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.
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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
CHAPTER TWO
INTRODUCTION
2.1 Head losses-------------------------------------------------------------17
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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
CHAPTER THREE
RESEARCH METHODOLOGY
3.1 Research design-------------------------------------------------------42
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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. 1Computation 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
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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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CHAPTER ONE
INTRODUCTION
1.1. Background of the study
Fluid mechanics deals with the study of all fluids under static and dynamic situations. Fluid mechanics is a branch of continuous mechanics which deals with a relationship between forces, motions, and statical conditions in a continuous material. This study area deals with many and diversified problems such as surface tension, fluid statics, flow in enclose bodies, or flow round bodies (solid or otherwise), flow stability, etc. In fact, almost any action a person is doing involves some kind of a fluid mechanics problem. Researchers distinguish between orderly flow and chaotic flow as the laminar flow and the turbulent flow. The fluid mechanics can also be distinguished between a single phase flow and multiphase flow (flow made more than one phase or single distinguishable material).
Fluid flow in circular and noncircular pipes is commonly encountered in practice. The hot and cold water that we use in our homes is pumped through pipes. Water in a city is distributed by extensive piping networks. Oil and natural gas are transported hundreds of miles by large pipelines. Blood is carried throughout our bodies by veins. The cooling water in an engine is transported by hoses to the pipes in the radiator where it is cooled as it flows. Thermal energy in a hydraulic space heating system is transferred to the circulating water in the boiler, and then it is transported to
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the desired locations in pipes. Fluid flow is classified as external and internal, depending on whether the fluid is forced to flow over a surface or in a conduit. Internal and external flows exhibit very different characteristics. In this chapter we consider internal flow where the conduit is completely filled with the fluid, and flow is driven primarily by a pressure difference. This should not be confused with open-channel flow where the conduit is partially filled by the fluid and thus the flow is partially bounded by solid surfaces, as in an irrigation ditch, and flow is driven by gravity alone. We then discuss the characteristics of flow inside pipes and introduce the pressure drop correlations associated with it for both laminar and turbulent flows. Finally, we present the minor losses and determine the pressure drop and pumping power requirements for piping systems. Pipes 611
14–5Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications, and fluid distribution networks. The fluid in such applications is usually forced to flow by a fan or pump through a flow section. We pay particular attention to friction, which is directly related to the pressure drop and head loss during flow through pipes and ducts. The pressure drop is then used to determine the pumping power requirement. A typical piping system
involves pipes of different diameters connected to each other by various fittings or elbows to direct the fluid, valves to control the flow rate, and pumps to pressurize the fluid. The terms pipe, duct, and conduit are usually used interchangeably for flow sections. In general, flow sections of circular cross section are referred to as
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pipes (especially when the fluid is a liquid), and flow sections of noncircular cross section as ducts (especially when the fluid is a gas). Small-diameter pipes are usually referred to as tubes. Given this uncertainty, we will use more descriptive phrases (such as a circular pipe or a rectangular duct) whenever necessary to avoid any misunderstandings. You have probably noticed that most fluids, especially liquids, are transported in circular pipes. This is because pipes with a circular cross section can withstand large pressure differences between the inside and the outside without undergoing significant distortion. Noncircular pipes are usually used in applications such as the heating and cooling systems of buildings where the pressure difference is relatively small, the manufacturing and installation costs are lower, and the available space is limited for duct work. Although the theory of fluid flow is reasonably well understood, theoretical solutions are obtained only for a few simple cases such as fully developed laminar flow in a circular pipe. Therefore, we must rely on experimental results and empirical relations for most fluid-flow problems rather than closed form analytical solutions. Noting that the experimental results are obtained under carefully controlled laboratory conditions, and that no two systems are exactly alike, we must not be so naive as to view the results obtained as â€•exact.â€– The fluid velocity in a pipe changes from zero at the surface because of the no-slip condition to a maximum at the pipe center. In fluid flow, it is convenient to work with an average or mean velocity _m, which remains constant in incompressible flow when the cross-sectional area of the pipe is
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constant. The mean velocity in heating and cooling applications may change somewhat because of changes in density with temperature. But, in practice, we evaluate the fluid properties at some average temperature and treat them as constants. The convenience of working with constant properties usually more than justifies the slight loss in accuracy.
Also, the friction between the fluid layers in a pipe does cause a slight rise in fluid temperature as a result of the mechanical energy being converted to sensible thermal energy. But this temperature rise due to fictional heating is usually too small to warrant any consideration in calculations and thus is disregarded. For example, in the absence of any heat transfer, no noticeable difference can
be detected between the inlet and exit temperatures of water flowing in a pipe. The primary consequence of friction in fluid flow is pressure drop, and thus any significant temperature change in the fluid is due to heat transfer.