Fluid flow in a duct of varying cross-section Essay Example

Fluid flow in a duct of varying cross-section Paper The purpose of this experiment was to demonstrate the relation between pressure and fluid velocity in a duct of varying cross-sectional area. This experiment is carried out on the basis of conservation of mass and energy. Both the Bernoullis equation and the Continuity equation are essential analytical tools used for the analysis of problems in the subject of Mechanics of Fluids, in this case flow of fluid in the venturi. The constant flow rate in the varying cross-section duct suggests that the fluid velocity and pressure should compensate this varying cross-section accordingly. As the varying cross-section becomes convergent the velocity and pressure of the fluid is at its highest value. Thus signifying that the at the divergent or diffuser end the velocity and pressure of the fluid should progressively go back to its original values. Theory The continuity equation states that the fluid must remain constant and is in essence a state of the conservation of mass. For an incompressible flow, which involves a liquid or a gas at low velocity, the equation of continuity is; AV = Q = CONSTANT Where; A Cross-Sectional Area V Mean Velocity. Q Volumetric Flow Rate Bernoullis theorem shows the principle of conservation of energy for a steady flow. For an inviscid or frictionless flow, the following equation is applied; Where; P Static Pressure p Density Z Elevation above an arbitrary value V- Fluid velocity Bernoullis equation shows that the sum of the three quantities is a constant. In this experiment, the duct is horizontal; therefore, there is no gravitational effect. In this case we could ignore the gz term. It is then convenient to express the static pressure, P as an equivalent head of liquid h (=p/? We will write a custom essay sample on Fluid flow in a duct of varying cross-section specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Fluid flow in a duct of varying cross-section specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Fluid flow in a duct of varying cross-section specifically for you FOR ONLY $16.38 $13.9/page Hire Writer g), and hence the Bernoullis equation becomes: h + v2 = CONSTANT 2g Apparatus The set-up consists of a pipe of constant diameter, then a short contraction to a narrow throat followed by a long diffuser and finally a pipe of the same size as the original one. This arrangement is referred to as a Venturi. Experimental Procedure Start the pump and initiate a flow of water through the test section. Regulate the flow using the flow meter to 46 Litres/Min. Allow the some few minutes for the flow to regulate and then take manometer readings for tapings 1 to 10. Repeat the procedure for different flow rates; 34 Litres/Min. and 24 Litres/Min. Results The table shows the tapping numbers, the distance from the tapping number 1 and the cross-section diameter at each tapping Tapping Number 1 2 3 4 5 6 7 8 9 10 Distance, x (mm) 0 80 122 164 238 312 386 460 534 607 Diameter, d (mm) 41 41 28 15. 5 21. 4 27. 8 34. 1 40. 5 40. 5 40. 5 Discussion From analysing the results we can see that as cross-sectional area decreases the velocity of the fluid inside increases to maintain continuity and constant volumetric flow. The velocity of the fluid reaches its maximum at the throat where the venturi converges so that the cross-sectional area is at its minimum value. Graph One represents the change in static head (pressure difference) along the duct. From the continuity equation; smaller the area, greater the velocity of the flow and hence the greater the velocity, lower the pressure. This can be clearly seen from the graph. Taping number 4 shows the greatest pressure difference in each flow rate. This is because it is the minimum cross-sectional area of the duct. The pressure head then decreases as the cross-sectional area increases (Tapings 5 10). Different flow rate also have different change in pressure head at each tapping. In this case, the change in pressure head is the greatest when the flow rate is at 46Litres/Min. Hence, it can be stated that fluids at high velocity experience low pressure. Therefore, it can concluded from the graph that as the cross-sectional area reduces, the velocity increases and hence the pressure reduces. Graph Two, it is clearly noted that the variations of the normalised total head are very similar to the normalised static head. The normalised static head given by the formula [1-(d1/dn)4] represents the theoretical values of fluid flow. However, the values do not return to the zero value which shows that there is energy loss along the duct. This may be due to friction. The normalised head graphs vary slightly from the theoretical graphs which may be due high friction at higher velocities. There is usually a noted difference in readings and analysis of experiments compared to theory. This take place due to several reasons; more common, the human reading error. There is an allowance of certain percentage to give the accuracy of value to be with a confined range. Reading error: i 0. 1cm Flow meter: i 1Litre/Min Graph Three shows the variant of normalised static pressure along the duct. We can visualise this from the flow rates of 34 l/min and 46 l/min after the decrease in pressure there is a rise in pressure variation then it falls again. This can be a human error created by misread readings or a fault with the apparatus. The variation should in theory look more like the 26 l/min flow plot. Error Analysis Variations between practical and theoretical results are common in most experiments. Due to the conditions of our investigations our results are always suspect to error, which is why an error analysis calculation is used to give us a clearer idea of how accurate our results are. The main errors are usually caused by human error due to misread readings. Error build up due to use of approximated values carried out in calculations and errors due to incorrect calibration of equipment are also key factors. Every measurement made is susceptible to error. In many investigations errors can be deduced at the beginning of the test. In this case the static head is the only unit measured in the investigation it has an error of:- ?Q = i 1 l/min The data obtained from the flow rate (Q) is used in the continuity equation to find velocity (V). As it has been established an error is found in the flow rate it is obvious then to state that there is an error in the velocity. To find the error in the velocity, it must be known that the proliferation of errors in a quotient is expressed by this formula. Conclusion After the analysing the data we have concluded that the error of our experiment has come to be 15. 4%. The percentage of confidence is 84. 6%, which is reasonably accurate. So our findings support the continuity equation. It is noted that velocity is proportional to the cross-sectional area of the duct, hence smaller the area, higher the velocity and vice-versa. This corresponds to the equation of continuity. It is also observed that when the velocity of fluid increases, the pressure decreases. Hence as the velocity of water in the venturi increased as it passed through the contraction, the pressure decreased and as the velocity decreased over a larger cross sectional area, the pressure increased. This proves Bernoullis theorem which states that at any point in a pipe through which a fluid is flowing, the sum of the pressure energy, the kinetic energy, and the potential energy of a given mass of the fluid is constant. This corresponds to the law of conservation of energy.

The words heal Essay Example

The words heal Essay Example The words heal Essay The words heal Essay 1991). And He closed the book, gave it back to the attendant and sat down; and the eyes of all in the synagogue were fixed on Him. And He began to say to them, Today this Scripture has been fulfilled in your hearing (Luke 4:18-21). Luke includes all of the healing events in Mark except Mark 6:45-8:26. The healing ministry of Jesus points to the arrival of the kingdom of God as promised in the Old Testament. Christ healed men not only of bodily diseases but also of demon possession. With the coming of Christ the Satanic powers were subject to His power and spoken word. They glimpse the splendour of Christ the King as He casts out demons. Here is evidence the kingdom has come (Clowes et al, 1817). Jesus trained His disciples, empowered them and sent them out to minister to the needy. His disciples were empowered with Holy Spirit and they went into the cities and towns and proclaim the love of God to the sick, poor and needy. Encourage people to live 3 good and healthy lifestyles in order to keep their health. They also teach and also heal the sick in the name of the God. Without fear of their lives they often go into the foreign countries and do ministerial work. They often adapted to the new environment by adopting their cultures, beliefs and values. By doing so they get acquainted with people concern hence provide better service to them. The Gospel of John has only four examples of Jesus healing ministry even though John was with Jesus during the three year ministry. Jesus healed the royal officials sick son at Capernaum, the cripple who had been helpless for 38 years, the man blind from birth, and  rising of Lazarus from the dead. These miracles were attesting signs pointing to Jesus as the Son of God. (Bosworth, et al, 1973). Therefore many other signs Jesus also performed in the presence of the disciples, which are not written in this book; but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name (John 20:30-31). The healing ministry was a ministry of proclamation of the kingdom of God. The kingdom had arrived with the coming of the King. When Christ returns we will see the consummation of the kingdom of God. There will be the manifestation of the glory of the King and His reign. The healing ministry of Jesus is simply the outworking of His majesty and power. In Matthew 8:16-17, quoting Isaiah 53:4 we see the Suffering Servant of the LORD is fulfilling the Old Testament prophecies by His healing miracles. The healings give evidence that He is the Anointed of the LORD. This is a necessary element of His messianic work. This is why He has the authority to heal on the Sabbath (Borg, Marcus and Wright. 1999). 4 What Jesus began to do in His first coming He continues to do through His Body, the church (Acts 1:1-8). This is the work of the Holy Spirit in the Body. The main emphasis of Acts is on proclamation. The disciples of Jesus went about doing what Jesus was doing by proclaiming the good news of Jesus and calling men to put their faith in the risen Christ. People were healed in the name of Jesus. The apostles Peter and John healed a poor lame beggar. But when Peter saw this, he replied to the people, Men of Israel, why are you amazed at this, or why do you gaze at us, as if by our own power or piety we had made him walk? (Borg et al, 1999). The God of Abraham, Isaac and Jacob, the God of our fathers, has glorified His servant  Jesus, the one whom you delivered and disowned in the presence of Pilate, when he had decided to release Him. But you disowned the Holy and Righteous One and asked for a murderer to be granted to you, but put to death the Prince of life, the one whom God raised from the dead, and a fact to which we are witnesses. And on the basis of faith in His name, it is the name of Jesus which has strengthened this man whom you see and know; and the faith which comes through Him has given him this perfect health in the presence of you all (Acts 3:12-16). This is the thrust of the healing done by the apostles in Acts. The stress is upon the  resurrection of Jesus Christ. The risen Christ is doing these things (Acts of the Apostles 1911). The authorities could not silence the apostles. They wouldnt shut up talking about the resurrection of Jesus Christ. And now, Lord, take note of their threats, and grant that Your bond-servants may speak Your word with all confidence, while You extend Your hand to heal, and signs and wonders take place through the name of Your holy servant Jesus (Acts 4:29- 30). Peter healed Aeneas and raised Tabitha from the dead. Philip, the lay evangelist went about preaching the gospel and healing the sick and the unclean spirits. Remember, he was one of the first deacons in Acts 6. The apostle Paul went about preaching and establishing 5 new churches, healed the sick, cast out demons, and raised Eutychus from dead after he went to sleep and fell out a window and died during Pauls sermon. I think it is important to note that Paul says very little about healings in his letters (Acts of the Apostles 1911). In 1 Corinthians 12:9, 28 Paul wrote about the gift of healing. The word healing, literally healings (plural) can refer to various healings such as emotional as well as physical ailments by natural as well as miraculous means. The context determines the interpretation. The context of this passage teaches that not every believer is given all these gifts, and that God is sovereign in His distribution of gifts for the edification of the body (Andrew et al , 1982). The Bible reveals that God not only advocates health, but He actually abhors or hates sickness. Leviticus 21 clearly reveals that God would not allow sickness in His presence, which in those days was in the temple. Now, in New Testament times, our bodies are His temple. According to 1 Corinthians 3:16: â€Å"Don’t you know that you yourselves are God’s  temple and that God’s Spirit lives in you? † If you are sick, the fact that God hates sickness does not mean that you are unworthy or that He hates you. He just hates the sickness that you have, because it is not from Him It is His perfect will to heal you and for you to be in health (3 John 2) (Bosworth et al , 1973). In Old Testament passages such as Deuteronomy chapter 28 where it appears that God is putting sickness on people, Jim Glennon (1980) explains that the nuance of the Hebrew wording shows that because of the people’s disobedience, the text really means that God is â€Å"caused to allow† the sicknesses. Our behaviour can â€Å"cause him to allow† sickness to come upon us, even though it is not His perfect will. For example, suffering from AIDS is not his will, but if man indulges in promiscuous behaviour by his own free will, which God will not 6 violate, God is caused to allow AIDS. Man has brought it upon himself, as did the ancient Israelites. Rebellion against God and His commands can cause him to remove his protective shield over us, such as promised in Psalm 91 and elsewhere, and allow the natural consequences. However, do not despair if you have a disease caused by sin. If you confess your sin to God, His grace and mercy can still provide your forgiveness and healing. Other reasons for sickness are: (1) Some people abuse their bodies, using harmful substances, or not allowing enough rest; (2) excessive stress; and (3) some people do not provide the body with nutritious food, often substituting junk or processed food. Much modern commercial food is deficient in nutrients and contains chemical additives, such as hormones and antibiotics in excessive exposure to meat and dairy products, and  environmental pollutants (Counsels on Health, 1923. ) Also, many people violate God’s food guidelines in the Bible and still expect to remain healthy. Examples are in Leviticus chapter 11, no longer a legal requirement but still the wisdom of God. Paul said, Everything is permissible but not everything is beneficial (1 Corinthians 10:23). God’s law of sowing and reaping always applies, but His grace transcends our past mistakes. Allow God to show you any area that needs attention. When sick people came to Jesus and asked to be healed, He did not reject them nor refer them to the doctors. He did not ask them to make an appointment with Luke because he is a doctor. God uses doctors, who can be especially helpful with things like fractures and wounds. Those in healing ministries usually encourage the sick not to ignore proper medical attention, nor to stop their medications, possibly to protect themselves against lawsuits, but also maybe wisdom in many cases. It is not necessarily a lack of faith to see a doctor, and your healing will be a witness to the doctor of God’s power (The Ministry of Healing, 1905). 7 However, be careful, because doctors’ three main methods slash, burn and poison  often do more harm than good: (1) slash (surgery, often dangerous and mutilating), (2) burn (radiation, with bad side effects) and (3) poison (drugs, most all with bad side effects that you may not be told about). If Jesus tarries, I believe someday current medical practices will be considered primitive and outrageous. More people are refusing these highly invasive and potentially harmful medical procedures and are opting to trust God, and perhaps also using natural alternatives. Even many medical doctors have become disenchanted with the failures of their profession and are turning to alternative (complimentary) medicine. Studies show that doctor and healthcare mistakes are the third leading cause of death in the world, whereas God has never made a mistake. (Jim Glennon ,1980). To conclude, Jesus set a foundation for all of us to follow in our Christian journey. He healed the sick, feed the hungry, and teach the people on how to care for themselves. During his ministry on earth, he had endured many challenges in terms of health. People often coming with all sorts of problem with the hope that he will heal them. He performed miracles and also raised death and gave them the second chance to live. As future nurse of this  country, the challenge is whether we will go and minister to the sick, lame and broken hearted like Jesus did or we will hide our identity as Christ chosen generation to work in his field. 8 Reference Pilch, John J, (1991). Sickness and Healing in Luke’s Acts: The social world of Luke’s Acts. Peabody MA: Hendricksons Publishers. The Acts of the Apostles. (1911). Mountain View, CA: Pacific Press Publishing Association, Borg, Marcus J. , and N. T. Wright. (1999). The Healing of Jesus: Two Visions. New York: HarperCollins Publishers. Counsels on Health. (1923. ) Mountain View, CA: Pacific Press Publishing Association,  Davies, Stevan L. , (1995). Jesus the Healer: Possession, Trance and the Origins of Christianity. New York: Continuum Publishing Company. The Ministry of Healing. (1905). Mountain View, CA: Pacific Press Publishing Association, F. F. Bosworth, Fleming H. Revell. , (1973). Christ the Healer. Grand Rapids, MI) The Holy Bible. (1985) . Mountain View, CA: Pacific Press Publishing Association Andrew M and Whitaker H, (1982, Divine Healing. New Kinsington: PA. Jim Glennon (1980). Your Healing is Within You. South Plainfield, NJ: Bridge Publishing. Clowes S and John H, (1817). The Miracles of Jesus Christ. Manchester, UK: J. Gleave.