HEAD LOSES IN HORIZONTAL AND VERTICAL ORIFICE METER A COMPARATIVE EVALUATION AND ANALYSES WITH APPLICATION OF STATISTICAL METHOD OF DATA RELIABILITY

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 Bernoullis 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.

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 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 openchannel 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.

1.2. Historical Developments

The continuous scientific development of fluid mechanics started with Leonardo da Vinci 14521519. Through his ingenious work, methods were devised that were suitable for fluid mechanics investigations of all kinds. Earlier efforts of Archimedes 287212 B.C. to understand fluid motions led to the understanding of the hydro mechanical buoyancy and the stability of floating bodies. His discoveries remained, however, without further impact on the development of fluid mechanics in the following centuries.

1.3. Significance of the study

Flows occur in all fields of our natural and technical environment and anyone perceiving their surroundings with open eyes and assessing their significance for themselves and their fellow beings can convince themselves of the far reaching effects of fluid flows.

We somewhat arbitrarily classify these in two main categories: i physical and natural science, and ii technology. Clearly, the second thesis often of more interest to an engineering student, but in the modern era of emphasis on interdisciplinary studies, the more scientific and mathematical aspects of fluid phenomena are becoming increasingly important.

Fluids in technology It is easily recognized that a complete listing of fluid applications would be nearly impossible simply because the presence of fluids in technological devices is ubiquitous. The following provide some particularly interesting and important examples from an engineering standpoint.

1. Internal combustion enginesall types of transportation systems

2. Turbojet, scramjet, rocket enginesaerospace propulsion systems

3. Waste disposal

a Chemical treatment

b Incineration

c Sewage transport and treatment

4. Pollution dispersalin the atmosphere smog; in rivers and oceans

5. Steam, gas and wind turbines, and hydroelectric facilities for electric power generation

6. Pipelines

a Crude oil and natural gas transferral

b Irrigation facilities

c Office building and household plumbing

7. Fluid/structure interaction

a Design of tall buildings

b Continental shelf oildrilling rigs

c Dams, bridges, etc.

d Aircraft and launch vehicle airframes and control systems

8. Heating, ventilating and airconditioning HVAC systems

9. Cooling systems for highdensity electronic devicesdigital computers from PCs to supercomputers

10. Solar heat and geothermal heat utilization

1.4. Problem statement

Fluid mechanics is a science that makes use of the basic laws of mechanics and thermodynamics to describe the motion of fluids. Here fluids are understood to be all the media that cannot be assigned clearly to solids, no matter whether their properties can be described by simple or complicated material laws. Gases, liquids and many plastic materials are fluids whose movements are covered by fluid mechanics. Fluids in a state of rest are dealt with as a

special cases of flowing media, i.e. the laws for motionless fluids are deduced in such a way that the velocity in the basic equations of fluid mechanics is set equal to zero.

In fluid mechanics, however, one is not content with the formulation of the laws by which fluid movements are described, but makes an effort beyond that to find solutions for flow problems, i.e. for given initial and boundary conditions. To this end, there are three major flow problems encountered in fluid mechanics:

a Analytical fluid mechanics problems:

Analytical methods of applied mathematics are used in this field to solve the basic flow equations, taking into account the boundary conditions describing the actual flow problem.

b Numerical fluid mechanics problems:

Numerical methods of applied mathematics are employed for fluid flow simulations on computers to yield solutions of the basic equations of fluid mechanics.

c Experimental fluid mechanics problems:

This subdomain of fluid mechanics uses similarity laws for the transferability of fluid mechanics knowledge from model flow investigations. The knowledge gained in model flows by measurements is transferred by means of the constancy of known characteristic quantities of a flow field to the flow field of actual interest.

1.5. Objective of the study

The general objective of this study is to examine the head losses in flow through horizontal and vertically mounted orifices with statistical methods of data reliability. The goal of these experimental remains to test the reliability of the result from the heat transfer and fluid mechanics trainer. The results however, can only attain this objective through these:

1. To convert volume flow rate in m/s1 to m3s1 and also h1 and h2 in mm to m. also convert D1 and D2 in mm to m.

2. To compute P1, P2, V1, V2, A1, A2, and HL for the set points of 900, 750, 600, 450, 300, and 150 using the analytical equations.

3. Plot HL versus V2/2g and discuss the plot.

4. To test the statistical hypotheses of the result

5. To provide suggestion for further improvement

1.6. Scope of the study

The study will make a great emphasis on the performance of head losses in pipe flow using fluid mechanics and heat transfer trainer. It tends to explain the statistical reliability of the experimental results and the usefulness of such results.