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2D Representation of Inviscid Air Flow over a Sphere

Abstract This lab is a 2D representation of inviscid air flow over a sphere using the analogy of constant voltage lines on conductive paper with stream lines and potential lines. Lines were traced at several voltages measured along the paper. These lines, depending on how the paper was oriented in relationship to the current flow, corresponded to streamlines and velocity potential lines. Streamlines and velocity potential lines can dramatically simplify the analysis of a fluid flow. The results of the experiment were valid for inviscid fluid flows only and therefore did not exhibit rotational or boundary layer conditions. Table of Contents Abstract..………………………………………………………………………………..…ii Table of Contents…………………………………………………………………………iii Nomenclature………………………………………………………………………………iv List of Figures……………………………………………………………….…………….v List of Tables……………………………………………………………………….…….vi Introduction…………………………………………………………………………………1 Discussion of Relevant Theory………………………………………………..……………2 Methods…………………………………………………………………………..…………6 Results………………….….………………………………………………………………7 Discussion…………………………………………………………………………………8 Conclusions………………………………………………………………………………..10 References……….…………………………………………………………………………11 Figures and Tables………..…………………………………………….………………….12 Appendices……………………………………………………………………………….14 Nomenclature Arbitrary Constant…………………………………………………………………………………c Direction Components of Velocity……………………………..………………………………….…u,v,w Coordinate System Variables…………………………………………………………………. x,y,z Voltage…………………………………………………………………………………………….V Velocity………………………………………………………………………………………….. V Gradient………………………………………………………………………………………….. ∇ Laplace Operator………………………………………………………………………………… ∇2 Stream Function………………………………………………………………………………….. Ψ Velocity Potential Function……………………………………………………………………… Φ Vorticity………………………………………………………………………………………….. ξ Angular Velocity………………………………………………………………………………… ω List of Figures Figure 1: Anderson Figure 2.28 Streamlines………………………….…………………12 Figure 2: White Figure 1-4 Flow Past a Circular Cylinder……………….……..….……12 Figure 3: Marking Points of Constant Voltage…………………………………………..13 Figure 4: Experimental Drawing………………………………………………..….……13 List of Tables No Tables Used in this Experiment Introduction This experiment uses the analogy between the aerodynamic stream function, velocity potential, and voltage in 2D to represent inviscid air flow around a circle. According to Anderson, “A streamline is a curve whose tangent at any point is in the direction of the velocity vector at that point” [1], as shown in figure 1. Streamlines are important to aerodynamicists because they are a visualization of airflow. Visualization is key to understanding and developing proper dynamic models of flowing gasses. Streamlines are designated by setting the stream function ( Ψ ) equal to a constant. When differentiated, the stream function gives the flow-field velocities. This is a very important characteristic of the stream functions. In a similar manner, the derivatives of the velocity potential give flow-field velocities. Unlike the stream function, the velocity potential is in the same direction as the flow-field velocities, can be applied to 3D flows, and can be applied to irrotational flows only. The velocity potential is important because it allows aerodynamicists to drastically simplify flow fields. By running a voltage around a circular shape on a piece of conductive paper an illustration of velocity potential and streamlines of an inviscid flow is created. This is a very simplified example of airflow, but with real world applications. This experiment is meant to help the aerodynamicist visualize the stream and potential functions and understand how using an analogy can be beneficial in science and engineering. Discussion of Relevant Theory Visualization of fluid flow over a solid object is a key component of dynamic modeling and aerodynamics. “Inviscid flows do not truly exist in nature; however, there are many practical aerodynamic flows (more than you would think) where the influence of transport phenomena is small, and we can model the flow as being inviscid” states Anderson [2]. The analogous affect in this lab is credible due to the fact that the stream function, velocity potential function and voltage (V) all simultaneously appease the Laplace Equation. ∇2Ψ=0, ∇2Φ=0, ∇2V=0 For this to hold true in aerodynamics, there must be a complete absence of shear forces in the flow field. Those shear forces include sources, sinks and rotation. Electrostatically this analogy is satisfied if there is no net charge present on the conducting paper. The stream function ( Ψ ) and velocity potential (Φ) are two mathematical constructs that are used to describe a flow and its interaction with a solid object. One can use the equation for the incompressible stream function to give the equation for a streamline by setting the stream function equal to a constant, as shown here Ψ(x,y ) = c The velocity is acquired by differentiating ψ in as shown below Vu=∂Ψ∂y Vv=–∂Ψ∂x The boundary condition of this function is that the derivative parallel to the solid surface is zero. The comparison with the voltage in the experiment is that the voltage is constant along a perfect conductor and therefore is analogous with the stream function. This is to say that the fluid cannot flow into the solid and voltage cannot flow into a perfect conductor. Setting the stream function equal to several different constants allows for the sketching of the fluid flow around a solid. This is important because it allows aerodynamicists to be able to represent two velocity components with one variable. Before describing the velocity potential, it is important to establish that this experiment is valid only for an inviscid flow. As stated by White, this lab “illustrates a characteristic of inviscid flow without a free surface or ‘deadwater’ region: There are no parameters such as Reynolds number and no dependence upon physical properties… the integrated surface pressure force in the streamwise direction, the cylinder drag, is zero. This is an example of the d’Alembert paradox for inviscid flow past immersed bodies” [3]. This being true allows for a vacancy of viscosity in the lab’s analogy. Viscosity gives rise to two major factors in real flow: boundary layer thickening and vorticity effects on the trailing edge of the solid object. The boundary layer thickening effect can be simulated in this analogy by simply drawing the shape of the circle thicker than normal to account for the additional layer. The vorticity effects are created by viscosity, rotation, and distortion in a fluid. These effects cause circulation of the airflow around the solid body. The equation for vorticity (ξ) is given by ξ=2ω Where ω is the angular velocity of the solid body. This gives us a relationship between vorticity and the velocity field by the equation ξ= ∇ × V The above equation says that the curl of the velocity field is equal to the vorticity. This relationship allows for a distinction between rotational and irrotational flows. If the flow is irrotational, ξ = 0. Irrotational flows are much simpler to analyze than rotational flows. The velocity potential (Φ) can now be used to mathematically describe the flow. The equation for the velocity potential is expressed by V= ∇ Φ This equation says that for an irrotational flow there is a scalar function Φ such that the velocity is given by the gradient of Φ. The velocity function can then be differentiated to yield u= ∂Φ∂x, v= ∂Φ∂y, w= ∂Φ∂z These equations show the characteristics stated earlier that the velocity potential is valid for 3D flows, it is in the same direction as the velocity vectors, and it applies to irrotational flows only. Furthermore, the equations reveal the orthogonal nature of the potential function to the stream function. u= ∂Φ∂x= ∂Ψ∂y Except at the stagnation points, where the velocity vanishes, the streamlines and potential lines are orthogonal to each other because the ratios of the partial differentiations are negative reciprocals. Now the flow can be expressed as a one equation dealing with one unknown which is a dramatic simplification of the fluid flow. The boundary condition for the velocity potential is that the derivative normal to a solid body is zero, so the lines must approach perpendicularly to the surface body. Likewise, the voltage lines must be perpendicular to the outline of the perfect insulator in the experiment. This is equivalent, as with the stream function, of the flow not going through the solid. Assuming there is no net charge on the conducting paper, flow around the circle should resemble that as shown in figure 2. Symmetric streamlines and velocity potential lines will remain continuous and reflect across the stagnation voltage line through the center of the circle. No viscosity shall be present, and no flow separation shall be experienced. Methods This experiment used a 23-inch square board with electrodes on two opposite sides. The electrodes were connected to a DC power source. A piece of conducting paper with a high resistance was placed on the board and a voltage drop of 10 volts was established through the paper from the electrodes. An outline of a circle was drawn and filled in with very conductive nickel paint. The lines of constant voltage ran parallel to the two electrodes, so the circle had to be oriented such that it too is parallel. After allowing the paint to dry, a digital voltmeter was used to measure voltages. As pictured in Figure 3, several (5 – 10) measurements were taken across the board and the lines of constant voltage were traced with a pen. These lines were analogous to the streamlines. After turning off the power supply, the paper was removed, and the outline of the circle was cut out of the paper leaving a hole in the same shape. The paper was replaced on the board but rotated 90 degrees from the original orientation. Repeating the previous process, constant voltage lines were once again measured and traced. These lines were representative of the potential function lines. The area was then cleaned up and everything returned to its place. Results The experiment showed the constant voltage lines flowing around the circle in a manner that is analogous to inviscid air flow. For the sake of time, only 5 lines were drawn for the potential lines, but this was sufficient to represent the analogy effectively. An image of the lab test results is shown in figure 4. The circular body was oriented such that the flow was moving from left to right, with the left-hand side of the circle being the leading edge. Measurements for the streamlines were taken at 3.60, 4.25, 4.85, 6.00, 6.50, and 7.00 volts. The flow velocity should always be tangential to these lines, which is reflected in the figure. The closer the lines are to each other around the body is where the air flow would be moving faster. Measurements for the potential lines were taken at 2.5, 3.65, 4.5, 5.45, and 6.70 volts. The velocity of the flow should always be perpendicular to these lines, which is once again reflected in the figure. Discussion Inviscid flow is attained as the Reynolds number approaches infinity in theory. In the case of very high but a finite Reynolds number, the flow can be practically assumed to be inviscid. Anderson notes that “For such flows, the influence of friction, thermal conduction, and diffusion is limited to the boundary layer, and the remainder of the flow outside is essentially inviscid…For flows over slender bodies, inviscid theory adequately predicts the pressure distribution and lift on the body and gives a valid representation of the streamlines and flow field away from the body.” [2]. The vorticity condition was not seen acting along the trailing edge of the circle. In figure 4 it is observable that there was no circulation of the constant voltage lines (streamlines) around the trailing edge. This was due to the lack of viscosity and rotation as discussed in the relevant theory section. If the flow was viscid there would also have been a boundary layer thickness on the body, separation of the boundary layer at the trailing edge, and turbulence in the flow. None of these conditions were present in this experiment. Since there was no friction in the flow there was also no lift or drag on the circle as evident during the experiment since the paper had no forces acting upon it. Upon inspection of figure 4, the streamlines appear approximately symmetric across the stagnation value. Minute fluctuation in the results are most likely the result of human error. These errors could include not painting a symmetric circle causing an imperfect conductor, or unsteadiness while tracing the points of constant voltage. Fluctuations in the potential lines are suspect to similar human errors. Cutting out an unsymmetrical circle leading to an imperfect insulator, and again errors while tracing the points of constant voltage. Overall the experiment worked well to convey the analogy of electric current to inviscid air flow. Conclusion Overall this lab was about visualization of air flow and understanding how useful analogies can be. The results of the lab turned out as expected. The streamlines and potential lines were clearly visible flowing around the circle in a manner similar to inviscid airflow. The absence of viscosity meant that there was no boundary layer thickness or separation. It also meant there was no vorticity. This is a major difference from real viscous flow, but inviscid flow is easily analyzed and easily produced. References [1] Anderson, J. D. Jr., “Fundamentals of Aerodynamics”, 5th ed., McGraw Hill, New York, 2011, pp. 158-185. [2] Anderson, J. D. Jr., “Fundamentals of Aerodynamics”, 5th ed., McGraw Hill, New York, 2011, pp. 62-64. [3] White, Frank M., “Viscous Fluid Flow”, 3rd ed., McGraw Hill, New York, 2006, pp. 4-12.
FIU Non Verbal Communication between Western Culture and Asian Culture Essay.

Your essay is designed to increase your understanding of nonverbal communication in different cultures. For this essay, you should choose 2 cultures and evaluate the nonverbal communication using your textbook. Choose a specific topic reviewed in this class (for example, eye contact) and reflect on the two cultures based on the interactions. Make sure to include terminology and theory connections to describe the specific interaction and/or relationship.Be sure to use specific details and cite your textbook and/or external sources. This writing assignment should include four major sections: the Title Page, Abstract, Main Body, and References (please see Purdue University’s APA Style Guide (Links to an external site.) for more information). Review the assignment rubric available in the assignment description.
FIU Non Verbal Communication between Western Culture and Asian Culture Essay

Digital Evidence Essay

Technology is present in the modern world in the form of gadgets and screens while invading regular life with digitalization. This matter causes the rise in the importance of digital evidence while being a driver for the establishment of a new branch in the legal sphere related to cyber law. In this case, the digital evidence could be defined as “any digital data that may be used to establish that the crime has been committed” (Don, 2010, p. 22; Purpura, 2013). In this instance, the critical goal of this essay is to highlight the importance of digital evidence while using examples and providing the guidelines for the working place. In the end, the conclusions are depicted to offer a clear understanding of the importance of the discussed concept and its need to comply with the established legal system. In this case, digital evidence is highly important in the modern world, as it contributes to the understanding of the presence of crimes. Meanwhile, it assists in the clear identifications of the suspect, as some types of information are only present in the digital form (Casey, 2011; Cruz-Cunha

The Socialist Challenge The Socialist Challenge

essay writing help The Socialist Challenge The Socialist Challenge.

Read The Socialist Challenge: Link (Links to an external site.)Links to an external site.http://www.historyisaweapon.com/defcon1/socchal13….Read War is the Health of the State Link (Links to an external site.)Links to an external site. http://www.historyisaweapon.com/defcon1/zinnwarhea…Please read chapters to do assignment Study Guide: The Socialist Challenge1. Child labor was common at the turn of the century. Describe these conditions and refer to the primary sources.2. Explore the governments role in the labor movement. 3. Describe the IWW and its goals in the US. Who supported the IWW and who was opposed?4. How did race, skill and gender affect union organization?5. What laws protected workers? What laws undermined workers?6. Who was Eugene Debs and what was his vision for working Americans? 7. What was the 19th Amendment? What groups supported the amendment? What groups opposed it?8. Describe the NAACP and its founding. What were its goals? 9. How did President Roosevelt respond to the challenges facing the nation? What motivated his actions?10. Describe events in Ludlow Colorado. How did the government respond? Study Guide: WAR IS THE HEALTH OF THE STATE1) What was the role of the US during World War I? Who did they support? Why did the US decide to enter the war?2) What advantages did the US see to getting involved in World War I? How did entering the war serve the interests of the US at the time?3) Who was W.E.B. DuBois? What were the ideas he is most known for? What did he believe Blacks of the time should strive for? What was his reasoning? Why did he believe this?4) How did citizens see World War I? Were they eager to volunteer for the war? Why or why not? Did citizens support the war effort in general? What evidence does the author provide for this?5) What was the Espionage Act? What purpose did it serve? What was the government responding to when it passed the legislation?6) What was the American Protective League? Why was it created? What purpose did it serve? Who were the members of the APL?7) How did radicals see the war? Were unions supportive or against the war? What evidence did the text offer to support this?8) What was the IWW? What were their goals? How did they see the war? Did they agree with the US decision to enter the war? Were they in favor of the war?9) How did the government respond to those who resisted the war effort? What reforms did the government make in the hopes of dealing with resistance?10) What was the role of the FBI according to the text? What is the role of the Department of Homeland Security? How are they similar or different from one another?Assignment: Please take quiz https://hartnell.instructure.com/courses/8362/quiz… User:0223385Pass-02181988
The Socialist Challenge The Socialist Challenge

The Nature and Course of the African American Experience Between 1850 and 1915 was a Historical Change Essay

The period of 1850 to 1915 offered great historical experience to the African American in the United States. It was characterized by historic events that served to change the course of the African American from that of being dominated upon in economic, social, and cultural affairs to that of emancipation in these areas. This essay explains why the experience is best described as a historical change rather than an historical continuity. During the period under examination, the African American culture changed significantly. Families did not take meals times as family time and have conversations on the table during meal times. It was very odd to find a whole family in a house having meal at the same time (Washington p.114). Another notable change was in churches, where the emancipation of the African Americans from slavery resulted in a movement of churches that were mostly Baptist (Johnson p.135) that developed a district characteristic in worship that previously was only noticed in songs sung from generation to generations in their houses. New freedoms allowed the African American to incorporate his tradition in their church and this attracted various people into the church ministry such that there was a notable increase in formation of new churches during this period (Du Bois p.121-123). African Americans during this period started gathering in public, especially on Sundays when there were no work in the field. Washington writes that women spent their leisure Sunday afternoons in the towns, with the excuse of going shopping (p.115). African Americans could now be able to participate and get involved with other Americans as equals even though they still faced some prejudice (Johnson p.13). They attended schools together with other Americans and participated in sports and other activities up to a national level. Another first for African Americans was that they now could interact with other Americans based on what they were and not what the color of their skin was. This was also characterized by newer choices of careers that previously were not known to be adopted by African Americans especially in art (Johnson p.59

Contribution of SMEs to the Malaysian economy

Today, economic development is fast becoming the focus of many governments. In this, businesses are springing up and forth from different dimension. One of these businesses prominently known in Malaysia is the SME which stands for small and medium enterprises. The growth and roles of SMEs has risen to become one vital and crucial in the Malaysia economy. At the turn of the 21st century, Malaysia is fast pursuing its goals to becoming a vision 2020 nations and thus with SME being a visible player in the economy, this review will critically analyze the concept of SME, the contribution as well as the existing problems facing it. It is however worthy to note that SME is very vital to the Malaysia economy as will be discussed in this review. Definition of Malaysia SMEs In Malaysia, the true meaning of small and medium enterprises (SMEs) cannot be conceptualized in detail is because there are several definitions ofsmall and medium enterprises (Jafari et al, 2007; Fathian et al, 2008). While according to (Thassanabanjong et al, 2009; Mirbargkar, 2009; Ghabatabadai, 2005) definition of small and medium enterprises vary by country. According to Hor (September 2001), The Small and Medium Sized Industries Development Corporation (SMIDES) also defined small and medium enterprises in industries with the number of workers who work full-time employees not exceeding 150 people, while total sales revenue is RM25 million. For the total annual sales of the company is the factory must have an annual value not exceeding RM25 million and the number of permanent workers is less than 150 people (Malaysia, 2002). (Fong, 1987) is an organization of small companies that have a fixed asset less than RM250, 000. According to (Moha ,1997) small and medium enterprises (SMEs) can be divided into three (3) parts, depending on the operation, the small industries and companies carrying out business operations with a number of permanent workers is less than 50 0rang, medium-sized industries The operating businesses and companies that have a fixed number of 50 employees to 199 people and industries that have a large number of permanent workers for more than 200 people. In summary, defining SME in Malaysia is confined to two major requirements: “number of workers and annual turnover”. Operating environment of Malaysia SME Today small and medium enterprises (SMEs) is a syringe to the economic development in the country, with the small and medium enterprises, the prospect of realizing the dream of the achieving and sustaining the vision 2020 target. Small and medium enterprises (SMEs) are companies that process and provide the raw material that is derived not from toxic materials which include electronic equipment, jewelry, stationeries and so on. According to (Entrepreneur Success, 2002) medium companies are more oriented towards the production of fast food, fruit canning, production of furniture and so forth. According to Ozcan (1995) smaller companies include three (3) primes focus in the business, employees who work full time and number of employees a little bit and have a personal management structure. Small and medium enterprises are an important asset to the country as it contributes to economic development in the country and the APEC and OECD member countries. I personally believe that the operating environment of Malaysia SMEs is favourable on the overall. According to the work of Hosmel, et al,(1993), they argued for the fact the role of SMEs in Malaysia is helping in the production and distribution of goods and services. Contribution of small and medium enterprises to the economy SMEs are a major contributor to economic growth of Malaysia. With advances in small and medium enterprises (SMEs) are expected to realizing a dream for Malaysia to become a developed nation in the field of industrial policy in 2020 through the vision 2020. The development of small and medium enterprises (SMEs) can indirectly provide the changes in technology and the growth rate is closely related to the Development of technology in this century (Storey, 1996). In addition to changes in technology (Hosmel et al, 1993) describes (SMEs) also opened up employment opportunities with the most productive working environment is informal. In addition to providing employment opportunities (SMEs) also increases the amount of national savings and could reduce the rate of foreign exchange to foreign countries, as well as an impetus to economic growth in the country (Okpara, 2009). Small and medium enterprises (SMEs) also play a role as a bastion of economic growth in the long term (Thasasanabanjong et al, 2009). Having analyzed all these review, I partly agree these researchers but the need to understand that SME provides and stimulates entrepreneurship spirit should be considered. SMEs furthermore, create relationship between customers, entrepreneurs and government. In supporting this claim, Gadenne and Sharma (2009) have suggested that the entrepreneurship spirit is a contribution of SME. Likewise, Hodgetts

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