.1 Major head-----------------------------------------------------------20
2.2.2 Minor head-----------------------------------------------------------20
2.3 Total head loss equation---------------------------------------------23
2.4 Statistical analysis----------------------------------------------------24
2.4.1 Accuracy of measurement-----------------------------------------24
2.4.2 Precision of measurement-----------------------------------------27
2.5 Reliability of measurement------------------------------------------28
2.6 The nature of statistical hypotheses-------------------------------29
2.6.1 The null and alternate hypotheses-------------------------------29
2.6.2 Two tailed and one tailed test-------------------------------------30
2.6.3 Two types of errors-------------------------------------------------31
2.6.4 Level of significance------------------------------------------------31
2.6.5 The critical region and acceptance region----------------------32
2.7 Test involving the t-distribution------------------------------------34
2.8 The z-test---------------------------------------------------------------37
2.9 The x2-test--------------------------------------------------------------38
2-10 Test concerning more than two population proportions-------39
2.11 Test of independence------------------------------------------------40
2.12 Test of goodness fit--------------------------------------------------40
2.4 Statistical analysis----------------------------------------------------24
2.4.1 Accuracy of measurement-----------------------------------------24
2.4.2 Precision of measurement-----------------------------------------27
2.5 Reliability of measurement------------------------------------------28
2.6 The nature of statistical hypotheses-------------------------------29
2.6.1 The null and alternate hypotheses-------------------------------29
2.6.2 Two tailed and one tailed test-------------------------------------30
2.6.3 Two types of errors-------------------------------------------------31
2.6.4 Level of significance------------------------------------------------31
2.6.5 The critical region and acceptance region----------------------32
2.7 Test involving the t-distribution------------------------------------34
2.8 The z-test---------------------------------------------------------------37
2.9 The x2-test--------------------------------------------------------------38
2-10 Test concerning more than two population proportions-------39
2.11 Test of independence------------------------------------------------40
2.12 Test of goodness fit--------------------------------------------------40
CHAPTER THREE
RESEARCH METHODOLOGY
3.1 Research design-------------------------------------------------------42
3.2 Equipment setup------------------------------------------------------43
3.2.1 Sump tank-----------------------------------------------------------44
3.2.2 Test pipes------------------------------------------------------------44
3.2.3 Instrumentation panel---------------------------------------------45
3.3 Assumptions ----------------------------------------------------------46
3.4 Procedures-------------------------------------------------------------47
3.5 Apparatus--------------------------------------------------------------48
RESEARCH METHODOLOGY
3.1 Research design-------------------------------------------------------42
3.2 Equipment setup------------------------------------------------------43
3.2.1 Sump tank-----------------------------------------------------------44
3.2.2 Test pipes------------------------------------------------------------44
3.2.3 Instrumentation panel---------------------------------------------45
3.3 Assumptions ----------------------------------------------------------46
3.4 Procedures-------------------------------------------------------------47
3.5 Apparatus--------------------------------------------------------------48
CHAPTER FOUR
DATA PRESENTATION AND ANALYSIS
4.1 Data analysis----------------------------------------------------------49
4.1.1 Measurements------------------------------------------------------50
4.2 Treatment of data-----------------------------------------------------52
4.2. Computation of pressure drop------------------------------------52
4.2.2 Computation of velocity change----------------------------------53
4.2.3 Computation of pump power--------------------------------------54
4.2.4 Computation of head loss for horizontal orifice----------------54
4.2.5 Summation of the head loss coefficient--------------------------63
4.2.6 Computation of the head loss for vertical orifice---------------63
4.2.7 Summation of the head loss coefficient--------------------------71
DATA PRESENTATION AND ANALYSIS
4.1 Data analysis----------------------------------------------------------49
4.1.1 Measurements------------------------------------------------------50
4.2 Treatment of data-----------------------------------------------------52
4.2. Computation of pressure drop------------------------------------52
4.2.2 Computation of velocity change----------------------------------53
4.2.3 Computation of pump power--------------------------------------54
4.2.4 Computation of head loss for horizontal orifice----------------54
4.2.5 Summation of the head loss coefficient--------------------------63
4.2.6 Computation of the head loss for vertical orifice---------------63
4.2.7 Summation of the head loss coefficient--------------------------71
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
5.1 Conclusion-------------------------------------------------------------72
5.2 Recommendation------------------------------------------------------73
REFERENCES---------------------------------------------------------------------------75
NOTATIONS------------------------------------------------------------------------------77
APPENDIX A -----------------------------------------------------------------------------78
APPENDIX B------------------------------------------------------------------------------95
APPENDIX C----------------------------------------------------------------------------105
APPENDIX D----------------------------------------------------------------------------110
APPENDIX E----------------------------------------------------------------------------137
HEAD LOSES IN HORIZONTAL AND VERTICAL ORIFICEMETER A COMPARATIVE EVALUATION AND ANALYSES WITH APLLICATION OF STATISTICAL METHOD OF DATA RELIABILITYCONCLUSION AND RECOMMENDATION
5.1 Conclusion-------------------------------------------------------------72
5.2 Recommendation------------------------------------------------------73
REFERENCES---------------------------------------------------------------------------75
NOTATIONS------------------------------------------------------------------------------77
APPENDIX A -----------------------------------------------------------------------------78
APPENDIX B------------------------------------------------------------------------------95
APPENDIX C----------------------------------------------------------------------------105
APPENDIX D----------------------------------------------------------------------------110
APPENDIX E----------------------------------------------------------------------------137
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