The document discusses the equation of continuity, which is a mathematical expression of the principle of mass conservation. It states that for incompressible steady flow through a pipe of varying cross-sectional area, the mass flow rate entering must equal the mass flow rate exiting. It defines volumetric flow rate and mass flow rate, and provides the equations relating flow rate, velocity, density and cross-sectional area. It also lists the assumptions and characteristics of the equation, and provides examples of its application to fluid dynamics problems.
Laminar Flow in pipes and Anuli Newtonian FluidsUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process.
Pipe Flow Friction factor in fluid mechanicsUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process. ,education ,chemical engineerin ,chemical engineering ,fluid mechanics ,heat transfer ,chemical process principles ,macdonald ,kfc ,mazeo ,chemicals ,engineers ,cv formatin ,law ,laptop.
Laminar Flow in pipes and Anuli Newtonian FluidsUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process.
Pipe Flow Friction factor in fluid mechanicsUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process. ,education ,chemical engineerin ,chemical engineering ,fluid mechanics ,heat transfer ,chemical process principles ,macdonald ,kfc ,mazeo ,chemicals ,engineers ,cv formatin ,law ,laptop.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Diapositivas ecuación de continuidad
1. UNIVERSIDAD DE LAS FUERZAS
ARMADAS ESPE-L
FISÍCA II
ECUACION DE CONTINUIDAD
DOCENTE:
Ing. Proaño Molina Diego Msc.
INTEGRANTES :
Stalin Valverde
Erik Calvopiña
Ruth Solís
2. ¿Qué es la ecuación de la continuidad?
La ecuación de continuidad es simplemente una expresión matemática del principio de
conservación de la masa. Para un volumen de control que tiene una sola entrada y una única
salida, el principio de conservación de la masa establece que, para el flujo en estado
estacionario, la tasa de flujo másico hacia el volumen debe ser igual a la tasa de flujo másico
hacia afuera.
𝑀𝑑𝑒𝑛𝑡𝑟𝑜 = 𝑀𝑓𝑢𝑒𝑟𝑎
𝑄1 = 𝑄2 → 𝑆1 ∗ 𝑉1 = 𝑆2 ∗ 𝑉2
Donde:
S es la superficie de las secciones transversales de los puntos 1 y 2 del conducto.
V es la velocidad del flujo en los puntos 1 y 2 de la tubería.
3. ECUACION DE CONTINUIDAD
Para explicar mejor esta ley definiremos lo que es el caudal.
CAUDAL: Cantidad de sustancia que atraviesa una sección determinada en la unidad de
tiempo, se representa por la letra Q.
El caudal puede ser de dos tipos:
- Caudal másico.
- Caudal volumétrico.
CAUDAL MASICO: Es la cantidad de masa de una sustancia que atraviesa una determinada
sección en un segundo. Sus unidades son: (Kg/s).
𝑄 = 𝜌 ∗ 𝑉 ∗ 𝐴
CAUDAL VOLUMETRICO: Es la cantidad de volumen de una sustancia que atraviesa una
determinada sección en un segundo, y sus unidades son: (m³ / s).
𝑄 = 𝑉 ∗ 𝐴
4. CARACTERISTICAS DE LA ECUACION DE CONTINUIDAD
La ecuación de continuidad parte de las bases ideales
siguientes:
1.- El fluido es incompresible.
2.- La temperatura del fluido no cambia.
3.- El flujo es continuo, es decir su velocidad y presión no dependen
del tiempo.
4.- El flujo es laminar. No turbulento.
5.- No existe rotación dentro de la masa del fluido, es un flujo
irrotacional.
6.- No existen pérdidas por rozamiento en el fluido, es decir no hay
viscosidad.
5. ECUACION DE CONTINUIDAD PARA UN
FLUIDO INCOMPRESIBLE
Si no hay pérdidas de fluido dentro de un tubo uniforme, la masa de fluido que entra es igual
a la que sale en un tubo en un tiempo.
∆𝑚1 = 𝜌1∆𝑉1 = 𝜌1𝐴1∆𝑥1= 𝜌1𝐴1𝑉1∆𝑡
∆𝑚2 = 𝜌2∆𝑉2 = 𝜌2𝐴2∆𝑥2= 𝜌2𝐴2𝑉2∆𝑡
Donde 𝐴1 y 𝐴2 son las áreas transversales del tubo en la entrada y salida. Puesto que la
masase conserva (∆𝑚1 = ∆𝑚2) se tiene, este resultado se denomina ecuación de
continuidad.
𝜌1𝐴1𝑉1∆𝑡 = 𝜌2𝐴2𝑉2∆𝑡
Si un fluido es incompresible, su densidad ρ es constante, así que
𝐴1𝑉1 = 𝐴2𝑉2
6. Donde dicho resultado se conoce como la ecuación de continuidad un fluido ideal. Por otro
lado la cantidad Av se conoce como caudal promedio Q y representa el volumen del fluido
que pasa por un punto en el tubo por unidad de tiempo.
Nota: la definición formal para el caudal es
𝑄 =
𝑑𝑉
𝑑𝑡
7. VARIABLES ASOCIADAS A UN FLUIDO
1. Flujo laminar:
Se llama flujo laminar al tipo de movimiento de un fluido cuando éste es perfectamente
ordenado, estratificado, suave, de manera que el fluido se mueve en láminas paralelas sin
entremezclarse. Las capas adyacentes del fluido se deslizan suavemente entre sí. El
mecanismo de transporte es exclusivamente molecular.
8. 2. Flujo turbulento:
Flujo turbulento es aquel en el que las partículas de fluido tienen desplazamiento en sentidos
diferentes al del movimiento principal del fluido.
En el flujo turbulento, a diferencia del laminar, la diferencia de velocidad entre láminas de
fluido es elevada y, a causa del rozamiento, al deslizarse una lámina con un cuerpo rompe la
estructura laminar adquiriendo movimientos y formando remolinos aleatorios.
9. 3. Contados Venturi
Un fluido incompresible de densidad ρ fluye por un canal de diámetro variable Debido a que
la sección transversal decrece de Ao (mayor) a A (menor), la velocidad del fluido incrementa
de νo a ν. La tasa de flujo R (volumen/tiempo) del fluido por el tubo, está relacionada con la
velocidad del fluido (distancia/tiempo) y el área de la sección transversal del tubo. El flujo
debe ser constante sobre la longitud del tubo.
Esta relación es conocida como la ecuación de continuidad, y es expresada como:
𝑅 = 𝐴0𝑉0 = 𝐴 ∗ 𝑉
Como el fluido viaja de la parte ancha del tubo a la constricción, la velocidad
Incrementa de νo a ν, y la presión decrece de Po a P. Si la presión cambia, será debido solo al
cambio de velocidad. La ecuación de Bernoulli puede ser simplificada a
𝑃1 +
1
2
𝜌𝑉1 = 𝑃2 +
1
2
𝜌𝑉2
𝑣1 =
2 𝑃2 − 𝑃1
𝜌
1 −
𝐴1
𝐴2
2
=
2 ∗ 𝑔 ∗ ℎ
𝐴1
𝐴2
2
− 1
10. 4. Ecuación de Bernoulli
Al moverse el elemento entre las dos configuraciones ni se acumula, ni se genera, masa
durante su traslado entre esos dos puntos. Debido al cambio en la sección transversal del tubo
de flujo, al pasar el sistema de la configuración (a) a la configuración (b), su anchura cambia
de a. El trabajo hecho por la fuerza neta, sobre el sistema, para trasladar el elemento de masa
desde la posición a la posición es
𝑊 = 𝑃1𝐴1∆𝑋1 − 𝑃2𝐴2∆𝑋2 − ∆𝑚𝑔 𝑦2 − 𝑦1
Donde se ha tomado que en las configuraciones (a) y (b) el volumen es constante, debido a las
propiedades de incompresibilidad del fluido; es decir
𝐴1∆𝑋1= 𝐴2∆𝑋2= ∆𝑉
𝑤 =
𝑃2−𝑃1 ∆𝑚
𝜌
− ∆𝑚𝑔 𝑦2 − 𝑦1 (1)
11. Al pasar el elemento de fluido de la configuración (a) a la configuración (b) su cambio de
energía cinética es:
∆𝐾 =
∆𝑚
2
𝑣2
2
− 𝑣1
2
(2)
En donde 𝑣1 es la velocidad del elemento de fluido en la configuración (a), y 𝑣2 es su
velocidad en la configuración (b).
Ahora haciendo uso del teorema del trabajo y la energía cinética
𝑊 = ∆𝐾 (3)
Sustituyendo las Ecs. (1) y (2) en la Ec. (3) se obtiene
∆𝑚
𝜌
𝑃1 − 𝑃2 − ∆𝑚𝑔 𝑦2 − 𝑦1 =
∆𝑚
2
𝑣2
2
− 𝑣1
2
Reordenando términos se llega a
𝑃1 +
1
2
𝜌𝑉1
2
+ 𝜌𝑔𝑦1 = 𝑃2 +
1
2
𝜌𝑉2
2
+ 𝜌𝑔𝑦2
Para cualquier configuración arbitraria del elemento de fluido de masa ∆𝑚 a lo largo del tubo
de flujo se tiene
𝑃1 +
1
2
𝜌𝑉1
2
+ 𝜌𝑔ℎ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑒
12. 5. Ecuación de Torricelli
Mediante la aplicación del teorema de Bernoulli calcularemos la velocidad de salida del
líquido de un recipiente.
Vamos a plantear la ecuación de Bernoulli en dos puntos extremos del sistema, el punto A en
el borde superior del líquido y el punto B en el orificio de salida del recipiente. La ecuación
de Bernoulli para este caso es
1
2
𝛿𝑉𝐴
2
+ 𝛿𝑔𝑦𝐴 + 𝑃𝐴 =
1
2
𝛿𝑉𝐵
2
+ 𝛿𝑔𝑦𝐵 + 𝑃𝐵Los valores correspondientes al punto B son
𝑃𝐵, que, igual que en el caso anterior es la presión atmosférica, la altura 𝑌𝐵 que es dato
del problema y la velocidad vB que es nuestra incógnita. Finalmente reemplazando y
resolviendo queda
𝑉𝐵 = 2𝑔 𝑌
𝐴 − 𝑌𝐵
13. 6. Velocidad de salida de un liquido
La velocidad de salida es igual a la adquirida por cualquier cuerpo al caer libremente a una
altura h (teorema de Torricelli).
Este teorema es también aplicable a cualquier orificio en las paredes a profundidad h. ρ es la
densidad del fluido que sale por el orificio.
𝑉2 = 2𝑔ℎ
14. Estructura de la pregunta Tipo 1 2
Enunciado:
Si 2200
𝐿
𝑚𝑖𝑛
de agua fluyen a través de una tubería de 300 mm de diámetro se
reduce a 200 mm.
Conector:
Calcule la velocidad promedio del flujo en cada tubería.
Opciones 1. 𝑉1 = 0.619
𝑚
𝑠𝑒𝑔
𝑉2 = 3.1688
𝑚
𝑠𝑒𝑔
2. 𝑉1 = 0.719
𝑚
𝑠𝑒𝑔
𝑉2 = 2.1688
𝑚
𝑠𝑒𝑔
3. 𝑉1 = 0.519
𝑚
𝑠𝑒𝑔
𝑉2 = 1.1688
𝑚
𝑠𝑒𝑔
4. 𝑉1 = 0.59
𝑚
𝑠𝑒𝑔
𝑉2 = 1.18
𝑚
𝑠𝑒𝑔
REACTIVOS RESUELTOS
17. Estructura de la pregunta Tipo 1 2
Enunciado:
Una tubería de 180 mm de diámetro transporta agua a razón de 0.09
𝑚3
𝑠𝑒𝑔
La
tubería se ramifica en dos de menor diámetro tal y como la muestra la figura. Si la
velocidad en el conducto de 60mm de diámetro es 15
𝑚
𝑠𝑒𝑔
Conector:
Calcule la velocidad en la tubería de 120 mm de diámetro
Opciones 1. . 𝑉2 = 4.323
𝑚
𝑠𝑒𝑔
2. 𝑉2 = 5.2088
𝑚
𝑠𝑒𝑔
3. 𝑉2 = 4.2088
𝑚
𝑠𝑒𝑔
4. 𝑉2 = 3.2088
𝑚
𝑠𝑒𝑔
20. Estructura de la pregunta Tipo 1 2
Enunciado:
Por el extremo de un tubo horizontal de 2 cm de diámetro ingresa agua a una
velocidad de 0,2 m/s.
Conector:
¿: ¿A qué velocidad saldrá el agua si el diámetro del extremo de salida es de 1 cm.
Opciones 1.
2.
3
4.
REACTIVO PROPUESTO
21. Bibliografía:
1. CONNOR, N. (2008), “¿Qué es la ecuación de continuidad? definición”, en Thermal
Engineering, <<https://www.thermal-engineering.org/es/que-es-la-ecuacion-de-continuidad-
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3. Inacap. “Ecuación de Continuidad, de Bernoulli y sus aplicaciones”. Área de
construcción, Mecánica de fluidos, Universidad tecnológica de chile instituto profesional,
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Ecuacion-de-Continuidad.pdf>>, [Consulta: 11 de febrero 2021].
4. Sabelotodo. (2007). Ecuación de continuidad de fluidos. Física: <<
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5. Daniilopez10, (2011). Ecuación de la continuidad. En wordpress:
<<https://daniilopez10.wordpress.com/primer-corte/ecuacion-de-la-continuidad/>>,
[Consulta: 11 de febrero 2021].
6. TORRES, J. “7. Dinámica de fluidos. <https://www.ugr.es/~jtorres/t7.pdf> [Consulta: 11
de febrero 2021].
22. 7. GONZALES, M. (2011). ”Flujo laminar y flujo turbulento” en la Guía, 6 de Junio.
<https://fisica.laguia2000.com/dinamica-clasica/flujo-laminar-y-flujo-turbulento> [Consulta:
11 de febrero 2021].
8. Rivas Acosta, I. (2001). Tubos Venturi, Dall y Tobera.
9. Mott, R. L. (2006). Mecanica de Fluidos 6/e. Pearson educación
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Wilmington, 1995).
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de Newton. Lat. Am. J. Phys. Educ, 6(4), 585-588.
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13. Hernández, Ángel, E. (2014). ”Hidronímica” en la Universidad autónoma del estado de
hidalgo, Noviembre 2014.
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(11) November 2003, pp. 1204-1207