Flow in Pipe Network Analysed Using Hardy Cross Method

Flow in Pipe Network Analysed Using Hardy Cross Method Table of Contents 1.0 Introduction 2.0 Procedure for Hardy Cross method: 3.0 Flow in Pipe Network analysed using Hardy Cross method 4.0 Advantages 5.0 Conclusion 6.0 References 1.0 Introduction Piping networks have quite a wide range of practical applications, from water and gas distribution systems to air conditioning installations. Although simple problems, such as for instance, a single branch connecting two reservoirs, may be solved analytically, more complex network problems need an iterative approach, recurring to a digital computer. The most popular method for solving this type of problems is the Hardy-Cross method. The Hardy Cross method is an iterative method for determining the flow in pipe network systems where the input and output flows are known, but the flow inside the network is unknown. Also, the pipe length, diameter, roughness and other key characteristics should be known. Before the method was introduced, solving complex pipe systems for distribution was extremely difficult due to the nonlinear relationship between head loss and flow. Water distribution system models have become very important and practical tool for civil engineers. Models are often used to optimize the design of new distribution systems or analyze major extensions or modifications to existing distribution systems. The introduction of the Hardy Cross method for analyzing pipe flow networks revolutionized  municipal water supply design (Pdhengineer.com, 2014). The Hardy Cross method is normally used as the pipe network analysis by most engineers. Computer models help engineers to solve difficult situations, namely: What is the maximum fire flow at a given point in the system? How long can that fire flow be provided for? What size pipe installation would be necessary between two points in a system to increase the pressure at one of the points to the minimum pressure required? If a subdivision or commercial development is built, will adequate pressures and flows exist? If not, what length and size of water mains must be upgraded by the developer to allow for the proposed construction? 2.0 Procedure for Hardy Cross method: This method is applicable to closed-loop pipe networks. The outflows from the system are assumed to occur at the nodes, where a node is the end of each pipe. This assumption would therefore result uniform flow in the pipelines distribution systems. The Hardy-Cross analysis is based on the principles that At each junction, the total inflow must be equal to total outflow. Head balance criterion: algebraic sum of the head losses around any closed-loop is zero. For a given pipe system, with known junction outflows, the Hardy-Cross method is an iterative procedure based on initially estimated flows in pipes. Estimated pipe flows are corrected with iteration until head losses in the clockwise direction and in the anticlockwise direction are equal within each loop. A trial distribution is madearbitrarily but in such a way that continuity equation is satisfied at each juction. With the assumed value of Q, the head loss in each pipe is calculated according to the equation Where : head loss r : head loss per unit flow n : flow exponent The net headloss around each loop is calculated. If the net head loss due to assumed values of Q round the loop is zero, then the assumed values of Q in that loop are correct. If this is not the case, then the assumed values of Q are corrected by including a correction à ¯Ã‚ Ã¢â‚¬Å¾Q for the flows till the circuit is balanced. The correction factor à ¯Ã‚ Ã¢â‚¬Å¾Q is obtained by For turbulent flow, the value of n=2 and hence the correction factor becomes If the value of à ¯Ã‚ Ã¢â‚¬Å¾Q is positive, then it is added to the flow in the clockwise direction and subtracted from the flows in the anticlockwise direction. After the correction have been applied to each pipe in a loop and to all loops, a second trial calculation is made for all loops. This procedure is repeated till à ¯Ã‚ Ã¢â‚¬Å¾Q becomes negligible. 3.0 Flow in Pipe Network analysed using Hardy Cross method 4.0 Advantages The Hardy Cross method is useful because it relies on only simple math, circumventing the need to solve a system of equations. Without the Hardy Cross methods, engineers would have to solve complex systems of equations with variable exponents that cannot easily be solved by hand. The Hardy Cross method iteratively corrects for the mistakes in the initial guess used to solve the problem. Subsequent mistakes in calculation are also iteratively corrected. If the method is followed correctly, the proper flow in each pipe can still be found if small mathematical errors are consistently made in the process. This method is based on the successive addition of flow-rate corrections in each branch, in order to achieve satisfaction of energy conservation along every path in the network. The easiness of building a new network or modifying an existing one allows the engineer to readily observe how small changes in the network configuration may produce interesting results such as a flow reversal in a certain branch. 5.0 Conclusion Distribution system is a network of pipelines that distribute water to the consumers. They are designed to adequately satisfy the water requirement for a combination of domestic, commercial, industrial and fire fighting purposes. In any pipe network, the algebraic sum of pressure drops around a closed loop must be zero (there can be no discontinuity in pressure) as well as the flow entering a junction must be equal to the flow leaving that junction; i.e. the law of continuity must be satisfied (Nptel.ac.in, 2014). A good distribution system should provide adequate water pressure at the consumers taps for a specific rate of flow. The pressures should not only be great enough to adequately meet fire fighting needs, but should also not be excessive due to pressure leakages which is cost-effective. However, in tall buildings, booster pumps are required to elevate the water to upper floors. Moreover, distribution system of purified water should be completely water-tight and the purity of distributed water should be maintained. Maintenance of the distribution system should be easy and economical. Even, during breakdown periods of pipeline, water should remain available. If a particular pipe length is under repair and has been shut down, the water to the population living in the down-stream side of this pipeline should be available from other pipeline. The distribution pipes systems should not be placed under highways, carriage ways as they will obstruct any traffic flow, but should be laid under foo t paths. Figure 1: Pipe network for Municipal water distribution systems in cities (Scribd.com, 2014) 6.0 References Gupta, R.K., 2005. A Text Book of Fluid Mechanics and Hydraulic Machines. 9th ed. New Delhi: Laxmi Publications. Nptel.ac.in, (2014).Objectives template. [Online] Available at: http://nptel.ac.in/courses/Webcourse-contents/IIT-KANPUR/FLUID-MECHANICS/lecture-36/36-3_pipe_soln_hardy.htm [Accessed on 27 March 2014]. Nptel.ac.in, (2014).Water Supply Network Design. [Online] Available at: http://nptel.ac.in/courses/Webcourse-contents/IIT KANPUR/wasteWater/Lecture%2015.htm [Accessed on 27 March 2014]. Pdhengineer.com, (2014).The Hardy Cross Method and its Successors in Water Distribution PDHengineer Course EN-2034. [Online] Available at: http://www.pdhengineer.com/catalog/index.php?route=product/productproduct_id=1320 [Accessed on 31 March 2014]. Scribd.com, (2014).Pipe Network Analysis using Hardy Cross method. [Online] Available at: http://www.scribd.com/doc/42173408/Pipe-Network-Analysis-using-Hardy-Cross-method [Accessed on 29 March 2014]. https://estudogeral.sib.uc.pt/bitstream/10316/8169/1/obra.pdf) http://en.wikipedia.org/wiki/Hardy_Cross_method

“The Metamorphosis” Expressionism

Expressionism An expressionist piece of literature portrays a vision of the real world through the author’s point of view. â€Å"The Metamorphosis† is an excellent example of expressionism. It shows Franz Kafka’s honest interpretation of the world. His endless fears from his life can be seen in â€Å"The Metamorphosis†. Two fears of Frank Kafka’s that keep re-appearing in â€Å"The Metamorphosis† are displacement in society and strained relationships with society. After Gregor’s metamorphosis he also is no longer a part of his human society and can no longer preserve his relationships with his family.Gregor’s metamorphosis symbolizes Frank Kafka’s every nightmare and hardship in life. Franz Kafka was born in a Jewish family in Prague in 1833. He wasn’t a part of the Jewish community whole heartedly nor was he a part of the German community wholeheartedly. He was out of place in society much like the main character, Gregor in â€Å"The Metamorphosis†. Gregor was an insect in a human world. Everything about him differed from a human’s. He went from a young and capable man one night to an â€Å"old dung beetle† (42). he next morning. A man can never be part of society if he doesn’t know how to fit in. How was Gregor to fit in as an insect? It’s impossible. Some might argue looks aren’t everything one can be an important figure in society and make an impact just through the power of speech. But Gregor couldn’t even do that. To everything that Gregor wished to say the response he received in return was â€Å"Did you understand even a single word? † (18). Neither Franz Kafka or Gregor were able to truly fit in their society.Another key component in Franz Kafka’s life was his strained relationship with his father. This is evident in Gregor’s life as well. The novelette does not tell the reader information on Gregor’s relati onship with his father before the metamorphosis. But from the astonishment of Gregor in response to his father’s actions and words the reader can conclude that his behavior towards Gregor was not always like this. No matter what Gregor did â€Å"his father was in no mood for such niceties† (37). This portrays Franz Kafka’s failure in ever making his father proud of him.Franz Kafka was the eldest yet he could not carry the pride of the family. Gregor has carried his family’s burden for a long time. In fact â€Å"he was hot all over with shame and sorrow† (30) when he thought of his family having to make a living for themselves. He had always been the provider. However he was never appreciated, yet another message of Franz Kafka. No one appreciated him in his lifetime. Therefore his character was never appreciated. They were both stepped on as if they were no more significant than an insect.

The Simple Pleasures of Life Bring Happiness Essay

I am determined to be cheerful and happy in whatever situation I may find myself. For I have learned that the greater part of our misery or unhappiness is determined not by our circumstance but by our disposition. -- Martha Washington Happiness is not something ready made. It comes from your own actions. -- Dalai Lama An emotion is an intense feeling. Happiness is one of the many emotions humans experience. It may perhaps be the most important feeling a person can have and it is the one feeling everyone strives to achieve, yet strangely, for the most part, people seem to only get a glimpse of it. Pleasurable satisfaction, a state of well-being and contentment are the more outstanding elements of happiness. Happiness, known†¦show more content†¦Happiness is denoted by the way a person behaves. Usually when someone is happy it is obvious and they express this feeling outwardly, whether by their actions or verbally. The facial area is the main part through which happiness is shown. The expressions of the face such as a twinkle in the eyes when joyous, the ever-present laugh lines around the eyes, which constantly smile at you, makes the on-looker aware of a happy person. The mouth plays an important role in showing that a person is content, through both physical and verbal means. The ra diant smiles with the accompanying dimple, spreads delight and pleasure. Laughter, a universal expression of joy, travels through the air spreading cheer to all that hear it. Other verbal expressions of gaiety take the form of song singing, which has always been used over the years to express feelings of happiness, and exuberant chatter, which infuses the air with excitement and enthusiasm. Physical expressions of joy are not limited to the facial area alone. Extending to the whole body, happiness is shown through skipping, the swinging of hands, twirling, dancing and almost any rhythmic movement of the limbs. 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Waste Disposal and Recycling Where the Trash Goes

Take a look inside your garbage can.  How much garbage does your family throw away each day? Each week? Where does all of that trash go? Its tempting to think that the trash we throw away actually goes away, but we know better. Heres a look at what actually happens to all of that trash after it leaves your can. Solid Waste Fast Facts and Definitions First, the facts. Did you know that every hour, Americans throw away 2.5 million plastic bottles? Every day, each person living in the U.S. generates an average of 2 kilograms (about 4.4 pounds) of trash.   Municipal solid waste is defined as the trash produced by homes, businesses, schools, and other organizations within the community. It differs from other waste generated such as construction debris, agricultural waste, or industrial waste. We utilize three methods for dealing with all of this waste - incineration, landfills, and recycling. Incineration  is a waste treatment process that involves the burning of solid waste. Specifically, incinerators burn the organic material within the waste stream.A Landfill  is a hole in the ground designed for the burying of solid waste. Landfills are the oldest and most common method of waste treatment.Recycling  is the process of reclaiming raw materials and reusing them to create new goods. Incineration Incineration has a few advantages from an environmental perspective. Incinerators dont take up much space. Nor do they pollute groundwater. Some facilities even use the heat generated by burning waste to produce electricity. Incineration also has a number of disadvantages. They release a number of pollutants into the air, and roughly 10 percent of what is burned is left behind and must be handled in some way. Incinerators can also be expensive to build and operate. Sanitary Landfills Before the invention of the landfill, most people living in communities in Europe simply tossed their trash into the streets or outside the city gates. But somewhere around the 1800s, people began to realize that the vermin attracted by all of that trash were spreading diseases. Local communities began to dig landfills that were simply open holes in the ground where residents could dispose of their garbage. But while it was good to have the waste out of the streets, it didnt take long for town officials to realize that these  unsightly  dumps still attracted vermin. They also  leached chemicals from the waste materials, forming  pollutants  called leachate that ran off into  streams and lakes or seeped into the local groundwater supply. In 1976, the U.S. banned the use of these open dumps and set up guidelines for the creation and use of sanitary landfills. These types of landfills are designed to hold municipal solid waste as well as construction debris and agricultural waste while preventing it from polluting nearby land and water. The key features of a sanitary landfill include: Liners:  Layers of clay and plastic at the bottom and on the sides of the landfill that prevent leachate from leaking into the soil.Leachate treatment: A holding tank where leachates are collected and treated with chemicals so that they do not pollute water supplies.Monitoring wells:  Wells in close proximity to the landfill are tested regularly to ensure that pollutants are not leaching into the water.Compacted layers:  Waste is compacted in layers to prevent it from settling unevenly. Layers are lined with plastic or clean soil.Vent pipes:  These pipes allow the gases produced as waste decomposes - namely methane and carbon dioxide - to vent into the atmosphere and prevent fires and explosions. When a landfill is full, its covered with a clay cap to keep rainwater from entering. Some are reused as parks or recreation areas, but government regulations prohibit the reuse of this land for housing or agricultural purposes. Recycling Another way that solid waste is treated is by reclaiming the raw materials within the waste stream and reusing them to make new products. Recycling reduces the amount of waste that must be burned or buried. It also takes some pressure off of the environment by reducing the need for new resources, such as paper and metals. The overall process of creating a new process from a reclaimed, recycled material also uses less energy than the creation of a product using new materials. Fortunately, there are a lot of materials in the waste stream - such as oil, tires, plastic, paper, glass, batteries, and electronics - that can be recycled. Most recycled products fall within four key groups: metal, plastic, paper, and glass. Metal:  The metal in most aluminum and steel cans is 100 percent recyclable, meaning that it can be completely reused over and over again to make new cans. Yet every year, Americans throw away more than $1billion in aluminum cans. Plastic:  Plastic is made from the solid materials, or resins, left over after oil (a fossil fuel) has been refined to make gasoline. These resins are then heated and stretched or molded to make everything from bags to bottles to jugs. These plastics are easily collected from the waste stream and converted into new products. Paper:  Most paper products can only be recycled a few times as recycled paper is not as strong or sturdy as virgin materials. But  for every metric ton of paper that is recycled, 17 trees are saved from logging operations.   Glass:  Glass is one of the easiest materials to recycle and reuse because it can be melted down over and over again. It is also less expensive to make glass from recycled glass than it is to make it from new materials because the recycled glass can be melted at a lower temperature. If you arent already recycling materials before they hit your trash can, now is a good time to start. As you can see, every item that gets hauled away in your trash causes an impact on the planet.