problemas presión - compilado

Compilado Problemas Manmetros y transmisin de Presin: Cengel Munson White. Ing. Waldo Lizcano Gmez.

Conocimiento General Esta seccin contiene situaciones reales de la vida diaria en las cuales se encuentran directamente las relaciones entre la altura del fluido esttico y la presin generada por el mismo. Se sugiere esquematizarlas y solucionarlas para ser conscientes de las mismas. (Seleccionar las que se consideren pertinentes LEER y esquematizar TODAS)

Aplicaciones Bsicas Recorridos Manomtricos de uno a varios fluidos. (Seleccionar las que se consideren pertinentes LEER y esquematizar TODOS)

(Otra Respuesta: 1,34)

3-4C Se suspende un diminuto cubo de acero en agua por me-dio de un cable. Si las longitudes de los lados del cubo son muypequeas, qu comparacin habra entre las magnitudes de laspresiones sobre la parte superior, el fondo y las superficies late-rales de ese cubo?

3-5C Exprese la Ley de Pascal y d un ejemplo de aplicacinreal de ella.

3-6C Considere dos ventiladores idnticos, uno a nivel delmar y el otro en la cima de una montaa alta, que funcionan avelocidades idnticas. Qu comparacin habra entre a) losgastos volumtricos y b) los gastos de masa de estos dos venti-ladores?

3-7 Un manmetro de vaco conectado a una cmara da unalectura de 24 kPa, en un lugar donde la presin atmosfrica esde 92 kPa. Determine la presin absoluta en la cmara.

3-8I Se usa un manmetro para medir la presin del aire enun tanque. El fluido tiene una gravedad especfica de 1.25 y ladiferencia de alturas entre los dos ramos del manmetro es de28 in. La presin atmosfrica local es de 12.7 psia. Determinela presin absoluta en el tanque si el ramo del manmetro suje-to al tanque tiene el nivel del fluido a) ms alto y b) ms bajoque otro ramo.

3-9 Se presuriza el agua que est en un tanque mediante airey se mide la presin con un manmetro de fluidos mltiples,como se muestra en la figura P3-9. Determine la presinmanomtrica del aire en el tanque si h1 ! 0.2 m, h2 ! 0.3 m, yh3 ! 0.46 m. Tome las densidades del agua, el aceite y el mer-curio como 1 000 kg/m3, 850 kg/m3, y 13 600 kg/m3, respecti-vamente.

3-12 En una localidad se lee que la presin absoluta en agua auna profundidad de 5 m es de 145 kPa. Determine a) la presinatmosfrica local y b) la presin absoluta, en la misma locali-dad, a una profundidad de 5 m en un lquido cuya gravedad es-pecfica es de 0.85.3-13I Demuestre que 1 kgf/cm2 ! 14.223 psi.3-14I Un hombre que pesa 200 lb tiene un rea total de im-presin de sus pies de 72 in2. Determine la presin que estehombre ejerce sobre el suelo si a) est parado sobre los dos piesy b) est parado sobre uno de ellos.3-15 Considere una mujer de 70 kg que tiene un rea total deimpresin de sus pies de 400 cm2. Quiere caminar sobre la nie-ve, pero sta no soporta presiones mayores de 0.5 kPa. Deter-mine el tamao mnimo de los zapatos para nieve que ella nece-sita (rea de impresin por zapato) para que pueda caminarsobre la nieve sin hundirse.3-16 Un medidor de vaco est conectado a un tanque y da unalectura de 30 kPa en un lugar donde la lectura baromtrica es de755 mm Hg. Determine la presin absoluta en el tanque. TomerHg ! 13 590 kg/m3. Respuesta: 70.6 kPa3-17I Un manmetro est conectado a un tanque y da unalectura de 50 psi en un lugar donde la lectura baromtrica es de29.1 in Hg. Determine la presin absoluta en el tanque. Tome rHg ! 848.4 lbm/ft3. Respuesta: 64.29 psia3-18 Un manmetro est conectado a un tanque y da una lec-tura de 500 kPa en un lugar donde la presin atmosfrica es de94 kPa. Determine la presin absoluta en el tanque.3-19 El barmetro de un montaista da una lectura de 930mbars al principio de una caminata y de 780 mbars al final deella. Desprecie el efecto de la altitud sobre la aceleracin gravi-tacional local y determine la distancia vertical que ha escalado.Suponga una densidad promedio del aire de 1.20 kg/m3. Res-puesta: 1274 m

3-20 Se puede usar un barmetro bsico para medir la alturade un edificio. Si las lecturas baromtricas en las partes supe-rior e inferior del edificio son de 730 y 755 mm Hg, respectiva-mente, determine la altura del edificio. Suponga una densidadpromedio del aire de 1.18 kg/m3.

104PRESIN Y ESTTICA DE FLUIDOS

3-10 Determine la presin atmosfrica en un lugar donde lalectura baromtrica es de 750 mm Hg. Tome la densidad delmercurio como 13 600 kg/m3.3-11 Se lee que la presin manomtrica en un lquido a unaprofundidad de 3 m es de 28 kPa. Determine la presinmanomtrica en el mismo lquido a una profundidad de 12 m.

FIGURA P3-9

FIGURA P3-20

3-21 Resuelva el problema 3-20 usando el software deEES (o cualquier otro programa de este tipo). Im-

Cengel 03.qxd 2/22/06 5:26 AM Page 104

prima la solucin completa, inclusive los resultados numricoscon unidades apropiadas y tome la densidad del mercurio como13 600 kg/m3.3-22 Determine la presin que se ejerce sobre un buzo a 30 mpor abajo de la superficie libre del mar. Suponga una presinbaromtrica de 101 kPa y una gravedad especfica de 1.03 parael agua de mar. Respuesta: 404.0 kPa3-23I Determine la presin ejercida sobre la superficie de unsubmarino que viaja a 300 ft por abajo de la superficie libre delmar. Suponga que la presin baromtrica es de 14.7 psia y lagravedad especfica del agua de mar es 1.03.3-24 Un gas est contenido en un dispositivo de cilindro ymbolo en posicin vertical. El mbolo tiene una masa de 4 kgy un rea de la seccin transversal de 35 cm2. Un resorte com-primido arriba del mbolo ejerce una fuerza de 60 N sobre ste.Si la presin atmosfrica es de 95 kPa, determine la presin enel interior del cilindro. Respuesta: 123.4 kPa

presin. Si la lectura en el manmetro de cartula es de 80 kPa,determine la distancia entre los dos niveles del fluido en el detubo en U, si el fluido es a) mercurio (r ! 13 600 kg/m3) o b)agua (r ! 1 000 kg/m3).3-27 Vuelva a considerar el problema 3-26. Use el soft-

ware de EES (o cualquier otro programa de este ti-po) e investigue el efecto de la densidad del fluido manomtri-co, en el rango de 800 hasta 13 000 kg/m3 sobre la diferenciaen los niveles del fluido del manmetro de tubo en U. Trace lagrfica de la diferencia de alturas del fluido contra la densidady comente los resultados.3-28 Un manmetro de tubo en U que contiene aceite (r !850 kg/m3) est sujeto a un tanque lleno con aire. Si la diferen-cia del nivel del aceite entre las dos columnas es de 45 cm y lapresin atmosfrica es de 98 kPa, determine la presin absolutadel aire dentro del tanque. Respuesta: 101.75 kPa3-29 Un manmetro de mercurio (r ! 13 600 kg/m3) est co-nectado a un ducto de aire para medir la presin en el interior.La diferencia en los niveles del manmetro es de 15 mm y lapresin atmosfrica es de 100 kPa. a) Establezca un juicio conbase en la figura P3-29 y determine si la presin en el ducto es-t por arriba o por abajo de la atmosfrica. b) Determine la pre-sin absoluta en el ducto

105CAPTULO 3

3-25 Vuelva a considerar el problema 3-24. Use el soft-ware de EES (o cualquier otro programa de este ti-

po) e investigue el efecto de la fuerza del resorte, en el rango de0 hasta 500 N. Trace la grfica de la presin contra la fuerzadel resorte y discuta los resultados.3-26 Dos manmetros, uno de cartula y otro de tubo en

U, estn sujetos a un tanque de gas para medir su

FIGURA P3-24

FIGURA P3-26

FIGURA P3-29

3-30 Repita el problema 3-29 para una diferencia en los nive-les del mercurio de 30 mm.3-31 La presin sangunea suele medirse colocando alrede-dor del antebrazo de una persona, al nivel del corazn, un tuboaplanado de tela que se llena con aire y que viene equipadocon un manmetro. Con un manmetro de mercurio y un este-toscopio se miden la presin sistlica (la presin mximacuando el corazn est bombeando) y la diastlica (la presinmnima cuando el corazn est en reposo) en mm Hg. Las pre-siones sistlica y diastlica de una persona sana son de alrede-dor de 120 mm Hg y 80 mm Hg, respectivamente y se indicancomo 120/80. Exprese estas dos presiones manomtricas enkPa, psi y altura de una columna de agua (en m).3-32 La presin sangunea mxima en el antebrazo de unapersona sana es de alrededor de 120 mm Hg. Se conecta a lavena un tubo vertical abierto a la atmsfera, en el brazo de unapersona. Determine la altura hasta la que ascender la sangreen el tubo. Tome la densidad de la sangre como 1 050 kg/m3.





105CAPTULO 3




FIGURA P3-24

FIGURA P3-26

FIGURA P3-29



presin vence su peso. De esta manera, el escape peridico delvapor impide que se cree cualquier presin potencialmente peli-grosa, y mantiene a su vez la presin en el interior en un valorconstante. Determine la masa de la tapa de la vlvula de escapede una olla de presin cuya presin manomtrica de operacines de 100 kPa y que tiene un rea de seccin transversal de laabertura de 4 mm2. Suponga una presin atmosfrica de 101kPa y dibuje el diagrama de cuerpo libre de la tapa de la vlvu-la de escape. Respuesta: 40.8 g3-119 Se sujeta un tubo de vidrio a un tubo de agua, como semuestra en la figura P3-119. Si la presin del agua en el fondodel tubo es de 115 kPa y la presin atmosfrica local es de 92kPa, determine hasta qu altura se elevar el agua en el tubo, enm. Suponga g ! 9.8 m/s2 en ese lugar y tome la densidad delagua como 1 000 kg/m3.

ma abierta est inclinada 35 respecto a la horizontal, como semuestra en la figura P3-121. La densidad del lquido en el ma-nmetro es 0.81 kg/L y la distancia vertical entre los niveles defluido en las dos ramas es de 8 cm. Determine la presin mano-mtrica del aire en el ducto y la longitud de la columna de flui-do en la rama inclinada por arriba del nivel del mismo en la ra-ma vertical.3-122I Considere un tubo en U cuyas ramas estn abiertas ala atmsfera. Ahora, se vierten volmenes iguales de agua y deaceite ligero (r ! 49.3 lbm/ft3) en ramas diferentes. Una per-sona sopla por el lado del aceite hasta que la superficie de con-tacto de los dos fluidos se mueve hasta el fondo del propio tubo

115CAPTULO 3

3-120 Se encuentra un valor aproximado de la presin atmos-frica promedio sobre la Tierra, como una funcin de la altitud,por la relacin Patm ! 101.325 (1 " 0.02256z)5.256, donde Patmes la presin atmosfrica en kPa y z es la altitud en km, tomn-dose z ! 0 en el nivel del mar. Determine las presiones atmos-fricas aproximadas en Atlanta (z ! 306 m), Denver (z ! 1 610m), ciudad de Mxico (z ! 2309 m), y la punta del Monte Eve-rest (z ! 8848 m).3-121 Cuando se miden las pequeas diferencias en la pre-sin con un manmetro, con frecuencia se inclina una de sus ra-mas con el fin de mejorar la exactitud de la lectura. (La diferen-cia de presin todava es proporcional a la distancia vertical yno a la longitud real del fluido a lo largo del tubo.) Se medir lapresin del aire en un ducto circular con un manmetro cuya ra-

FIGURA P3-119 y, de este modo, los niveles de los lquidos en las dos ramasson los mismos. Si la altura del fluido en cada una de las ra-mas es de 30 in, determine la presin manomtrica que la per-sona ejerce sobre el aceite cuando sopla.3-123 Las infusiones intravenosas suelen impulsarse por gra-vedad cuando se cuelga la botella de fluido a una altura sufi-ciente para contrarrestar la presin sangunea en la vena y for-zar ese fluido hacia el interior del cuerpo. Cuanto ms alto secoloque la botella, mayor ser el gasto del fluido. a) Si se ob-serva que se equilibran entre s las presiones del fluido y la san-gunea cuando la botella est 1.2 m arriba del nivel del brazo,determine la presin sangunea manomtrica. b) Si la presinmanomtrica del fluido a nivel del brazo es de 20 kPa para te-ner un gasto suficiente, determine a qu altura debe colocarsela botella. Tome la densidad del fluido como 1 020 kg/m3.

FIGURA P3-121

FIGURA P3-122I

FIGURA P3-123


CHAPTER 3115

and prevents steam from escaping until the pressure forceovercomes the weight of the petcock. The periodic escape ofthe steam in this manner prevents any potentially dangerouspressure buildup and keeps the pressure inside at a constantvalue. Determine the mass of the petcock of a pressurecooker whose operation pressure is 100 kPa gage and has anopening cross-sectional area of 4 mm2. Assume an atmos-pheric pressure of 101 kPa, and draw the free-body diagramof the petcock. Answer: 40.8 g3119 A glass tube is attached to a water pipe, as shown inFig. P3119. If the water pressure at the bottom of the tube is115 kPa and the local atmospheric pressure is 92 kPa, deter-mine how high the water will rise in the tube, in m. Assumeg ! 9.8 m/s2 at that location and take the density of water tobe 1000 kg/m3.

cular duct is to be measured using a manometer whose openarm is inclined 35 from the horizontal, as shown in Fig.P3121. The density of the liquid in the manometer is 0.81kg/L, and the vertical distance between the fluid levels in thetwo arms of the manometer is 8 cm. Determine the gagepressure of air in the duct and the length of the fluid columnin the inclined arm above the fluid level in the vertical arm.3122E Consider a U-tube whose arms are open to theatmosphere. Now equal volumes of water and light oil (r! 49.3 lbm/ft3) are poured from different arms. A personblows from the oil side of the U-tube until the contact surfaceof the two fluids moves to the bottom of the U-tube, and thus

3120 The average atmospheric pressure on earth isapproximated as a function of altitude by the relation Patm! 101.325 (1 " 0.02256z)5.256, where Patm is the atmosphericpressure in kPa and z is the altitude in km with z ! 0 at sealevel. Determine the approximate atmospheric pressures atAtlanta (z ! 306 m), Denver (z ! 1610 m), Mexico City (z! 2309 m), and the top of Mount Everest (z ! 8848 m).3121 When measuring small pressure differences with amanometer, often one arm of the manometer is inclined toimprove the accuracy of reading. (The pressure difference isstill proportional to the vertical distance and not the actuallength of the fluid along the tube.) The air pressure in a cir-

Patm = 92 kPa

h = ?

Water

FIGURE P3119

the liquid levels in the two arms are the same. If the fluidheight in each arm is 30 in, determine the gage pressure theperson exerts on the oil by blowing.3123 Intravenous infusions are usually driven by gravityby hanging the fluid bottle at sufficient height to counteractthe blood pressure in the vein and to force the fluid into thebody. The higher the bottle is raised, the higher the flow rateof the fluid will be. (a) If it is observed that the fluid and theblood pressures balance each other when the bottle is 1.2 mabove the arm level, determine the gage pressure of theblood. (b) If the gage pressure of the fluid at the arm levelneeds to be 20 kPa for sufficient flow rate, determine howhigh the bottle must be placed. Take the density of the fluidto be 1020 kg/m3.

Duct

35

8 cmL

Air

FIGURE P3121

Air

Water 30 inOil

FIGURE P3122E

1.2 m

Patm

IV bottle

FIGURE P3123

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105CAPTULO 3




FIGURA P3-24

FIGURA P3-26

FIGURA P3-29



3-33 Considere a un hombre de 1.8 m de altura que est enposicin vertical en agua y sumergido por completo en una al-berca. Determine la diferencia entre las presiones que actan enla cabeza y en los dedos de los pies de este hombre en kPa.3-34 Considere un tubo en U cuyas ramas estn abiertas a laatmsfera. Ahora se vierte agua en una de las ramas del tubo yaceite ligero (r ! 790 kg/m3) en la otra. Una de las ramas con-tiene agua en un tramo de 70 cm de altura, en tanto que la otracontiene los dos fluidos con una proporcin de alturas aceite-agua de 6. Determine la altura de cada fluido en esa rama.

metro de tubo en U doble, como se muestra en la figura P3-36.Determine la diferencia de presin entre las dos tuberas. Tomela densidad del agua de mar en ese lugar como r ! 1035kg/m3. Puede ignorarse la columna de aire en el anlisis?3-37 Repita el problema 3-36, reemplazando el aire con aceitecuya gravedad especfica es de 0.72.3-38I Se mide la presin en una tubera de gas natural con elmanmetro que se muestra en la figura P3-38I, con una de lasramas abierta a la atmsfera en donde la presin atmosfrica lo-cal es de 14.2 psi. Determine la presin absoluta en la tubera.


h

FIGURA P3-32

70 cmAgua

Aceite

FIGURA P3-34

3-35 El elevador hidrulico en un taller de reparacin deautomviles tiene un dimetro de salida de 30 cm y se debenlevantar automviles hasta de 2 000 kg. Determine la presinmanomtrica del fluido que debe mantenerse en el depsito.3-36 Agua dulce y agua de mar fluyen en tuberas horizonta-les paralelas, las cuales estn conectadas entre s por un man-

60 cm

10 cm

70 cm

40 cmAguadulce

Aguade mar

Mercurio

Aire

FIGURA P3-36

10 pulg

6 pulg

2 pulg

25 pulg

Gasnatural

Agua

Aire

MercurioSG = 13.6

FIGURA P3-38I

3-39I Repita el problema 3-38I, ahora reemplazando el airepor aceite con una gravedad especfica de 0.69.3-40 Se mide la presin manomtrica del aire que est en el tanque, como se muestra en la figura P3-40, y resulta ser de65 kPa. Determine diferencia h en los niveles de mercurio.

Aire

30 cm

75 cm

h MercurioSG = 13.6

Agua

AceiteSG = 0.7265 kPa

FIGURA P3-40

3-41 Repita el problema 3-40, para una presin manomtricade 45 kPa.3-42 La parte superior de un tanque de agua est dividida endos compartimentos, como se muestra en la figura P3-42.Ahora se vierte un fluido con una densidad desconocida en unode los lados y el nivel del agua se eleva cierta cantidad en elotro lado para compensar el efecto que se produce. Con base enlas alturas finales de los fluidos, mostradas en la figura, deter-mine la densidad del fluido aadido. Suponga que el lquido nose mezcla con el agua.


Chapter 3 Pressure and Fluid Statics

PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.

3-15

3-31 Solution The systolic and diastolic pressures of a healthy person are given in mm of Hg. These pressures are to be expressed in kPa, psi, and meters of water column.

Assumptions Both mercury and water are incompressible substances.

Properties We take the densities of water and mercury to be 1000 kg/m3 and 13,600 kg/m3, respectively.

Analysis Using the relation ghP = for gage pressure, the high and low pressures are expressed as

kPa 10.7

kPa 16.0

=

==

=

==

2223

lowlow

2223

highhigh

N/m 1000kPa 1

m/skg 1N 1

m) )(0.08m/s )(9.81kg/m (13,600

N/m000 1kPa 1

m/skg 1N 1

m) )(0.12m/s )(9.81kg/m (13,600

ghP

ghP

Noting that 1 psi = 6.895 kPa,

psi 2.32=

=

kPa6.895psi 1

kPa) 0.(16highP and psi 1.55=

=

kPa6.895psi 1

Pa)k (10.7lowP

For a given pressure, the relation ghP = is expressed for mercury and water as waterwater ghP = and mercurymercury ghP = . Setting these two relations equal to each other and solving for water height gives

mercurywater

mercurywatermercurymercurywaterwater hhghghP

===

Therefore,

m 1.09

m 1.63

===

===

m) 08.0(kg/m 1000kg/m 600,13

m) 12.0(kg/m 1000kg/m 600,13

3

3

low mercury,water

mercurylow water,

3

3

high mercury,water

mercuryhigh water,

hh

hh

Discussion Note that measuring blood pressure with a water monometer would involve water column heights higher than the persons height, and thus it is impractical. This problem shows why mercury is a suitable fluid for blood pressure measurement devices.

3-32 Solution A vertical tube open to the atmosphere is connected to the vein in the arm of a person. The height that the blood rises in the tube is to be determined.

Assumptions 1 The density of blood is constant. 2 The gage pressure of blood is 120 mmHg.

Properties The density of blood is given to be = 1050 kg/m3. Analysis For a given gage pressure, the relation ghP = can be expressed for mercury and blood as bloodblood ghP = and mercurymercury ghP = . Setting these two relations equal to each other we get

mercurymercurybloodblood ghghP == Solving for blood height and substituting gives

m 1.55=== m) 12.0(kg/m 1050kg/m 600,13

3

3

mercuryblood

mercuryblood hh

Discussion Note that the blood can rise about one and a half meters in a tube connected to the vein. This explains why IV tubes must be placed high to force a fluid into the vein of a patient.

hBlood

h




105CAPTULO 3




FIGURA P3-24

FIGURA P3-26

FIGURA P3-29



CHAPTER 3105

numerical results with proper units, and take the density ofmercury to be 13,600 kg/m3.322 Determine the pressure exerted on a diver at 30 mbelow the free surface of the sea. Assume a barometric pres-sure of 101 kPa and a specific gravity of 1.03 for seawater.Answer: 404.0 kPa

323E Determine the pressure exerted on the surface of asubmarine cruising 300 ft below the free surface of the sea.Assume that the barometric pressure is 14.7 psia and the spe-cific gravity of seawater is 1.03.324 A gas is contained in a vertical, frictionless pistoncylinder device. The piston has a mass of 4 kg and a cross-sectional area of 35 cm2. A compressed spring above the pis-ton exerts a force of 60 N on the piston. If the atmosphericpressure is 95 kPa, determine the pressure inside the cylinder.Answer: 123.4 kPa

the pressure gage is 80 kPa, determine the distance betweenthe two fluid levels of the manometer if the fluid is (a) mer-cury (r ! 13,600 kg/m3) or (b) water (r ! 1000 kg/m3).327 Reconsider Prob. 326. Using EES (or other)

software, investigate the effect of the manometerfluid density in the range of 800 to 13,000 kg/m3 on the dif-ferential fluid height of the manometer. Plot the differentialfluid height against the density, and discuss the results.328 A manometer containing oil (r ! 850 kg/m3) isattached to a tank filled with air. If the oil-level differencebetween the two columns is 45 cm and the atmospheric pres-sure is 98 kPa, determine the absolute pressure of the air inthe tank. Answer: 101.75 kPa329 A mercury manometer (r ! 13,600 kg/m3) is con-nected to an air duct to measure the pressure inside. The dif-ference in the manometer levels is 15 mm, and the atmos-pheric pressure is 100 kPa. (a) Judging from Fig. P329,determine if the pressure in the duct is above or below theatmospheric pressure. (b) Determine the absolute pressure inthe duct.

325 Reconsider Prob. 324. Using EES (or other)software, investigate the effect of the spring

force in the range of 0 to 500 N on the pressure inside thecylinder. Plot the pressure against the spring force, and dis-cuss the results.326 Both a gage and a manometer are attached to a

gas tank to measure its pressure. If the reading on

A = 35 cm2

P = ?

Patm = 95 kPamP = 4 kg

60 N

FIGURE P324

Gas h = ?

Pg = 80 kPa

FIGURE P326

AIR

h = 15 mmP = ?

FIGURE P329

330 Repeat Prob. 329 for a differential mercury height of30 mm.331 Blood pressure is usually measured by wrapping aclosed air-filled jacket equipped with a pressure gage aroundthe upper arm of a person at the level of the heart. Using amercury manometer and a stethoscope, the systolic pressure(the maximum pressure when the heart is pumping) and thediastolic pressure (the minimum pressure when the heart isresting) are measured in mmHg. The systolic and diastolicpressures of a healthy person are about 120 mmHg and 80mmHg, respectively, and are indicated as 120/80. Expressboth of these gage pressures in kPa, psi, and meter watercolumn.332 The maximum blood pressure in the upper arm of ahealthy person is about 120 mmHg. If a vertical tube open tothe atmosphere is connected to the vein in the arm of the per-son, determine how high the blood will rise in the tube. Takethe density of the blood to be 1050 kg/m3.

cen72367_ch03.qxd 10/29/04 2:22 PM Page 105


3-48 Considere un manmetro de doble fluido sujeto a un tubo de aire, como se muestra en la figura P3-48. Si la gravedadespecfica de uno de los fluidos es 13.55, determine la grave-dad especfica del otro para la presin absoluta indicada del ai-re. Tome la presin atmosfrica como de 100 kPa. Respuesta:5.0

3-51 Dos tanques de agua estn interconectados mediante unmanmetro de mercurio con los tubos inclinados, como semuestra en la figura P3-51. Si la diferencia de presin entre losdos tanques es de 20 kPa, calcule a y u.

GE2

AireP = 76 kPa

22 cm

40 cm

GE1 = 13.55

FIGURA P3-48

3-49 Se mide la diferencia de presin entre un tubo de aceitey uno de agua con un manmetro de doble fluido, como semuestra en la figura P3-49. Para las alturas y las gravedadesespecficas dadas de los fluidos calcule la diferencia de presin!P " PB # PA.

AceiteSG = 0.88

GlicerinaSG = 1.26Agua

SG = 1.0

MercurioSG = 13.5

A

B

20 cm

60 cm

10 cm

15 cm

FIGURA P3-49

3-50 Considere el sistema que se muestra en la figura P3-50.Si un cambio de 0.7 kPa en la presin del aire causa que la in-terfaz salmuera-mercurio de la columna derecha descienda 5mm, en tanto que la presin en el tubo de la salmuera se man-tiene constante, determine la razn A2/A1.

MercurioGE = 13.56

Agua

Aire

rea, A1

rea, A2

Tubo desalmueraGE = 1.1

FIGURA P3-50

AguaA

MercurioSG = 13.6

2a26.8 cma

a

AguaB

FIGURA P3-51

3-52 Un recipiente con fluidos mltiples est conectado a untubo en U, como se muestra en la figura P3-52. Para lasgravedades especficas y las alturas de las columnas de los flui-dos dadas, determine la presin manomtrica en A. Ademsdetermine la altura de una columna de mercurio que creara lamisma presin en A. Respuestas: 0.471 kPa, 0.353 cm




3-4

3-9 Solution The pressure in a pressurized water tank is measured by a multi-fluid manometer. The gage pressure of air in the tank is to be determined.

Assumptions The air pressure in the tank is uniform (i.e., its variation with elevation is negligible due to its low density), and thus we can determine the pressure at the air-water interface.

Properties The densities of mercury, water, and oil are given to be 13,600, 1000, and 850 kg/m3, respectively.

Analysis Starting with the pressure at point 1 at the air-water interface, and moving along the tube by adding (as we go down) or subtracting (as we go up) the gh terms until we reach point 2, and setting the result equal to Patm since the tube is open to the atmosphere gives

atmPghghghP =++ 3mercury2oil1water1 Solving for P1,

3mercury2oil1wateratm1 ghghghPP += or,

)( 2oil1water3mercuryatm1 hhhgPP =

Noting that P1,gage = P1 - Patm and substituting,

kPa 56.9=

=

223

332,1

N/m 1000kPa 1

m/skg 1N 1m)] 3.0)(kg/m (850-

m) 2.0)(kg/m (1000m) 46.0)(kg/m )[(13,600m/s (9.81gageP

Discussion Note that jumping horizontally from one tube to the next and realizing that pressure remains the same in the same fluid simplifies the analysis greatly.

3-10 Solution The barometric reading at a location is given in height of mercury column. The atmospheric pressure is to be determined.

Properties The density of mercury is given to be 13,600 kg/m3.

Analysis The atmospheric pressure is determined directly from

( )( )( )3 2 2 21 N 1 kPa13,600 kg/m 9 81 m/s 0 750 m 1 kg m/s 1000 N/m100 1 kPa

atmP gh . .

.

= = = 100 kPa

Discussion We round off the final answer to three significant digits. 100 kPa is a fairly typical value of atmospheric pressure on land slightly above sea level.

Water

h1

Air 1

h3

h2



3-15





kPa 10.7

kPa 16.0

=

==

=

==

2223

lowlow

2223

highhigh

N/m 1000kPa 1

m/skg 1N 1

m) )(0.08m/s )(9.81kg/m (13,600

N/m000 1kPa 1

m/skg 1N 1

m) )(0.12m/s )(9.81kg/m (13,600

ghP

ghP


psi 2.32=

=

kPa6.895psi 1


=

kPa6.895psi 1

Pa)k (10.7lowP


mercurywater


===

Therefore,

m 1.09

m 1.63

===

===

m) 08.0(kg/m 1000kg/m 600,13

m) 12.0(kg/m 1000kg/m 600,13

3

3

low mercury,water

mercurylow water,

3

3

high mercury,water

mercuryhigh water,

hh

hh






m 1.55=== m) 12.0(kg/m 1050kg/m 600,13

3

3

mercuryblood

mercuryblood hh


hBlood

h



3-15





kPa 10.7

kPa 16.0

=

==

=

==

2223

lowlow

2223

highhigh

N/m 1000kPa 1

m/skg 1N 1

m) )(0.08m/s )(9.81kg/m (13,600

N/m000 1kPa 1

m/skg 1N 1

m) )(0.12m/s )(9.81kg/m (13,600

ghP

ghP


psi 2.32=

=

kPa6.895psi 1


=

kPa6.895psi 1

Pa)k (10.7lowP


mercurywater


===

Therefore,

m 1.09

m 1.63

===

===

m) 08.0(kg/m 1000kg/m 600,13

m) 12.0(kg/m 1000kg/m 600,13

3

3

low mercury,water

mercurylow water,

3

3

high mercury,water

mercuryhigh water,

hh

hh






m 1.55=== m) 12.0(kg/m 1050kg/m 600,13

3

3

mercuryblood

mercuryblood hh


hBlood

h



3-76

3-123 Solution It is given that an IV fluid and the blood pressures balance each other when the bottle is at a certain height, and a certain gage pressure at the arm level is needed for sufficient flow rate. The gage pressure of the blood and elevation of the bottle required to maintain flow at the desired rate are to be determined.

Assumptions 1 The IV fluid is incompressible. 2 The IV bottle is open to the atmosphere.

Properties The density of the IV fluid is given to be = 1020 kg/m3. Analysis (a) Noting that the IV fluid and the blood pressures balance each other when the bottle is 1.2 m above the arm level, the gage pressure of the blood in the arm is simply equal to the gage pressure of the IV fluid at a depth of 1.2 m,

Pak 12.0=

===

2223

bottle-armatmabsarm gage,

kN/m 1kPa 1

m/skg 0001kN 1

m) )(1.20m/s )(9.81kg/m (1020

ghPPP

(b) To provide a gage pressure of 20 kPa at the arm level, the height of the bottle from the arm level is again determined from bottle-armarm gage, ghP = to be

m 2.0=

=

=

kPa 1kN/m 1

kN 1m/skg 0001

)m/s )(9.81kg/m (1020kPa 20 22

23

arm gage,bottle-arm g

Ph

Discussion Note that the height of the reservoir can be used to control flow rates in gravity driven flows. When there is flow, the pressure drop in the tube due to friction should also be considered. This will result in raising the bottle a little higher to overcome pressure drop.

1.2 m

Patm IV

Bottle



3-76

3-123 Solution It is given that an IV fluid and the blood pressures balance each other when the bottle is at a certain height, and a certain gage pressure at the arm level is needed for sufficient flow rate. The gage pressure of the blood and elevation of the bottle required to maintain flow at the desired rate are to be determined.

Assumptions 1 The IV fluid is incompressible. 2 The IV bottle is open to the atmosphere.

Properties The density of the IV fluid is given to be = 1020 kg/m3. Analysis (a) Noting that the IV fluid and the blood pressures balance each other when the bottle is 1.2 m above the arm level, the gage pressure of the blood in the arm is simply equal to the gage pressure of the IV fluid at a depth of 1.2 m,

Pak 12.0=

===

2223

bottle-armatmabsarm gage,

kN/m 1kPa 1

m/skg 0001kN 1

m) )(1.20m/s )(9.81kg/m (1020

ghPPP

(b) To provide a gage pressure of 20 kPa at the arm level, the height of the bottle from the arm level is again determined from bottle-armarm gage, ghP = to be

m 2.0=

=

=

kPa 1kN/m 1

kN 1m/skg 0001

)m/s )(9.81kg/m (1020kPa 20 22

23

arm gage,bottle-arm g

Ph

Discussion Note that the height of the reservoir can be used to control flow rates in gravity driven flows. When there is flow, the pressure drop in the tube due to friction should also be considered. This will result in raising the bottle a little higher to overcome pressure drop.

1.2 m

Patm IV

Bottle



3-14

3-29 Solution The air pressure in a duct is measured by a mercury manometer. For a given mercury-level difference between the two columns, the absolute pressure in the duct is to be determined.

Properties The density of mercury is given to be = 13,600 kg/m3. Analysis (a) The pressure in the duct is above atmospheric pressure since the fluid column on the duct side is at a lower level.

(b) The absolute pressure in the duct is determined from

3 2 2 21 N 1 kPa(100 kPa) (13,600 kg/m )(9.81 m/s )(0.015 m)

1 kg m/s 1000 N/m102.00 kPa

atmP P gh= + = + = 102 kPa

Discussion When measuring pressures in a fluid flow, the difference between two pressures is usually desired. In this case, the difference is between the measurement point and atmospheric pressure.

3-30 Solution The air pressure in a duct is measured by a mercury manometer. For a given mercury-level difference between the two columns, the absolute pressure in the duct is to be determined.

Properties The density of mercury is given to be = 13,600 kg/m3. Analysis (a) The pressure in the duct is above atmospheric pressure since the fluid column on the duct side is at a lower level.

(b) The absolute pressure in the duct is determined from

3 2 2 21 N 1 kPa(100 kPa) (13,600 kg/m )(9.81 m/s )(0.030 m)

1 kg m/s 1000 N/m104.00 kPa

atmP P gh= + = + = 104 kPa

Discussion The final result is given to three significant digits.

Air

P

15 mm


348 Consider a double-fluid manometer attached to an airpipe shown in Fig. P348. If the specific gravity of one fluidis 13.55, determine the specific gravity of the other fluid forthe indicated absolute pressure of air. Take the atmosphericpressure to be 100 kPa. Answer: 5.0

108FLUID MECHANICS

351 Two water tanks are connected to each other througha mercury manometer with inclined tubes, as shown in Fig.P351. If the pressure difference between the two tanks is20 kPa, calculate a and u.

SG2

AirP = 76 kPa

22 cm

40 cm

SG1 = 13.55

FIGURE P348

349 The pressure difference between an oil pipe and waterpipe is measured by a double-fluid manometer, as shown inFig. P349. For the given fluid heights and specific gravities,calculate the pressure difference !P " PB # PA.

OilSG = 0.88

GlycerinSG = 1.26Water

SG = 1.0

MercurySG = 13.5

A

B

20 cm

60 cm10 cm

15 cm

FIGURE P349

350 Consider the system shown in Fig. P350. If a changeof 0.7 kPa in the pressure of air causes the brine-mercuryinterface in the right column to drop by 5 mm in the brinelevel in the right column while the pressure in the brine piperemains constant, determine the ratio of A2/A1.

MercurySG = 13.56

Water

Air

Area, A1

Area, A2

Brine pipe

SG = 1.1

FIGURE P350

Water A

MercurySG = 13.6

2a

u

26.8 cm a

aWater

B

FIGURE P351

352 A multifluid container is connected to a U-tube, asshown in Fig. P352. For the given specific gravities andfluid column heights, determine the gage pressure at A. Alsodetermine the height of a mercury column that would createthe same pressure at A. Answers: 0.471 kPa, 0.353 cm

cen72367_ch03.qxd 10/29/04 2:22 PM Page 108




h

FIGURA P3-32

70 cmAgua

Aceite

FIGURA P3-34


60 cm

10 cm

70 cm

40 cmAguadulce

Aguade mar

Mercurio

Aire

FIGURA P3-36

10 pulg

6 pulg

2 pulg

25 pulg

Gasnatural

Agua

Aire

MercurioSG = 13.6

FIGURA P3-38I


Aire

30 cm

75 cm

h MercurioSG = 13.6

Agua


FIGURA P3-40



333 Consider a 1.8-m-tall man standing vertically in waterand completely submerged in a pool. Determine the differ-ence between the pressures acting at the head and at the toesof this man, in kPa.334 Consider a U-tube whose arms are open to the atmo-sphere. Now water is poured into the U-tube from one arm,and light oil (r ! 790 kg/m3) from the other. One arm con-tains 70-cm-high water, while the other arm contains bothfluids with an oil-to-water height ratio of 6. Determine theheight of each fluid in that arm.

106FLUID MECHANICS

manometer, as shown in Fig. P336. Determine the pressuredifference between the two pipelines. Take the density of sea-water at that location to be r ! 1035 kg/m3. Can the air col-umn be ignored in the analysis?337 Repeat Prob. 336 by replacing the air with oil whosespecific gravity is 0.72.338E The pressure in a natural gas pipeline is measured bythe manometer shown in Fig. P338E with one of the armsopen to the atmosphere where the local atmospheric pressureis 14.2 psia. Determine the absolute pressure in the pipeline.

h

FIGURE P332

70 cm WaterOil

FIGURE P334335 The hydraulic lift in a car repair shop has an outputdiameter of 30 cm and is to lift cars up to 2000 kg. Deter-mine the fluid gage pressure that must be maintained in thereservoir.336 Freshwater and seawater flowing in parallel horizontalpipelines are connected to each other by a double U-tube

60 cm

10 cm

70 cm40 cmFresh-water Sea-

water

Mercury

Air

FIGURE P336

10 in

6 in

2 in

25 in

NaturalGas

Water

Air

MercurySG = 13.6

FIGURE P338E

339E Repeat Prob. 338E by replacing air by oil with aspecific gravity of 0.69.340 The gage pressure of the air in the tank shown in Fig.P340 is measured to be 65 kPa. Determine the differentialheight h of the mercury column.

Air

30 cm

75 cm

h MercurySG = 13.6

Water

OilSG = 0.7265 kPa

FIGURE P340

341 Repeat Prob. 340 for a gage pressure of 45 kPa.342 The top part of a water tank is divided into two com-partments, as shown in Fig. P342. Now a fluid with anunknown density is poured into one side, and the water levelrises a certain amount on the other side to compensate forthis effect. Based on the final fluid heights shown on the fig-ure, determine the density of the fluid added. Assume the liq-uid does not mix with water.

cen72367_ch03.qxd 10/29/04 2:22 PM Page 106

3-4C Se suspende un diminuto cubo de acero en agua por me-dio de un cable. Si las longitudes de los lados del cubo son muypequeas, qu comparacin habra entre las magnitudes de laspresiones sobre la parte superior, el fondo y las superficies late-rales de ese cubo?

3-5C Exprese la Ley de Pascal y d un ejemplo de aplicacinreal de ella.

3-6C Considere dos ventiladores idnticos, uno a nivel delmar y el otro en la cima de una montaa alta, que funcionan avelocidades idnticas. Qu comparacin habra entre a) losgastos volumtricos y b) los gastos de masa de estos dos venti-ladores?

3-7 Un manmetro de vaco conectado a una cmara da unalectura de 24 kPa, en un lugar donde la presin atmosfrica esde 92 kPa. Determine la presin absoluta en la cmara.

3-8I Se usa un manmetro para medir la presin del aire enun tanque. El fluido tiene una gravedad especfica de 1.25 y ladiferencia de alturas entre los dos ramos del manmetro es de28 in. La presin atmosfrica local es de 12.7 psia. Determinela presin absoluta en el tanque si el ramo del manmetro suje-to al tanque tiene el nivel del fluido a) ms alto y b) ms bajoque otro ramo.

3-9 Se presuriza el agua que est en un tanque mediante airey se mide la presin con un manmetro de fluidos mltiples,como se muestra en la figura P3-9. Determine la presinmanomtrica del aire en el tanque si h1 ! 0.2 m, h2 ! 0.3 m, yh3 ! 0.46 m. Tome las densidades del agua, el aceite y el mer-curio como 1 000 kg/m3, 850 kg/m3, y 13 600 kg/m3, respecti-vamente.

3-12 En una localidad se lee que la presin absoluta en agua auna profundidad de 5 m es de 145 kPa. Determine a) la presinatmosfrica local y b) la presin absoluta, en la misma locali-dad, a una profundidad de 5 m en un lquido cuya gravedad es-pecfica es de 0.85.3-13I Demuestre que 1 kgf/cm2 ! 14.223 psi.3-14I Un hombre que pesa 200 lb tiene un rea total de im-presin de sus pies de 72 in2. Determine la presin que estehombre ejerce sobre el suelo si a) est parado sobre los dos piesy b) est parado sobre uno de ellos.3-15 Considere una mujer de 70 kg que tiene un rea total deimpresin de sus pies de 400 cm2. Quiere caminar sobre la nie-ve, pero sta no soporta presiones mayores de 0.5 kPa. Deter-mine el tamao mnimo de los zapatos para nieve que ella nece-sita (rea de impresin por zapato) para que pueda caminarsobre la nieve sin hundirse.3-16 Un medidor de vaco est conectado a un tanque y da unalectura de 30 kPa en un lugar donde la lectura baromtrica es de755 mm Hg. Determine la presin absoluta en el tanque. TomerHg ! 13 590 kg/m3. Respuesta: 70.6 kPa3-17I Un manmetro est conectado a un tanque y da unalectura de 50 psi en un lugar donde la lectura baromtrica es de29.1 in Hg. Determine la presin absoluta en el tanque. Tome rHg ! 848.4 lbm/ft3. Respuesta: 64.29 psia3-18 Un manmetro est conectado a un tanque y da una lec-tura de 500 kPa en un lugar donde la presin atmosfrica es de94 kPa. Determine la presin absoluta en el tanque.3-19 El barmetro de un montaista da una lectura de 930mbars al principio de una caminata y de 780 mbars al final deella. Desprecie el efecto de la altitud sobre la aceleracin gravi-tacional local y determine la distancia vertical que ha escalado.Suponga una densidad promedio del aire de 1.20 kg/m3. Res-puesta: 1274 m

3-20 Se puede usar un barmetro bsico para medir la alturade un edificio. Si las lecturas baromtricas en las partes supe-rior e inferior del edificio son de 730 y 755 mm Hg, respectiva-mente, determine la altura del edificio. Suponga una densidadpromedio del aire de 1.18 kg/m3.


3-10 Determine la presin atmosfrica en un lugar donde lalectura baromtrica es de 750 mm Hg. Tome la densidad delmercurio como 13 600 kg/m3.3-11 Se lee que la presin manomtrica en un lquido a unaprofundidad de 3 m es de 28 kPa. Determine la presinmanomtrica en el mismo lquido a una profundidad de 12 m.

FIGURA P3-9

FIGURA P3-20

3-21 Resuelva el problema 3-20 usando el software deEES (o cualquier otro programa de este tipo). Im-


34C A tiny steel cube is suspended in water by a string. Ifthe lengths of the sides of the cube are very small, howwould you compare the magnitudes of the pressures on thetop, bottom, and side surfaces of the cube?35C Express Pascals law, and give a real-world exampleof it.36C Consider two identical fans, one at sea level and theother on top of a high mountain, running at identical speeds.How would you compare (a) the volume flow rates and (b)the mass flow rates of these two fans?37 A vacuum gage connected to a chamber reads 24 kPaat a location where the atmospheric pressure is 92 kPa.Determine the absolute pressure in the chamber.38E A manometer is used to measure the air pressure in atank. The fluid used has a specific gravity of 1.25, and thedifferential height between the two arms of the manometer is28 in. If the local atmospheric pressure is 12.7 psia, deter-mine the absolute pressure in the tank for the cases of themanometer arm with the (a) higher and (b) lower fluid levelbeing attached to the tank.39 The water in a tank is pressurized by air, and the pres-sure is measured by a multifluid manometer as shown in Fig.P39. Determine the gage pressure of air in the tank if h1! 0.2 m, h2 ! 0.3 m, and h3 ! 0.46 m. Take the densities ofwater, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and13,600 kg/m3, respectively.

104FLUID MECHANICS

312 The absolute pressure in water at a depth of 5 m isread to be 145 kPa. Determine (a) the local atmospheric pres-sure, and (b) the absolute pressure at a depth of 5 m in a liq-uid whose specific gravity is 0.85 at the same location.313E Show that 1 kgf/cm2 ! 14.223 psi.314E A 200-lb man has a total foot imprint area of 72 in2.Determine the pressure this man exerts on the ground if (a)he stands on both feet and (b) he stands on one foot.315 Consider a 70-kg woman who has a total foot imprintarea of 400 cm2. She wishes to walk on the snow, but thesnow cannot withstand pressures greater than 0.5 kPa. Deter-mine the minimum size of the snowshoes needed (imprintarea per shoe) to enable her to walk on the snow withoutsinking.316 A vacuum gage connected to a tank reads 30 kPa at alocation where the barometric reading is 755 mmHg. Determinethe absolute pressure in the tank. Take rHg ! 13,590 kg/m3.Answer: 70.6 kPa

317E A pressure gage connected to a tank reads 50 psi at alocation where the barometric reading is 29.1 inHg. Determinethe absolute pressure in the tank. Take rHg ! 848.4 lbm/ft3.Answer: 64.29 psia

318 A pressure gage connected to a tank reads 500 kPa ata location where the atmospheric pressure is 94 kPa. Deter-mine the absolute pressure in the tank.319 The barometer of a mountain hiker reads 930 mbarsat the beginning of a hiking trip and 780 mbars at the end.Neglecting the effect of altitude on local gravitational accel-eration, determine the vertical distance climbed. Assume anaverage air density of 1.20 kg/m3. Answer: 1274 m320 The basic barometer can be used to measure theheight of a building. If the barometric readings at the top andat the bottom of a building are 730 and 755 mmHg, respec-tively, determine the height of the building. Assume an aver-age air density of 1.18 kg/m3.

310 Determine the atmospheric pressure at a locationwhere the barometric reading is 750 mmHg. Take the densityof mercury to be 13,600 kg/m3.311 The gage pressure in a liquid at a depth of 3 m is readto be 28 kPa. Determine the gage pressure in the same liquidat a depth of 12 m.

h1

h2 h3

Oil

Mercury

WATER

AIR1

2

FIGURE P39

Ptop = 730 mmHg

h = ?

Pbot = 755 mmHg

FIGURE P320

321 Solve Prob. 320 using EES (or other) software.Print out the entire solution, including the

cen72367_ch03.qxd 10/29/04 2:22 PM Page 104




GE2

AireP = 76 kPa

22 cm

40 cm

GE1 = 13.55

FIGURA P3-48


AceiteSG = 0.88


SG = 1.0

MercurioSG = 13.5

A

B

20 cm

60 cm

10 cm

15 cm

FIGURA P3-49


MercurioGE = 13.56

Agua

Aire

rea, A1

rea, A2


FIGURA P3-50

AguaA

MercurioSG = 13.6

2a26.8 cma

a

AguaB

FIGURA P3-51





3-31

3-52 Solution A multi-fluid container is connected to a U-tube. For the given specific gravities and fluid column heights, the gage pressure at A and the height of a mercury column that would create the same pressure at A are to be determined.

Assumptions 1 All the liquids are incompressible. 2 The multi-fluid container is open to the atmosphere.

Properties The specific gravities are given to be 1.26 for glycerin and 0.90 for oil. We take the standard density of water to be w =1000 kg/m3, and the specific gravity of mercury to be 13.6. Analysis Starting with the atmospheric pressure on the top surface of the container and moving along the tube by adding (as we go down) or subtracting (as we go up) the gh terms until we reach point A, and setting the result equal to PA give

Awatm PghghghP =++ glyglywoiloil

Rearranging and using the definition of specific gravity,

oil glySG SG SGA atm oil w w w w gly wP P gh gh gh = + or

( )gage oil oil gly glySG SG SGA, w w wP g h h h= + Substituting,

kPa 0.471==

+=

2

232

,

kN/m471.0

m/s kg1000 kN1m)] 70.0(26.1m) 3.0(1m) 70.0(90.0)[ kg/m)(1000m/s (9.81gageAP

The equivalent mercury column height is

cm 0.353 m 00353.0 kN1

m/s kg1000)m/s (9.81) kg/m0(13.6)(100

kN/m0.471 223

2, ==

==

gP

hHg

gageAHg

Discussion Note that the high density of mercury makes it a very suitable fluid for measuring high pressures in manometers.

A

90 cm

70 cm

30 cm

15 cm

Glycerin SG=1.26

Oil SG=0.90

Water

20 cm




GE2

AireP = 76 kPa

22 cm

40 cm

GE1 = 13.55

FIGURA P3-48


AceiteSG = 0.88


SG = 1.0

MercurioSG = 13.5

A

B

20 cm

60 cm

10 cm

15 cm

FIGURA P3-49


MercurioGE = 13.56

Agua

Aire

rea, A1

rea, A2


FIGURA P3-50

AguaA

MercurioSG = 13.6

2a26.8 cma

a

AguaB

FIGURA P3-51



348 Consider a double-fluid manometer attached to an airpipe shown in Fig. P348. If the specific gravity of one fluidis 13.55, determine the specific gravity of the other fluid forthe indicated absolute pressure of air. Take the atmosphericpressure to be 100 kPa. Answer: 5.0

108FLUID MECHANICS

351 Two water tanks are connected to each other througha mercury manometer with inclined tubes, as shown in Fig.P351. If the pressure difference between the two tanks is20 kPa, calculate a and u.

SG2

AirP = 76 kPa

22 cm

40 cm

SG1 = 13.55

FIGURE P348

349 The pressure difference between an oil pipe and waterpipe is measured by a double-fluid manometer, as shown inFig. P349. For the given fluid heights and specific gravities,calculate the pressure difference !P " PB # PA.

OilSG = 0.88

GlycerinSG = 1.26Water

SG = 1.0

MercurySG = 13.5

A

B

20 cm

60 cm10 cm

15 cm

FIGURE P349

350 Consider the system shown in Fig. P350. If a changeof 0.7 kPa in the pressure of air causes the brine-mercuryinterface in the right column to drop by 5 mm in the brinelevel in the right column while the pressure in the brine piperemains constant, determine the ratio of A2/A1.

MercurySG = 13.56

Water

Air

Area, A1

Area, A2

Brine pipe

SG = 1.1

FIGURE P350

Water A

MercurySG = 13.6

2a

u

26.8 cm a

aWater

B

FIGURE P351

352 A multifluid container is connected to a U-tube, asshown in Fig. P352. For the given specific gravities andfluid column heights, determine the gage pressure at A. Alsodetermine the height of a mercury column that would createthe same pressure at A. Answers: 0.471 kPa, 0.353 cm

cen72367_ch03.qxd 10/29/04 2:22 PM Page 108


3-124 Se conecta una lnea de gasolina a un manmetro decartula a travs de un manmetro de U doble, como se muestraen la figura P3-124. Si la lectura del manmetro de cartula esde 370 kPa, determine la presin manomtrica de la lnea degasolina.

3-125 Repita el problema 3-124 para una lectura de presinmanomtrica de 240 kPa.3-126I Se conecta un tubo de agua a un manmetro de U do-ble, como se muestra en la figura P3-126I, en un lugar donde lapresin atmosfrica local es de 14.2 psia. Determine la presinabsoluta en el centro del tubo.

3-127 Se mide la presin del agua que fluye por un tubomediante la disposicin que se muestra en la figura P3-127.Para los valores dados, calcule la presin en el tubo.

FIGURA P3-124

3-128 Considere un tubo en U lleno con mercurio, excepto laparte de 18 cm de alto de arriba, como se muestra en la figuraP3-128. El dimetro de la rama derecha del tubo es D = 2 cm yel de la izquierda es el doble de se. Se vierte aceite congravedad especfica de 2.72 en la rama izquierda, forzando aque algo del mercurio de la rama izquierda entre a la derecha.Determine la cantidad mxima de aceite que se puede agregaren la rama izquierda. Respuesta: 0.256 L

FIGURA P3-126I

FIGURA P3-127

FIGURA P3-128




3-21

3-40 Solution The gage pressure of air in a pressurized water tank is measured simultaneously by both a pressure gage and a manometer. The differential height h of the mercury column is to be determined.

Assumptions The air pressure in the tank is uniform (i.e., its variation with elevation is negligible due to its low density), and thus the pressure at the air-water interface is the same as the indicated gage pressure.

Properties We take the density of water to be w =1000 kg/m3. The specific gravities of oil and mercury are given to be 0.72 and 13.6, respectively.

Analysis Starting with the pressure of air in the tank (point 1), and moving along the tube by adding (as we go down) or subtracting (as we go up) the gh terms until we reach the free surface of oil where the oil tube is exposed to the atmosphere, and setting the result equal to Patm gives

atmw PghghghP =+ oiloilHgHgw1 Rearranging,

wghghghPP wHgHgoiloilatm1 += or,

whhhgP

+= HgHg s,oiloils,w

gage,1

Substituting,

m 3.013.6m) (0.7572.0m kPa.1m/s kg1000

)m/s (9.81) kg/m(1000 kPa65

Hg2

2

23 +=

h

Solving for hHg gives hHg = 0.47 m. Therefore, the differential height of the mercury column must be 47 cm.

Discussion Double instrumentation like this allows one to verify the measurement of one of the instruments by the measurement of another instrument.

Air

Water

hoil

65 kPa

hHg hw



3-4

3-9 Solution The pressure in a pressurized water tank is measured by a multi-fluid manometer. The gage pressure of air in the tank is to be determined.

Assumptions The air pressure in the tank is uniform (i.e., its variation with elevation is negligible due to its low density), and thus we can determine the pressure at the air-water interface.

Properties The densities of mercury, water, and oil are given to be 13,600, 1000, and 850 kg/m3, respectively.

Analysis Starting with the pressure at point 1 at the air-water interface, and moving along the tube by adding (as we go down) or subtracting (as we go up) the gh terms until we reach point 2, and setting the result equal to Patm since the tube is open to the atmosphere gives

atmPghghghP =++ 3mercury2oil1water1 Solving for P1,

3mercury2oil1wateratm1 ghghghPP += or,

)( 2oil1water3mercuryatm1 hhhgPP =

Noting that P1,gage = P1 - Patm and substituting,

kPa 56.9=

=

223

332,1

N/m 1000kPa 1

m/skg 1N 1m)] 3.0)(kg/m (850-

m) 2.0)(kg/m (1000m) 46.0)(kg/m )[(13,600m/s (9.81gageP

Discussion Note that jumping horizontally from one tube to the next and realizing that pressure remains the same in the same fluid simplifies the analysis greatly.

3-10 Solution The barometric reading at a location is given in height of mercury column. The atmospheric pressure is to be determined.

Properties The density of mercury is given to be 13,600 kg/m3.

Analysis The atmospheric pressure is determined directly from

( )( )( )3 2 2 21 N 1 kPa13,600 kg/m 9 81 m/s 0 750 m 1 kg m/s 1000 N/m100 1 kPa

atmP gh . .

.

= = = 100 kPa

Discussion We round off the final answer to three significant digits. 100 kPa is a fairly typical value of atmospheric pressure on land slightly above sea level.

Water

h1

Air 1

h3

h2



3-28

3-49 Solution The pressure difference between two pipes is measured by a double-fluid manometer. For given fluid heights and specific gravities, the pressure difference between the pipes is to be calculated.

Assumptions All the liquids are incompressible.

Properties The specific gravities are given to be 13.5 for mercury, 1.26 for glycerin, and 0.88 for oil. We take the standard density of water to be w =1000 kg/m3. Analysis Starting with the pressure in the water pipe (point A) and moving along the tube by adding (as we go down) or subtracting (as we go up) the gh terms until we reach the oil pipe (point B), and setting the result equal to PB give

BwA PghghghghP =+++ oilpilglyglyHgHgw


( )Hg gly oil

Hg gly oil

SG SG SG SG

SG SG SG SGB A w w w Hg w gly w oil w

w w w Hg gly oil

P P gh gh gh gh

g h h h h

= + += + +

Substituting,

kPa 27.7==

++=

2

232

kN/m7.27

m/s kg1000 kN1m)] 1.0(88.0m) 45.0(26.1m) 2.0(5.13m) 6.0(1)[ kg/m)(1000m/s (9.81AB PP

Therefore, the pressure in the oil pipe is 27.7 kPa higher than the pressure in the water pipe.

Discussion Using a manometer between two pipes is not recommended unless the pressures in the two pipes are relatively constant. Otherwise, an over-rise of pressure in one pipe can push the manometer fluid into the other pipe, creating a short circuit.

Mercury, SG=13.56

Glycerin, SG=1.26

Oil SG=0.88

Water, SG=1.0

A

B

60 cm

20 cm

15 cm

10 cm



3-31

3-52 Solution A multi-fluid container is connected to a U-tube. For the given specific gravities and fluid column heights, the gage pressure at A and the height of a mercury column that would create the same pressure at A are to be determined.

Assumptions 1 All the liquids are incompressible. 2 The multi-fluid container is open to the atmosphere.

Properties The specific gravities are given to be 1.26 for glycerin and 0.90 for oil. We take the standard density of water to be w =1000 kg/m3, and the specific gravity of mercury to be 13.6. Analysis Starting with the atmospheric pressure on the top surface of the container and moving along the tube by adding (as we go down) or subtracting (as we go up) the gh terms until we reach point A, and setting the result equal to PA give

Awatm PghghghP =++ glyglywoiloil


oil glySG SG SGA atm oil w w w w gly wP P gh gh gh = + or

( )gage oil oil gly glySG SG SGA, w w wP g h h h= + Substituting,

kPa 0.471==

+=

2

232

,

kN/m471.0

m/s kg1000 kN1m)] 70.0(26.1m) 3.0(1m) 70.0(90.0)[ kg/m)(1000m/s (9.81gageAP

The equivalent mercury column height is

cm 0.353 m 00353.0 kN1

m/s kg1000)m/s (9.81) kg/m0(13.6)(100

kN/m0.471 223

2, ==

==

gP

hHg

gageAHg

Discussion Note that the high density of mercury makes it a very suitable fluid for measuring high pressures in manometers.

A

90 cm

70 cm

30 cm

15 cm

Glycerin SG=1.26

Oil SG=0.90

Water

20 cm


*Recordar: En un gas, debido a su baja densidad, se considera se transmite la presin uniforme a lo largo de todo el fluido sin verse afectado por los cambios de alturas. Anlisis Situaciones de anlisis en las que se aplican los conceptos de: - Presiones Iguales a Alturas iguales en el mismo

fluido esttico - Relacin de la columna de lquido con la presin. - Transmisin de presin uniforme en gases (Independiente del cambio de altura en el fluido) Se sugiere hacer TODOS.

3124 A gasoline line is connected to a pressure gagethrough a double-U manometer, as shown in Fig. P3124. Ifthe reading of the pressure gage is 370 kPa, determine thegage pressure of the gasoline line.

116FLUID MECHANICS

3125 Repeat Prob. 3124 for a pressure gage reading of240 kPa.3126E A water pipe is connected to a double-U manome-ter as shown in Fig. P31026E at a location where the localatmospheric pressure is 14.2 psia. Determine the absolutepressure at the center of the pipe.

3127 The pressure of water flowing through a pipe is mea-sured by the arrangement shown in Fig. P3127. For the val-ues given, calculate the pressure in the pipe.

45 cm

10 cm22 cm50 cm

MercurySG = 13.6

Gasoline SG = 0.70

Water

Air

Oil SG = 0.79Pgage = 370 kPa

Pipe

FIGURE P3124

3128 Consider a U-tube filled with mercury except the 18-cm-high portion at the top, as shown in Fig. P3128. Thediameter of the right arm of the U-tube is D ! 2 cm, and thediameter of the left arm is twice that. Oil with a specificgravity of 2.72 is poured into the left arm, forcing some mer-cury from the left arm into the right one. Determine the max-imum amount of oil that can be added into the left arm.Answer: 0.256 L

MercurySG = 13.6

Oil SG = 0.80

Oil SG = 0.80

Waterpipe

15 in

40 in60 in35 in

FIGURE P3126E

Water15C

Air

P0 = 30 kPa

u

Gage fluidSG = 2.4

WaterPipe

h1 = 8 cmL1 = 6 cm

L2 = 6 cmh2 = 50 cm 15C

FIGURE P3127

OilSG = 2.72

D = 2 cm2D

18 cm

MercurySG = 13.6

FIGURE P3128

cen72367_ch03.qxd 10/29/04 2:22 PM Page 116




h

FIGURA P3-32

70 cmAgua

Aceite

FIGURA P3-34


60 cm

10 cm

70 cm

40 cmAguadulce

Aguade mar

Mercurio

Aire

FIGURA P3-36

10 pulg

6 pulg

2 pulg

25 pulg

Gasnatural

Agua

Aire

MercurioSG = 13.6

FIGURA P3-38I


Aire

30 cm

75 cm

h MercurioSG = 13.6

Agua


FIGURA P3-40



333 Consider a 1.8-m-tall man standing vertically in waterand completely submerged in a pool. Determine the differ-ence between the pressures acting at the head and at the toesof this man, in kPa.334 Consider a U-tube whose arms are open to the atmo-sphere. Now water is poured into the U-tube from one arm,and light oil (r ! 790 kg/m3) from the other. One arm con-tains 70-cm-high water, while the other arm con

problemas presión - compilado

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