Flow of a Free Air Jet Laboratory Exercise

Flow of a Free Air Jet Laboratory Exercise An investigation into the structure of a free air jet and how its velocity is distributed during interaction with its surroundings Summary Air jets have provided the basis for jet propulsion mechanisms, commonly used to provide movement in jet engines, spacecraft and even particular marine animals. In aviation, it is important to measure an aircrafts velocity, altitude and Mach number in order to monitor performance and determine areas of improvement. In this experiment, a pitot-static tube system was set up along the axis of a free air jet, and the local velocity of the air jet was calculated and recorded using measurements from an inclined manometer as the pitot-tube was displaced in both the horizontal and vertical planes. The experimental and theoretical results highlighted the same trends, confirming the expectation that as decreased (due to increased displacement), local velocity, , also decreased. A divergence angle of 10.1ÂÂ ° was calculated, and the volume flow rate varied between 0.0149 m3s-1 and 0.049 m3s-1. Introduction An air jet is a nozzle or tube from which a directed pressurised jet of air is emitted. (1) These have provided the basis for jet propulsion producing a thrust in the opposite direction of the jet as demonstrated through Newtons third law. Airs jets are commonly used to provide movement in jet engines and spacecraft, and even certain marine animals have evolved to rely on jet propulsion mechanisms. (2) There are two main types of jet; impinging and free. While an impinging jet is directed towards a surface, this experiment is concerned with the interactions of a free, submerged air jet, where the jet is discharged into an ambient fluid of similar physical properties. (3) A pitot tube is a pressure measurement instrument used to measure fluid flow velocity. (4) This is done by converting the kinetic energy of the flow into potential energy (5). Pitot-static systems, consisting of a pitot tube, a static port and the necessary measuring instruments (6), are often used in aviation to determine an aircrafts velocity, altitude and Mach number, as well as having nautical applications in the calculation of boat and vessel speeds. (7) Theory 3.1 Velocity A pitot static tube measures two separate pressures: the stagnation pressure,, and the static pressure, (8) Bernoullis equation states that the total stagnation pressure is equal to the sum of the static pressure and the dynamic pressure, . The dynamic pressure is proportional to the density of the concerned medium, , and the square of the local velocity, v, such that: (equation 1) If the pressure difference between the stagnation pressure and static pressure is applied to alter the water level of a manometer, equilibrium is achieved when: (equation 2) Therefore, by combining equation 1 and equation 2, and assuming = 1.225 kgm-3 and = 1000 kgm-3, the local velocity in ms-1 can then be calculated through the relationship: (equation 3) 3.2 Flow Rate The volume flow rate leaving the nozzle of a circular air jet, can be considered equal to exit velocity, , multiplied by nozzle surface area, A. (9) This relationship is represented through the equation: (equation 4) Beyond the nozzle exit, the velocity cannot be considered constant at all vertical points in the jet; therefore, it is necessary to integrate to find the volume flow rate. The expanded profile of the air jet can be considered circular, consisting of a series of annuli areas containing an air flow rate equal to for each respective measured value of velocity and calculated area. This is represented visually in figure 1 below. Recalling the area of an annulus as, where is the radius along the mid-point of the annulus, and considering the asymmetrical profile of the final jet requires separate measurements in each hemisphere, the total volume flow rate can be calculated through: (equation 5) Here, is the local velocity at the required radius and is the area of half an annulus, where is the radius at which the velocity was measured. Method Apparatus Nozzle of diameter 30mm, to create the uniform circular jet of air to be measured. Pitot-static tube system, consisting of a pitot-tube, static tube and axial scales,to collect the air from the nozzle and carry it to the manometer. Manometer, inclined at an angle, ÃŽÂ ¸, which holds the liquid and allows for its movement depending on the pressure apparent from the pitot-static tube system. A zero, to locate the starting point at which measurements of the fluid distance along the manometer will be taken from. A ruler, to manually measure the distance travelled by the liquid along the manometer, . Procedure The zero was adjusted along the manometer to indicate the point at which further measurements with the ruler would be taken from and the pitot-static tube was moved along the apparatus to the origin, at the centre of the nozzle, where the coordinates corresponded to (0, 0). The air jet was turned on and, after allowing sufficient time to warm up, the distance the liquid had moved along the manometer, was measured, using the ruler, and recorded. The tube was then moved along the centreline across a series of predetermined distances away from the air jet (see Appendix A) up to 500mm the point (500,0) and was again measured and recorded at each interval. The pitot-static tube was then returned to sit 60mm away from the air jet and lowered to a vertical height of -28mm from the origin where was again measured and recorded. Maintaining an axial distance of 60mm, the pitot-static tube was then raised in increments of 4mm up to a maximum height of 28mm and the distance, , measured for each step. This experiment was then repeated at axial distances of 180mm and 300mm, through ranges of -50mm to 50mm and -60mm to 60mm respectively, using increments of 5mm in both. Results 5.1 Velocity Profiles The recorded distances,, for the three vertical experiments, were then converted into vertical distances, h; in this experiment, ÃŽÂ ¸ = 13ÂÂ °. The velocities at each height were then calculated using equation 3 and graphs of velocity against height for all three axial distances were drawn as shown in figures 3a, 3b and 3c below. 5.2 Plan View The divergence angle can be calculated by forming a triangle between the edge of the jet and a line perpendicular to the nozzle boundary; see figure 4. For this experiment: 5.3 Centreline Velocity Distribution The recorded distances, , for the centreline experiment were converted into vertical distances, h, using ÃŽÂ ¸ = 13ÂÂ °. The axial distance, x, was then divided by the nozzle diameter, D = 30mm, and a graph of velocity against was plotted, as seen below in figure 5. 5.4 Volume Flow Rate Assuming is constant at the edge of the nozzle, the exit volume flow rate can be calculated through equation 4: m3s-1 Beyond the nozzle exit, values for, the annulus width, and , the outer radius, were required to calculate volume flow rate. The values for were 4mm at an axial distance of 60mm, and 5mm at axial distances of 180mm and 300mm, and values for corresponded to the radial distances; these can be found in Appendices B, C and D. Using equation 5, the volume flow rates were found at x = 2D, x = 6D and x = 10D respectively, and the results displayed through table 1. Axial Distance (mm) Volume Flow Rate (m3s-1) 60 0.01925 180 0.034475 300 0.048705 A graph of volume flow rate against axial distance was then plotted for comparison; see figure 6 below. 6.1 Structure of the Air Jet An air jet is comprised of three important regions: the core, the mixing region and the edge or boundary. Within the core, the velocity does not vary significantly from the nozzle exit speed. From the measurements in this experiment, this region exists up to around 180mm along the centreline (see figure 5). Outside of the core, illustrated in figure 4, the mixing region is encountered. Throughout this region, the local velocity,, is less than the exit velocity, , due to the reaction of the air jet with the ambient fluid. The edge or boundary of the jet represents the radial distance at which the local velocity is equal to zero at each centreline distance. The edge of the jet increases linearly at a rate dependent on the divergence angle, measured to be 10.1ÂÂ ° in this experiment. This is similar to the universal value for the divergence of a jet of 11.8ÂÂ °, which is independent of nozzle diameter, discharge speed or the medium involved. (10) 6.2 Diameter of the Air Jet From the plan view illustrated in figure 4, it can clearly be seen that the air jet spreads out as axial distance increases. This occurs as a consequence of the significant velocity difference between the jet and the ambient fluid, which creates a highly unstable shear layer at the edge of the jet. This shear layer is subject to large variance in local velocities, generating strong turbulent fluctuations which subsequently entrain the ambient fluid into the path of the jet, increasing the mixing of the two fluids. As a consequence of both the turbulent fluctuations and the entrainment of the ambient fluid, the shear layer continues to be pushed outwards as the jet flows downstream. (11) 6.3 Centreline Volume Distribution Figure 5, above, clearly illustrates that up to a value of = 6, the velocity along the centreline varies very little, with a range of 0.833 ms-1. This region is known as the core, where. The only source of momentum when the jet exits the nozzle is from the jet itself, as the surrounding fluid is at rest. The absence of external forces acting on the jet suggests that the centreline velocity will remain constant as distance increases. (11) Beyond an axial distance of 180mm, the velocity follows an inversely proportional relationship with distance, decreasing at a rate of (where k is an unknown constant). This occurs when the core of the jet interacts with entrained ambient fluid caused by significant velocity fluctuations at the edge of the jet, decreasing the velocity of the fluid as discussed in section 5.2. Due to the interaction between two different fluid flows, the region in which this occurs is referred to as the mixing region. 6.4 Volume Flow Rate Figure 6 suggests that volume flow rate increases linearly with axial distance, rising from 0.015m3s-1 at the nozzle exit to 0.049m3s-1 at an axial distance of 300mm. From section 4.4, it is known that the volume flow rate is a function of the jet area and local velocities across the diameter. Due to conservation of momentum, it is expected that as the area increases, the velocity decreases such that the volume flow rate remains constant across all axial distances. However, the increase in volumetric flow is a result of entrainment of the stationary surrounding fluid. The turbulent flow caused by the velocity fluctuations in the shear layers contributes to an increased local velocity across the diameter of the jet, increasing volume flow rate. 6.5 Experimental Errors and Uncertainties Although this experiment has successfully demonstrated the characteristics of a free air jet as highlighted in this discussion section, numerous errors and uncertainties were still encountered throughout the experiment which could have had a potentially significant effect on the results obtained. One of the most common sources of uncertainty was the use of a ruler to measure the distance of the fluid along the manometer. This combined human error, due to the estimation of both the zero position and the final position of the fluid meniscus with systematic error, as a consequence of the ruler measuring with an uncertainty of ÂÂ ±1mm and therefore, accurate measurements for were not obtained. Similarly, the location of the necessary axial and radial positions for the pitot-tube were subject to a similar human error. The fluid in the manometer also contained several air bubbles prior to the experiment; this is a systematic error as it would subsequently affect every manometer dista nce reading. Therefore, it is possible that the results obtained for could consistently higher than expected due to the presence of these air bubbles in the fluid. The final significant error involved in this experiment was the random error associated with the changing position of the static tube. For a set axial and radial positioning of the pitot-static tube, changing the height and geometry of the static tube caused the manometer reading to alter slightly as well. Although efforts were made to maintain the location of this tube, there is still the possibility it could have caused sporadic errors in the results. To conclude, the experiment outlined in this report was successful in demonstrating the interactions of a free air jet with an ambient fluid and, subsequently, the effects of the displacement of the pitot-tube on the local velocity along the centreline and throughout the mixing region. The decreasing local velocity as displacement increased was found to be a result of turbulent fluctuations causing entrainment of ambient fluid into the path of the jet. In the experiment, the maximum velocity was found to be around 20ms-1 for a distance of 180mm along the centreline of the jet and the divergence angle was calculated to be 10.1ÂÂ °. These results were useful in introducing the basic structure of an air jet, which comprises of three main regions: the core, the mixing region, and the edge. The slight discrepancy between the measured divergence angle and the universal angle of 11.8ÂÂ ° (9) can be considered due to the inaccuracy in measuring the position of the fluid meniscus in the manometer using a ruler, producing potentially unreliable results. The findings from this experiment are statistically insignificant due to the nature of the apparatus used and the various possible sources of error, both systematic, due to air bubbles present in the manometer fluid, and human, arising from the use of a ruler for distance measurements. However, the experiment was useful in demonstrating the interactions of an air jet with its surroundings, as well as introducing the concept of internal structures within a free air jet. [1] Oxford Dictionaries, Air Jet, [Online]. Available: https://en.oxforddictionaries.com/definition/air_jet. [Accessed 24 March 2017]. [2] LearningInfo, Which Animals use Jet Propulsion, [Online]. Available: http://www.learninginfo.org/sandbox/which-animals-use-jet-propulsion.htm. [Accessed 25 March 2017]. [3] W. Grassi, Impinging Jets, 2 February 2011. [Online]. Available: http://www.thermopedia.com/content/872/ . [Accessed 24 March 2017]. [4] Wikipedia, Pitot Tube, [Online]. Available: https://en.wikipedia.org/wiki/Pitot_tube. [Accessed 25 March 2017]. [5] Efunda, Pitot Tubes Theory, [Online]. Available: http://www.efunda.com/designstandards/sensors/pitot_tubes/pitot_tubes_theory.cfm. [Accessed 26 March 2017]. [6] P. Willits, Guided Flight Discovery Private Pilot, Jeppesen Sanderson, 2004. [7] S. Houston, Pitot Static System, 13 October 2016. [Online]. Available: https://www.thebalance.com/aircraft-systems-pitot-static-system-282605. [Accessed 26 March 2017]. [8] I. Gursal, Flow of a Free Air Jet, University of Bath, Bath, 2017. [9] Khan Academy, What is Volume Flow Rate, [Online]. Available: https://www.khanacademy.org/science/physics/fluids/fluid-dynamics/a/what-is-volume-flow-rate. [Accessed 27 March 2017]. [10] Dartmouth College, Turbulent Jets, [Online]. Available: https://thayer.dartmouth.edu/~d30345d/books/EFM/chap9.pdf. [Accessed 24 March 2017]. [11] Anon, Jet, [Online]. Available: https://www.eng.fsu.edu/~shih/succeed/jet/jet.htm. [Accessed 29 March 2017].

James Prescott Joule :: biographies biography bio

James Prescott Joule was born December 24, in 1818. James Joule was born into the wealthy brewing family of Benjamin and Alice Joule. In 1847 James Joule married Amelia Grimes, a daughter of the Liverpool Comptroller of Customs. James Joule and Amelia had three children: Benjamin Arthur (born 1849), Alice Amelia (born 1852) and a son who died in 1854 along with his wife during child birth. In 1843 James Joule read his paper to the British Association, entitled "On the Calorific Effects of Magneto-Electricity and on the Mechanical Value of Heat." This paper described the physical constant that showed that heat was a form of energy. This constant is known as "J", or "Joule's Equivalent." The unit of heat, work and internal energy are measured in joules (J). James Prescott Joule died October 11 in 1889. James Joule is buried in Westminster Abbey along with other famous people. Those Who Inspired John Dalton James Joule was tutored as a young boy by John Dalton: John Dalton was a well known Chemist and Physicist. John Dalton was born September 6 in 1766 and died July 27 in 1844. John Dalton is most recognized for his findings, which later is known as "the atomic theory". The atomic theory is the theory of the nature of matter. It states that: "all matter is composed of atoms." Lord Kelvin James Joule worked with Lord Kelvin on experiments, which later became know as the Joule-Thomson Effect: Lord Kelvin was a well known Mathematical Physicist. The well known "Lord Kelvin" born as William Thomson, June 26 in 1824 and later died December 17 in 1907. William Thomson later became the 1st Baron Kelvin, he was known as "Lord Kelvin." Lord Kelvin is most recognized for his work in thermodynamics and Kelvin temperature scale. Rudolf Julius Emanuel Clausius James Joule was inspired by the work of Rudolf Julius Emanuel Clausius: Rudolf Julius Emanuel Clausius was a Physicist and a Mathematician. Rudolf Julius Emanuel Clausius was born January 2 in 1822, and died August 24 in 1888. Rudolf Julius Emanuel Clausius is most recognized for his work in thermodynamics. Rudolf Julius Emanuel Clausius introduced the concept of entropy. The Experiments (Known Today as Research) Paddle Wheel Experiment James Joule's Paddle Wheel Experiment determined the existence of a relation between heat and mechanical work. He established this by a method involving the churning water in a calorimeter by means of paddles driven by various falling weights. Through this experiment James Joule established what we call today the First Law of Thermodynamics.

Basic Computer Memory Types Essay

Random Access Memory (RAM) RAM is a location within the computer system which is responsible for stacking away data on a temporary basis, so that it can be promptly accessed by the processor. The information stored in RAM is typically loaded from the computer’s hard disk, and includes data related to the operating system and certain applications. When the system is switched off, RAM loses all the stored information. The data remains stored and can be retained only when the system is running. When the RAM gets full, the computer system is more likely to operate at a slow peed. The data can be retrieved in any random order. Generally, there are two types of RAM; namely Static RAM (SRAM) and Dynamic RAM (DRAM). When many programs are running on the computer simultaneously, the virtual memory allows the computer to search in RAM for memory portions which havent been utilized lately and copy them onto the hard drive. This action frees up RAM space and enables the system to load different programs. Read Only Memory (ROM) This type of memory is active, regardless of whether the system is turned on or is switched off. It is a kind of permanent non-volatile storage memory. As the name ‘read only’ suggests, the contents in it cannot be changed or modified. It is an integrated circuit which is pre-programmed with important data that should necessarily be present for the computer to carry out its normal functionalities. Cache Cache is a kind of RAM which a computer system can access more responsively than it can in regular RAM. The central processing unit looks up in the cache memory before searching in the central memory storage area to determine the information it requires. This rules out the need for the system to search for information in larger and bigger memory storage areas, which in turn leads to a faster extraction of data. Computer Hard Drive These devices are important data storage components that are installed in the CPL]. Their memory ranges widely, and a user may choose the memory depending on the data needed to be stored and accessed. Nowadays, hard drives having a memory capacity of 120 gigabytes to 500 gigabytes are normally used. Flash Memory This is a non-volatile kind of memory which is intended to contribute to portable torage and a convenient transfer of data from one computer to another. The data in it can be erased and re-programmed as per the user’s requirements. It only has a specific number of erase and write cycles that it can withstand, after which it creates a tendency to lose out on the stored information. Memory cards and USB flash drives These are Just the common and main computer memory types which facilitate memory and data storage. However, there are many subtypes which are sorted out according to the memory-related functionalities they perform and the requirements they serve.

WhatisADD essays

WhatisADD essays What exactly is ADD? This is a question that has remained unanswered for a very long time. ADD, also known as attention deficit disorder, has to do with the brain. This disorder was at one time thought to be related to brain damage. Nowadays however, it is actually quite common. It is reported that about 40 percent of the student body of an average school is ADD. Scientists think that this is at least one student per classroom in a ADD has really been recognized over the past twenty years. This is when most of the research about it has been done. When someone has been diagnosed as having ADD it does not mean that they are lazy, stupid, or crazy. It only means that they have a difficult time trying to pay attention to a subject in which they have little or no interest. This is why ADD is usually first noticed in school. Before much research was done, ADD was not even called ADD. It had a different name. It was called Hyperknetics. This was really just a fancy term for saying that a child is easily distracted, and also very hyper. This was back in the days when doctors also thought that Hyperknesis was caused by some sort of brain damage. This was potentially true however; there were a few rare cases in which some brain damage actually occurred in a child. The brain damage only happened naturally, like when the child was being developed. ADD is something that an individual person is born with, and not something that is developed over time. Many Doctors and specialists have discovered over time that there is more than type of ADD. Doctors now recognize three distinct types of ADD, normal ADD, ADHD, and residual ADD. The second, ADHD is normal ADD coupled with a hyperactive tendency. The third type, residual ADD is the type of ADD that most commonly affects older children and adults. Hyperactivity is not usually associated with residual ADD. When it ...

Testing Cell Respiration and Alcoholic Fermentation essays

Testing Cell Respiration and Alcoholic Fermentation essays There will be a measurement of heat generation produced by seedlings during cell respiration. Using a thermometer, the heat of seedlings in a thermos bottle will be calculated over a period of at least 25 minutes in 5-minute increments. Using indicator TTC you will also be able to distinguish viable seeds. Along with studies of cell respiration through temperature readings there will also be investigation of alcoholic fermentation in yeast. A respirometer will be constructed for the ability of recording the effects of yeast concentration on the rate of fermentation. By doing this, the CO2 evolved can be measured over a 20 minute time period. There will be four different tubes filled with four different yeast concentrations for the comparison of rates. The energy yielding metabolism function in which oxygen is used is known as cell respiration. The chemical expression for cell respiration is: C6H12O6 + 6O2 yields to 6CO2 + 6H2O + Chemical Energy. Aerobic cell respiration is the metabolic pathway that requires oxygen. An example of this is glucose metabolism, which can be divided into three parts. The first part is glycolysis, which is the breakdown of glucose and substrate level phosphorylation and the formation of energy products. During glycolysis, glucose enters the pathway and gets phosphorylated by ATP twice. Once it is phosphorylated the glucose splits into tow 3-carbon fuels that are later oxidized by enzymes and phosphorylated. During the substrate-level phosphorylation 4 ATP are produced. However the end products of glycolysis are 2 ATP, 2 NADH, and 2 molecules of pyruvate. The second part of glucose metabolism is the citric acid cycle. This is the complete oxidation of glycolytic products to CO2 and H2O. The products that are produced are protons and electrons. With each turn of the cycle there is use of oxaloacetate. The oxaloacetate joins with acetyl-CoA and when water enters the coenzyme A is released which forms ...

Okonkwo as a tragic hero Research Paper Example | Topics and Well Written Essays - 1750 words

Okonkwo as a tragic hero - Research Paper Example Although Livingstone and Stanley's explorations contributed very little to deepen the Western understanding of the people or the land, they did encourage plenty of speculation and conjecture. It was these made-up ideas that became the foundation of several of the misunderstandings the West has held about Africa since then. Because of the one-sided discussion, Africa emerged as a land of possibility for Western enrichment through the unfettered exploitation of its resources. The West thinks of African people as mostly child-like, capable only of primitive understandings, and only slightly more than bestial in their natural environment. It took several years before native writers, such as Chinua Achebe were able to align Africa’s story with the West in the presentation of Okonkwo as a tragic hero in his story Things Fall Apart (1959). The tragic hero is a frequent character in numerous plays and dramas of the ancient Greeks into the modern day. The character type was present eve n before Aristotle's time, but it was Aristotle who codified the major elements that must be present for a character to be considered a tragic hero although these rules have changed some in the millennia since they were first described. In Aristotle's time, the tragic hero status could only be applied to characters with real potential for tremendous greatness. This meant people who were destined to be kings and princes or others who had some kind of noble claim. According to Zarro, â€Å"the tragic effect will be stronger if the hero is ‘better than we are’, in that he is of higher than ordinary moral worth. Such a man is shown as suffering a change in fortune from happiness to misery because of a mistaken act, to which he is led by his hamartia (his ‘effort of judgment’) or, as it is often literally translated, his tragic flaw.† In spite of this nobility, the tragic hero is destined to fail as a result of some tragic flaw inherent in their nature. T his tragic flaw is often associated in some way with their greatest strength and is therefore an aspect of their character that the individual becomes inordinately proud to exercise (Aristotle). As society has progressed, though, and new structures emerged in which wealthy businessmen took the place of kings and princes, the focus of the tragic hero has been less concerned with his noble status than it is with his progression through a three-fold process. According to Vest, heroism today, even tragic heroism, refers more to the actions of the character who embodies many of our ideals regarding what is good and noble in human nature than it is concerned with the birth or earned social status of the character himself. Although Okonkwo is not born a tribal chief, he earns his status as a tribal elder and this modern change in tragic hero definitions allows even the West to recognize his status. Before proving Okonkwo's actions qualify him as a tragic hero, it is necessary to understand what constitutes the progression of a tragic hero. The process of the tragic hero begins when the character commits some act in the excess of their pride that inevitably leads to their downfall (Aristotle). This is the first stage of the tragic cycle. The second stage

Interpersonal Communication Class - Final Paper Essay

Interpersonal Communication Class - Final Paper - Essay Example Culture plays a fundamental role in management and leadership especially in multicultural organizations. Two different approaches have been advanced in exploring the contribution of culture within a working environment. The convergence school of thought asserts that national or institutional culture has no significant influence on the leadership and management practices. The scientists in support of this school of thought argue that management has the same ‘best policies and practice’ that is applicable independent of the institutional and cultural context. The divergence school of thought, on the other hand asserts that best management policies and practices are culturally bounded, hence influenced by cultural and contextual factors. Although globalization has resulted to standardization of best management policies and practices, divergence theory on power distance cannot be overlooked; as confirms organizational literatures and psychology articles. Adler and Bartholemew (1994, p.429) concluded that culture was important management aspect that has the ability to cause a significant difference in the human resource management and organizational behavior. Therefore, it was inevitable to consider cultural aspect in managing human cultural diversity. The differences in the national management practices and the outcomes are indicators of the fact that cultural differences have a substantial influence on the management and leadership. It is on this account of cultural influence on management and leadership practice that this study examines cross-cultural differences with respect to international relationship that exist within the working environment between senior managers and the workforce of the organization. In par ticular, the role of power distance on employee’s participation and horizontal communications are emphasized in many cross-cultural