UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
UNIVERSIDAD NACIONAL DE INGENIERIA Facultad de Ingeniería Civil Departamento Académico de Hidráulica e Hidrología
2do LABORATORIO VISUALIZACION DE FLUJOS
Curso
: Mecánica de Fluidos I
Profesor
:
Alumnos
:
Ing.
MECÁNICA DE DE FL FLUIDOS
2DO IN INFORME DE DE LA LABORATORIO
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
UNI - 2012 -II
INTRODUCCIÓN
Muchos problemas de diseño en el área de flujo de fluidos requieren un conocimiento exacto de las distribuciones de velocidad y presión, por ejemplo, el flujo sobre superficies curvas a lo largo de las alas de un aeroplano, a través de los pasos en una bomba, en un compresor, o sobre la cresta de una compuerta. El conocimiento del flujo en dos o tres dimensiones de un fluido incompresible, no viscoso ofrece una visión más amplia de muchas situaciones reales del flujo. En esta práctica se desarrollan los principios del flujo irrotacional de un flui fluido do ideal ideal y se apli aplica can n a situ situac acio ione ness elem elemen enta tale les. s. Una Una vez vez establecidas las condiciones del flujo, se definen los conceptos de potencial de velocidad y función de corriente. Finalmente se estudian situaciones de flujo en dos dimensiones.
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
Laboratorio N°2 OBJETIVOS
MESA LAMINAR:
•
Observar el flujo uniforme
•
Obse Observ rvar ar la supe superp rpos osic ició ión n del del fluj flujo o unif unifor orme me co con n la inte intera racc cció ión n de fuen fuente tess y sumi sumide dero ross para para simu simula larr el compor comportam tamien iento to que tienen tienen los flujos flujos alrede alrededor dor de los cuerpos sólidos sumergidos.
MESA DE ANALOGÍAS DE STOKES .
• •
Visualizar mediante un colorante las líneas de corriente Visualizar el comportamiento de las líneas de corriente alrededor de perfiles.
CUBA DE REYNOLDS:
•
Ver la diferencia física existente ente un flujo laminar y un
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
FUNDAMENTO TEÓRICO DESCRIPCION DEL MOVIMIENTO DE LOS FLUIDOS En un flujo dado la determinación experimental o teórica de las prop propie ieda dade dess del del flui fluido do co como mo func funcio ione ness de la posi posició ción n y del del tiempo se considera solución del problema. En casi todos los casos el énfasis se hace sobre la distribución espacio-temporal de las propiedades fluidas. Existen dos puntos de vista posibles para analizar los problemas en mecánica: El Método descriptivo euleriano, apropiado para la Mecánica
de los los flu fluido idos, en es estte mé méto todo do calcu alcula lamo moss el ca cam mpo de presiones p(x, y, z, t) del flujo, y no los cambios de presión p(t) que experimenta una partícula al moverse.
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
En este método se identifica un punto en el espacio y podemos observar la razón de cambio de la velocidad ∂V/∂x, ∂V/∂y, ∂V/∂z, a medida que las partículas pasan por el punto, y podemos determinar si la velocidad está cambiando con el tiempo en ese punto en particular, esto es ∂V/∂t, en esta condición de análisis, en que las propiedades del flujo así como la velocidad son func funcio ione ness tant tanto o del del es espa paci cio o co como mo del del tiem tiempo po,, es esta ta regi región ón considerada se llama campo de flujo. El Método de descripción Lagrangiana, muy apropiado a la
mecáni mecánica ca de sól sólido idos, s, en este este método método nos concen concentra tramos mos en observar el movimiento de una partícula como una función del tiempo su posición s(t), velocidad V(t), y su aceleración a(t) nos permite calcular las cantidades de interés, esta tarea se vuelve abrumadora en el flujo de fluidos si el número de partículas se hace extremadamente grande.
Si las cantidades de interés no dependen del tiempo V(x, y, z) se dice que es un Flujo Estable o Estacionario. En este caso todas las cantidades de flujo en un punto dado son independientes del tiempo, es decir
Por mencionar unas cuantas
Líneas Líneas de trayector trayectoria ia, Lugar geométrico recorrido por una
partícula dada en un campo de flujo, es una historia de las posicione posicioness de una partícula partícula (una fotografía fotografía de una partícula partícula en exposiciones a intervalos regulares líne línea a inst instan antá táne nea a cuyo cuyoss punt puntos os es está tán n ocupados por todas las partículas que se originan en algún
Línea
de
traza,
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
línea a de fluj flujo o que pos osee ee las las Línea Línea de corrie corriente nte, es una líne siguientes propiedades •
El vector velocidad de cada partícula que ocupa un punto en la línea de corriente es tangente a la línea de corriente.
usarem emo os es esta ta exp expre ressión ión co como mo expr expres esió ión n V x dr = 0 usar matemática de una línea de corriente No podemos fotografiar una línea de corriente. En el caso de un flujo inestable general, las líneas de corriente pueden inferirse de foto fotogr graf afía íass de líne líneas as de tray trayect ector oria iass co cort rtas as de un gran gran número de partículas. Tubo de corriente, es un tubo cuyas paredes son líneas de
corriente, en donde el fluido no puede atravesar las paredes de un tubo de corriente. Por ejemplo una tubería es un tubo de corriente dado que sus paredes son líneas de corriente En un flujo estacionario, las líneas de trayectorias, las de traza y las de corriente coinciden. Todas las partículas que pasan por un punto siguen describiendo la misma trayectoria.
CLASIFICACION DE LOS FLUJOS Flujos uni, bi y tridimensional
En la descripción euleriana del movimiento del vector velocidad en general depende de 3 variables espaciales y del tiempo es decir V = V(x, y, z, t), un flujo así es un flujo tridimensional. El estudio de flujos planteados de esta manera es muy difícil y rebasan el alcance de un curso introductorio, aun considerando el flujo estable (no varia en el tiempo). Una aproximación es estudiar el flujo mediante un flujo bidimensional (flujo sobre una presa ancha en el intermedio se puede considerar bidimensional, por ejemplo el vector velocidad solo depende de
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
Aproximación de un flujo unidimensional y unidireccional para un ducto divergente a) Flujo bidimensional y bidirecci. Real. b) Aprox. Unidireccional y unidimensional unidimensional
Un flujo unidimens unidimensional ional, es un flujo en el que el vector velocidad solo depende de una variable espacial, tales flujos se presentan en tuberías largas y rectas o entre placas paralelas, ya que solo varia con una coordenada: u = u (y), incluso si el flujo es inestable de modo que u = u(y, t), como sería la situación durante el arranque, el flujo es unidimensional
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
afue afuera ra de un cuer cuerpo po.. Lo Loss fluj flujos os inte intern rnos os gene genera ralm lmen ente te en tuberías, es donde se observa mayor presencia de los efectos viscosos.
Las regiones de flujo con gradiente de velocidades pequeño y esfu esfuer erzo zo cort cortan ante te desp despre reci ciab able, le, como como la regi región ón cent centra rall del del cana canal, l, se deno denomi mina na fluj flujo o irro irrota taci cion onal al (par (para a refl reflej ejar ar el giro giro despreciable de la partícula) o no viscoso.
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
movi movimi mien ento to rela relati tivo vo de part partíc ícul ulas as oc ocur urri rien endo do a una una es escal cala a molecular, la viscosidad juega un papel significativo
El segundo tipo de flujo denominado flujo turbulento en donde las partículas muestran un movimiento irregular, en un intervalo muy breve de tiempo y una trayectoria errática de la partícula durante un intervalo mas largo de tiempo. Una característica part partic icul ular ar de la turb turbul ulen enci cia a es su irre irregu gula lari rida dad, d, co como mo en la acción de las olas, y no tiene una configuración observable como en los grandes torbellinos. (o flujos perturbados).
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
presión, el flujo de los gases se puede considerar también como incompresible. Aunque generalmente se debe tener en cuenta los efectos de compresibilidad del gas. El número de Mach es util util para para deci decidi dirr si un fluj flujo o de gas gas en part partic icul ular ar se pued puede e estudiar como compresible o incompresible, se define como:
Si M < 0.3 incompresible Si M > 0.3 compresible Flujos Permanentes e impermanentes
Deno Denomi mina nado doss tamb tambié ién, n, es esta taci cion onar ario io o no es esta taci cion onar ario io co con n respecto al tiempo, Los flujos estacionarios (o no estacionarios), y uniforme (o no uniforme), pueden existir independientemente uno de otro, de tal modo que cualquiera de las cuatro combinaciones es posible. El flujo de líquido a caudal constante a través de una tubería tubería recta y larga larga de diámetro constante constante es un fluj flujo o unif unifor orme me es esta taci cion onar ario io;; el fluj flujo o de líqu líquid ido o a ca caud udal al constante a través de una tubería cónica es un flujo no uniforme estacionario; mientras si hay un cambio de caudal, estos casos se co conv nvie iert rten en en fluj flujo o unif unifor orme me no es esta taci cion onar ario io y fluj flujo o no uniforme no estacionario respectivamente.
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
Incompres resibl ible e (ρ = const constant ante). e). - Incomp - No No vis visco coso so (μ = 0). 0). - Irrotacional. La hipótesis de un flujo ideal es de gran utilidad al analizar problemas que tengan grandes gastos de fluido, como en el movimiento de un aeroplano o de un submarino.
TEORIA DEL FLUJO POTENCIAL La teoría de flujo potencial pretende describir el comportamiento cinemático de los fluidos basándose en el concep concepto to matemá matemátic tico o de funció función n potenc potencial ial,, ase asegur gurand ando o que el campo de velocidades (que es un campo vectorial) del flujo de un fluido es igual al gradiente de una función potencial que determina el movimiento de dicho fluido:
Con: El sign signo o me meno noss en la ec ecua uaci ción ón de arri arriba ba es só sólo lo una una conven convenció ción n de signos signos sobre sobre la defini definició ción n de φ . φ puede puede defi defini nirs rse e sin sin el sign signo o me meno noss y la form formul ulac ació ión n que que se obtendría sería la misma. A un flui fluid do que que se co com mpor porta según egún es esta ta teo eorría se le denomina fluido potencial y a un flujo flujo potencial. Una de las primeras personas en aplicar esta formulación para el flujo de un fluido fue D'Alembert. Él estudió la
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UNIVERSIDAD NACIONAL DE INGENIERÍA
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CIVIL Dpto. de Hidráulica e Hidrología
D'Alembert definió la función de corriente, ψ , para describir la trayectoria que tuviera cada partícula de un fluido a través del tiempo. Esta función corriente está determinada, en el plano, por dos variables espaciales y para cada valor de ψ la igualdad ψ = ψ(x,y) determina un lugar geométrico llamado línea de corriente.
ENSAYOS: MESA DE FLUJO LAMINAR Este ensayo consiste en visualizar el flujo potencial haciendo uso de fuentes y sumideros en un campo de flujos paralelos (flujo uniforme)
DESCRIPCION DEL EQUIPO
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UNIVERSIDAD NACIONAL DE INGENIERÍA
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CIVIL Dpto. de Hidráulica e Hidrología
Los diferentes patrones de flujo se logran activando unos orificios ubicados en el vidrio inferior que pueden actuar ya sea como fuentes o sumideros según se utilicen las válvulas correspondientes que estén instalados conformando bancos de válvulas convenientemente identificados.
MESA DE FLUJO LAMINAR
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
MESA DE ANALOGIAS DE STOKES Este Este ensayo ensayo permit permite e visual visualiza izarr median mediante te un color colorant ante e las líne líneas as de co corrrient iente, e, adem además ás nos nos per ermi mite te vis visuali ualiza zarr el comportamiento de dichas líneas alrededor de perfiles. DESCRIPCION DEL EQUIPO •
Construido íntegramente en plexiglass, calidad cristal cero de 13 mm. de espesor unido con pegamento y tornillos que los hacen resistente a los impactos y con guarniciones de bronces cromados.
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•
Dimensiones:
Altura 170 mm. Ancho 440 mm. Largo 1150 mm. Espesor de las planchas 13 mm. Peso neto 26.6 Kg. Peso bruto 37.0 Kg
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
MESA DE ANALOGIAS DE STOKES
PROCEDIMIENTO EXPERIMENTAL El equi equip po está stá co conc nceb ebid ido o par ara a gener enerar ar fluj flujo os plan plano os bidimensionales en régimen laminar de apenas 3 mm. de espesor.
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
CUBA DE REYNOLDS Este ensayo permite ver la diferencia física existente ente un flujo laminar y un flujo turbulento. También nos permite determinar experimentalmente el Nº de Reynolds. DESCRIPCION DEL EQUIPO •
El equipo está concebido, con fines de facilidad de transporte en dos piezas (La cuba de Reynolds y la mesa de soporte)
•
La cuba tiene las siguientes dimensiones:
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
CUBA DE REYNOLDS
PROCEDIMIENTO EXPERIMENTAL El tanq tanque ue de obse observ rvac ació ión n pose posee e un sist sistem ema a disi disipa pado dorr de energía del agua de suministro de modo que el nivel sube sin
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UNIVERSIDAD NACIONAL DE INGENIERÍA
FACULTAD DE INGENIERÍA
CIVIL Dpto. de Hidráulica e Hidrología
MEDICION 1 2 3
OBSERVACIO VOLUMEN (ml) N Laminar 278 Transición 394 Turbulento 980
TIEMPO (s) 15.25 11.59 13.19
RESULTADOS El número de Reynolds queda determinada por la siguiente expresión:
Donde L y V son una longitud y velocidad características, respectivamente, y es la viscosidad cinemática. Para T=20ºc:
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CIVIL Dpto. de Hidráulica e Hidrología
De la misma manera, con la medicion 3 se llega a la conclusión de que el fluj flujo o trat tratad ado o es de tran transi sici ció ón (flu (flujo jo inte interrmit mitente ente), ), nuevamente no coincide con lo observado en el ensayo. El caso de la medición medición 2 se llega a determinar determinar que que el flujo es de transición, y coincide con lo observado en el ensayo. Sin embargo esto se da, ya que siempre existirá perturbaciones, y en tales condiciones será difícil observar un flujo como lo observado.
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UNIVERSIDAD NACIONAL DE INGENIERÍA
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CIVIL Dpto. de Hidráulica e Hidrología
En un fl flujo uni uniforme ( ), tie tiene der derivadas nul nulas, por por tan tanto, sati sa tisf sfac ace e la co cond ndic ició ión n de irro irrota taci cion onal alid idad ad y la ec ecua uaci ción ón de continuidad. Supóngase primero que el flujo es unidireccional en la dire direcc cció ión n del del eje eje x; las las func funcio ione ness pote potenc ncia iall (φ) y de corriente (ψ) resultantes son:
Integrando se obtiene:
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CIVIL Dpto. de Hidráulica e Hidrología
b) Flujo Flujo fuen fuente te
Una fuente o un sumidero de algún fluido tiene la particularidad de que el flujo sólo sale o entra, lo que implica que el vector velocidad para cada punto del flujo será colineal al origen para ambos casos. Es mucho más sencillo hallar esta función potencial usando coordenadas polares. Así:
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CIVIL Dpto. de Hidráulica e Hidrología
Donde, m es una constante y se le conoce como “intensidad” de la fuente o del sumidero. Si m es positivo se tiene una línea de
fuente bidimensional, y si m es negativo un sumidero bidi bidime mens nsio iona nal. l. Obvi Obviam amen ente te las líneas líneas de co corr rrie ient nte e (Ψ) de las
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Ocurre cuando la línea de corriente es una curva cerrada y se puede reemplazar por una superficie sólida, y tiene la forma de una elipse pero algo más achatado. Es la suma o superposición de un flujo sumidero, un flujo fuente y un flujo rectilíneo. Cuando Cuando una fuente fuente y un sumidero sumidero se alinean en la dirección dirección de una corriente uniforme, como en la figura 3a, se obtiene una forma elíptica denominada óvalo de Rankine, de longitud mayor
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