工程流體力學(xué)課后習(xí)題

工程流體力學(xué)課后習(xí)題

1.1Apressureof2?106N/m2isappliedtoamassofwaterthatinitially

filledal,000cm3volume.Estimateitsvolumeafterthepressureisapplied.

將2?106N/m2的壓強(qiáng)施加于初始體積為l,000cm3的水上，計(jì)算加壓

后水的體積。

(999.1cm3)

1.2AsshowninFig.1-9,inaheatingsystem

thereisadilatationwatertank.Thewholevolumeof

thewaterinthesystemis8m3.Thelargest

temperatureriseis500Candthecoefficientof

volumeexpansionis?v=0.00051/K,whatisthe

smallestcubageofthewaterbank?

如圖1-10所示，一采暖系統(tǒng)在頂部設(shè)一膨脹水

箱，系統(tǒng)內(nèi)的水總體積為8m3,最大溫升500C,膨

脹系數(shù)?v=0.0051/K,求該水箱的最小容積？

(0.2m3)Fig.1-9

Problem1.2

1.3Whentheincrementofpressureis50kPa,thedensityofacertain

liquidis0.02%.Findthebulkmodulusoftheliquid.

當(dāng)壓強(qiáng)增量為50kPa時(shí);某種液體的密度增加0.02%。求該液體的體

積模量。(2.5?108Pa)

1.4Fig.1-10showsthecross-sectionofanoil

tank,itsdimensionsarelengtha=0.6m,width

b=0.4m,heightH=0.5m.Thediameterofnozzle

isd=0.05m,heighth=0.08m.Oilfillstothe

upperedgeofthetank,find:

(1)Ifonlythethermalexpansion

coefficient?v=6.5?10-41/Koftheoiltankis

considered,whatisthevolumeFig.1-10

Problem1.4ofoilspilledfromthetankwhenthetemperatureofoilincreases

fromtl=-200Ctot2=200C?

(2)Ifthelinearexpansioncoefficient?l=1.2?10-51/Koftheoiltankis

considered,whatistheresultinthiscase?

圖1-10為一油箱橫截面,其尺寸為長(zhǎng)a=0.6m、寬b=0.4m、高H=0.5m,

油嘴直徑d=0.05m,高h(yuǎn)=0.08m。由裝到齊油箱的上壁，求：

(1)如果只考慮油液的熱膨脹系數(shù)?v=6.5?10-41/K時(shí)，油液從tl=-200C

上升到t2=200C時(shí)，油箱中有多少體積的油溢出？

(2)如果還考慮油箱的線膨脹系數(shù)?l=1.2?10-51/K,這時(shí)的情況如何？

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((l)2.492?10m(2)2.32?10m)

1.5Ametallicsleeveglidesdownbyself

weight,asshowninFig.1-11.Oilof

?=3?10-5m2/sand?=850kg/m3fillsbetweenthe

sleeveandspindle.Theinnerdiameterofthe

sleeveisD=102mm/theouterdiameterofthe

spindleisd=100mm,sleevelengthisL=250mm,

itsweightis100N.Findthemaximumvelocity

whenthesleeveglidesdownfreely(neglectair

resistance).

Fig.1-11Problem1.5

有一金屬套由于自重沿垂直軸下滑，如圖1-11所示。軸與套間充滿(mǎn)

了?=3?10-5m2/s、?=850kg/m3的油液。套的內(nèi)徑DM02mm,軸的外徑

d=100mm,套長(zhǎng)L=250mm,套重100N。試求套筒自由下滑時(shí)的最大速度

為多少(不計(jì)空氣阻力)。

(50m/s)

1.6Thevelocitydistributionforflowofkeroseneat200C

(?=4?10-3N?s/m2)betweentwowallsisgivenbyu=1000y(0.01-y)m/s,where

yismeasuredinmetersandthespacingbetweenthewallsis1cm.Plotthe

velocitydistributionanddeterminetheshearstressatthewalls.

在200c時(shí)，煤油(?=4?10-3N?s/m2)在兩壁面間流動(dòng)的速度分布由

u=1000y(0.01-y)m/s確定，式中y的單位為m,壁面間距為1cm。畫(huà)出速

度分布圖，并確定壁面上的剪應(yīng)力。

(4?10-2Pa)

1.7AsshowninFig.1-12,the

velocitydistributionforviscousflow

betweenstationaryplatesisgivenas

follows:

Fig.1-12Problem1.7

Ifglycerinisflowing(T=200C)andthepressuregradientdp/dxis

1.6kN/m3,whatisthevelocityandshearstressatadistanceof12mmfrom

thewallifthespacingByis5.0cm?Whataretheshearstressandvelocityat

thewall?

如圖1-12所示，兩固定平板間粘性流動(dòng)的速度分布由

給出。如果流體為甘油(T=200C)且壓強(qiáng)梯度dp/dx為1.6kN/m3,間距

By為5.0cm,距平板12mm

處的速度與剪應(yīng)力為多少？平板處的剪應(yīng)力與速度為多少？

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(ul2=0.59m/s；T12=20.8N/m；u0=0；T0=40.4N/m)

1.8Whatistheratioofthedynamicviscosityofairtothatofwaterat

standardpressureandT=200C?Whatistheratioofthekinematicviscosityof

airtowaterforthesameconditions?

在標(biāo)準(zhǔn)大氣壓、T=200C時(shí)、空氣與水的動(dòng)力粘度之比為多少？同樣條

件下它們的運(yùn)動(dòng)粘度之比又為多少？

(?A/?W=0.0018；?A/?W=15.1)

1.9ThedeviceshowninFig.

1-13consistsofadiskthatisrotated

byashaft.Thediskispositioned

veryclosetoasolidboundary.

Betweenthediskandboundaryis

viscousoil.

(1)Ifthediskisrotatedatarate

of1rad/s,whatwillbetheratioof

theshearstressintheoilatr=2cmtoFig.1-13Problem1.9

theshearstressatr=3cm?

(2)Iftherateofrotationis2rad/s,whatisthespeedofoilincontactwith

thediskatr=3cm?

(3)Iftheoilviscosityis0.01N?s/m2andthespacingyis2mm,whatis

theshearstressfortheconditionnotedin(b)?

圖1-13所示裝置由繞一根軸旋轉(zhuǎn)的圓盤(pán)構(gòu)成。圓盤(pán)放置在與固體邊界

很近的位置。圓盤(pán)與邊界間為粘性油。

(1)如果圓盤(pán)的旋轉(zhuǎn)速率為1rad/s,問(wèn)半徑為r=2cm與r=3cm處的剪

應(yīng)力之比為多少？

(2)如果旋轉(zhuǎn)速率為2rad/s,r=3cm處與

圓盤(pán)接觸的油層的速度為多少？

(3)如果油的粘度為0.01N?s/m2、且間

距y為2mm,(b)情況下的剪應(yīng)力為多少？

((1)2:3；(2)6cm/s；(3)0.3Pa)

1.10AsshowninFig.1-14,acone

rotatesarounditsverticalcenteraxisat

uniformvelocity.Thegapbetweentwocones

is?=lmm.Itfilledwithlubricantwhich

?=0.1Pa?s.IntheFigure,R=0.3m,H=0.5m,Fig.1-14Problem

1.10?=16rad/s.Whatisthemomentneededtorotatethecone?

如圖1-14所示，一圓錐體繞豎直中心軸等速旋轉(zhuǎn)，錐體與固定的外錐

體之間的隙縫?=lmm,其中充滿(mǎn)?=0.1Pa?s的潤(rùn)滑油。已知錐體頂面半徑

R=0.3m,錐體高度H=0.5m,當(dāng)旋轉(zhuǎn)角速度?=16rad/s時(shí)，，求所需要的旋

轉(zhuǎn)力矩。

(39.6N?m)

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2.1Twopressuregaugesarelocatedonthesideofatankthatisfilled

withoil.Onegaugeatanelevationof48mabovegroundlevelreads347kPa.

Anotheratelevation

2.2mreads57.5kPa.Calculatethespecificweightanddensityoftheoil.

兩個(gè)測(cè)壓計(jì)位于一充滿(mǎn)油的油箱的一側(cè)。一個(gè)測(cè)壓計(jì)高于地面的位置

高度為48m,讀數(shù)57.5kPa。另一個(gè)位置高度為2.2m,讀數(shù)347kPa。計(jì)算

油的重度與密度。(?=6.32kN/m3,?=644kg/m3)

2.2Twohemisphericalshellsareperfectlysealedtogether,andthe

internalpressureisreducedto20kPa,theinnerradiusis15cmandtheouter

radiusis15.5cm.Iftheatmosphericpressureis100kPa,whatforceis

requiredtopulltheshellsapart?

兩半球殼完美密閉在一起，內(nèi)壓減至20kPa,內(nèi)徑15cm,外徑15.5cm。

如果大氣壓強(qiáng)為100kPa,求要將半球拉開(kāi)所需的力為多少。(24.5kN)

2.3Asshowninthefigure,thereisa

quantityofoilwithdensityof800kg/m3,

andaquantityofwaterbelowitinaclosed

container.Ifhl=300mm,h2=500mm,and

h=400mmHg,findthepressureatthefree

surfaceoftheoil.

如圖所示，密閉容器中油的密度為800

kg/m3,其下方為水。如果hl=300mm,

h2=500mm,及h=400mmHg,求油的自由

表面上的壓強(qiáng)。(46.1kPa)Problem2.3

2.4Accordingtothediagram,oneendofatube

connectedtoanevacuatedcontainerandtheother

endisputintoawaterpoolwhosesurfaceis

exposedtonormalatmosphericpressure.Ifhv=2m,

whatisthepressureinsideofcontainerA?

如圖，一根管子一端與一抽空的容器相連，

另一端插入暴露于大氣的水池中。如hv=2m,容

器內(nèi)的壓強(qiáng)是多少？(81.7kPa)

P

Problem2.4

2.5Apressuregaugeisplacedundersealevel.Ifthegaugepressureata

point300mbelowthefreesurfaceoftheocean,itregisters309kPa,findthe

averagespecificweightofseawater.

一測(cè)壓計(jì)置于海平面下，如果在自由表面下300m深處測(cè)壓計(jì)的讀數(shù)

為309kPa,求海水的平均重度。(1.03kN/m3)

2.6Ifthelocalatmosphericpressureisgivenby98.1kPaabsolute,find

therelative

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pressureatpointsa,bandcinwater,(seeattachedfigure)

如果當(dāng)?shù)卮髿鈮旱慕^對(duì)壓強(qiáng)為98.1kPa,求水中a、b及c點(diǎn)的相對(duì)

壓強(qiáng)。(見(jiàn)附圖)(Pa=68.6kPa,Pb=31.3kPa,

Pc=-29.4kPa)

Problem2.6

2.7Thereisanappliedloadof5788Nonthepistonwithinacylindrical

container,inwhichisfilledwithoilandwater.Theoilcolumnheightis

hl=30cmwhenthewatercolumnh2=50cm.Thediameterofthecontaineris

giverasd=40cm.Thedensityofoilis?l=800kg/m3andthatofmercury

as?3=13600kg/m3.ComputetheheightH(cm)ofthemercurycolumninthe

U-tube.

圓柱形容器的活塞上作用一5788N的力，容器內(nèi)充有水和油。當(dāng)水柱

高h(yuǎn)2=50cm時(shí)，油柱高h(yuǎn)l=30cm。容器直徑d=40cm,油的密度？l=800kg/m3,

水銀密度?3=13600kg/m3。求U形管內(nèi)的汞柱高H(cm)。

(14.07cm)

Problem2.7

2.8Accordingtothediagram,aclosedtank

containswaterthathasarelativepressureonthe

watersurfaceofpo=-44.5kN/m2.

(1)Whatisthedistanceh?

(2)WhatisthepressureatpointMwith

0.3mbelowwatersurface?

(3)Whatisthepiezometricheadofpoint

Mrelativetodatumplanel-1?

如圖所示，一密閉容器內(nèi)盛有自由表面相對(duì)Problem2.8

壓強(qiáng)為po=-44.5kN/m2的水。

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⑴求距離h；

⑵水面下0.3m處的M點(diǎn)

的壓強(qiáng)為多少？

⑶M點(diǎn)相對(duì)于基準(zhǔn)面1-1的測(cè)壓管水頭是多少？

(h=4.54m,Pm=-41.6kPa,hm=-4.24m)

2.9AnuprightU-tubeisfixedonthehoodofa

carwhichtravelinginastraight-line,witha

constantaccelerationa=0.5m/s2.Thelength

L=500mm.Findtheheightdifferenceofthetwo

freesurfacesintheU-tube.

一豎直的U形管安裝在以勻加速度a=0.5m/s2作

直線運(yùn)行的車(chē)罩上，長(zhǎng)度L=500mm。求U形管

內(nèi)兩自由液面的高度差。

(25.5mm)

Problem2.9

2.10Accordingtothediagram,anopentank

containingwatermoveswithanacceleration

a=3.6m/s2,alongaslopeof30o.Whatisthe

inclinedangle?withthehorizontalplane

andtheequationofwaterpressurepatthe

freesurface?

如圖所示，一盛水的開(kāi)口容器以加速度

a=3.6m/s2沿30o的斜面運(yùn)動(dòng)。求自由液面與

水平面的夾角？，并寫(xiě)出水的壓強(qiáng)p的分布

方程。

(?=15o,p=pa+?gh)

Problem2.10

2.11Asshowninthefigure,agateof2m

wide,extendsoutoftheplaneofthediagram

towardthereader.Thegateispivotedathinge

H,andweighs500kg.Itscenterofgravityis

1.2mtotherightand0.9maboveH.Forwhat

valuesofwaterdepthxaboveHwillthegate

remainclosed?(Neglectfrictionatthepivot

pointandneglectthethicknessofthegate)

如圖所示，閘門(mén)寬2m,重500kg,繞錢(qián)鏈H

轉(zhuǎn)動(dòng)。閘門(mén)重心在距右端1.2m處且高于H

0.9m。問(wèn)較鏈H上方水深x為多少時(shí)，閘門(mén)

將關(guān)閉？(忽略錢(qián)鏈摩擦及閘門(mén)的厚度)(1.25m)

Problem2.11

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2.12Aflat1mhighgateishingedatpointO,

andcanrotatearoundthepoint(seeattached

diagram).TheheightofpointOisa=0.4m.

Whatisthewaterdepthwhenthegatecan

automaticallyopenaroundpointO?

一1米高的平板閘門(mén)在。點(diǎn)處用錢(qián)鏈連接，且

可繞較鏈轉(zhuǎn)動(dòng)(見(jiàn)附圖)。。點(diǎn)的高度為

水深多少時(shí)，閘門(mén)將自動(dòng)開(kāi)啟？

a=0.4mo

(h=1.33m)

Problem2.12

2.13Asshowninthediagram,aclosedtank

formingacubeishalffullofwater,find:(a)

theabsolutepressureonthebottomofthe

tank,(b)theforceexertedbythefluidsona

tankwallasafunctionofheight,(c)the

locationofthecenterofpressurebywater

onthetankwall.

如圖所示，一密閉立方體水箱裝了一半的

水，求：(a)箱底的絕對(duì)壓強(qiáng)；(b)將流體

對(duì)一側(cè)箱壁的作用力表示為高度的函數(shù)；

(c)水對(duì)箱壁的壓力中心位置。Problem2.13

(17.8kPa,F=2h(8000+0.5?gh),2/3)

2.14Acircularsluicegateofdiameterd=lmissubmergedinwateras

showninthefigure.Theslantangle?=60o,the

submergeddepthhc=4.0m,andtheweight

ofthegateFG=lkN.Determinethe

magnitudeoftheverticalforceTsoasto

makethegaterotateupwardaboutaxisa

(neglectfrictionataxisa).

如圖所示的一直徑d=lm圓形閘門(mén)淹沒(méi)于

水中。傾角?=60o,淹深hc=4.0m,閘門(mén)

重FG=lkN。求使閘門(mén)繞a軸向上轉(zhuǎn)動(dòng)的鉛

直力T的大小。(230kN)

Problem2.14

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2.15ThegateMshowninthefigure

rotatesaboutanaxisthroughN.Ifa=33m,

b=13m,d=20mandthewidth

perpendiculartotheplaneofthefigureis

3m,whattorqueappliedtotheshaft

throughNisrequiredtoholdthegate

closed?

圖示閘門(mén)M繞N軸轉(zhuǎn)動(dòng)。如a=33m、

b=13m、d=20m且與圖形垂直的寬度為

3m,要使閘門(mén)關(guān)閉，需要施加多大的力

矩在轉(zhuǎn)軸上？(666?103kN?m)

Problem2.15

2.16Findthehorizontalandverticalcomponentsoftheforceexertedby

fluidsonthefixedcircularcylindershowninthefigure,if:(l)thefluidtothe

leftofthecylinderisagasconfinedinaclosedtankatapressureof

35kPa,and(2)thefluidtotheleftofthe

cylinderiswaterwithafreesurfaceatan

elevationcoincidentwiththeuppermostpartof

thecylinder.Assuminginbothcasesthat

normalatmosphericpressureconditionsexist

totherightandtopofthecylinder.

求下述流體對(duì)圖示圓柱體所施加的水平與鉛

直方向的分力。(1)圓柱體左邊是壓強(qiáng)為

35kPa的密閉氣體；(2)圓柱體左邊是自由液

面剛好與柱頂平齊的水。設(shè)兩種情況下圓柱

體的右邊與頂部為標(biāo)準(zhǔn)大氣壓。Problem2.16

((1)Fx=130.5kN,Fz=35kN；(2)Fx=68.1kN,Fz=100.5kN)

2.17Thecrosssectionofatankisasshowninthefigure.BCisa

cylindricalsurfacewithr=6m,andh=10m.Ifthetankcontainsgasata

pressureof8kPa,determinethemagnitudeand

locationofthehorizontalandverticalforce

componentsactingonunitwidthoftankwallABC.

圖示為一容器的剖面，BC是半徑r=6m的圓柱面。

容器高h(yuǎn)=10m。如果容器裝有壓強(qiáng)為8kPa的氣體，

求作用在容器壁ABC上單位寬度的水平分力與

鉛直分力的大小與作用位置。

(Fx=80kN,Fz=48kN)Problem2.17

2.18Findtheminimumvalueofzforwhichthegateinthefigurewill

rotatecounterclockwiseifthegateis:(a)rectangular5mhighby4mwide;(b)

triangular,

4mbaseasaxis,height5m.neglectfrictioninbearings.

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Problem2.18

當(dāng)下述情況時(shí)，求使圖示閘門(mén)沿逆時(shí)針?lè)较蜣D(zhuǎn)動(dòng)的z的最小值：(a)閘

門(mén)為高5m、寬4m的矩形；(b)閘門(mén)為上底4m(轉(zhuǎn)軸)、高5m的三角形。

((a)z=307.5m,(b)305m)

2.19Acurvedsurfaceisformedasaquarterofacircularcylinderwith

R=0.75m,asshowninthefigure.Thecylindersurface

isw=3.55mwide(outoftheplaneofthe

figuretowardthereader).Water

standstilltotherightofthecurved

surfacetoadepthofH=0.65m.

Determine

(1)Themagnitudeofthe

hydrostaticforceonthesurface.

(2)Thedirectionofthehydrostaticforce.Problem2.19

一曲面由半徑為R=Q75m的四分之一的圓柱體組成，如圖所示。圓柱

面寬w=3.55m(垂直于圖形平面)。曲面右側(cè)靜水深度H=0.65m。試求：

(1)作用于曲面上靜水壓力的大小；

(2)靜水壓力的方向。

(Fx=7357N,Fz=6013N)

2.20Asshowninthediagram,thereisa

cylinderwithdiameterD=4mandlength

L=12minwater.Thedepthofwateronthe

rightandleftsideofthecylinderare4mand

2mrespectively.Findthemagnitudeand

directionoftheforceonthecylinderexertedby

water.

如圖所示，直徑D=4m、長(zhǎng)L=12mProblem2.20

的圓柱體放于水中，圓柱體左右兩邊水的深度分別為4m和2m。求

水對(duì)圓柱體的作用力的大小與方向。

(Fx=706kN,Fz=1579kN)

2.21Asshowninthefigure,determinethepivotlocationyofthe

rectangulargate,so

thatthegatewilljustopen.

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如圖所示，求閘門(mén)剛好開(kāi)啟時(shí)轉(zhuǎn)軸的位置y為多少。(y=Q44m)

Problem2.21

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Problems

3.1Atwo-dimensional,incompressibleflowfieldisgivenby

Findthevelocityandaccelerationatpoint(1,2).

二維不可壓縮流動(dòng)由確定。試求點(diǎn)(1,2)處的速度與加速度。(vx=5,

vy=?30；ax=75,ay=150)

3.2Supposevelocitydistributionofaflowfieldisgivenby

Find:(l)theexpressionoflocalacceleration;(2)theaccelerationofthe

fluidparticleatpoint(1,1)whent=0.

設(shè)流場(chǎng)的速度分布為。求：（1）當(dāng)?shù)丶铀俣鹊谋磉_(dá)式；（2）t=0時(shí)在

點(diǎn)(1,1)處流體質(zhì)點(diǎn)的加速度。

((1)?vx/?t=4,?vy/?t=O；(2)ax=3,ay=?l)

3.3Thevelocitycomponentsofaflowfieldis

Determinethestreamlineequationthroughpoint(xO,yO)att=tO.

一流場(chǎng)的速度分量為

確定在t=tO時(shí)刻通過(guò)點(diǎn)(xO,yO)的流線方程。(x2?y?Aty+C=0)

3.4Atwo-dimensionalvelocityfieldisgivenby

Whatisthestreamlineequationinthisflowfield?

已知二維速度場(chǎng)

3.5Itisknownthevelocityfieldis

Trytofindthestreamlineequationpassingthroughpoint(2,1,1).已

知速度場(chǎng)vx,求流線方程。(xl+t=cy),求通過(guò)點(diǎn)(2,1,1)的流線方程。

Page

(x=2,5-z=2z)

3.6Anoiltransportationpipeline,thevelocityatthesectionofdiameter

20cmis2m/s,whatisthevelocityandmassflowrateatthesectionof

diameter5cm?Thedensityoftheoilis850kg/m3.

有一輸油管道，在內(nèi)徑為20cm的截面上流速為2m/s,求在另一內(nèi)徑

為5cm的截面上的流速以及管內(nèi)的質(zhì)量流量。油的密度為850kg/m3。

(32m/s,53.4kg/s)

3.7Inapipelineofinnerdiameter5cm,themassflowrateofairis

0.5kg/s,pressureatacertainis5?105Pa,thetemperatureis1000C.Findthe

averageairflowvelocityonthissection.

在內(nèi)徑為5cm的管道中，流動(dòng)空氣的質(zhì)量流量為0.5kg/s,在某一截

面上壓強(qiáng)為5?105Pa,溫度為1000C。求該截面上氣流的平均速度。(54.5m/s)

3.8Thevelocitydistributionofanincompressiblefluidis

Trytodeducetheexpressionofvzbyadoptingcontinuityequation.

已知一不可壓縮流體的速度分布為

用連續(xù)方程推導(dǎo)出vz的表達(dá)式。(vz=-z(2x+2y+z+l)+c(x,y))

3.9AsshowninFig.3-25,water

flowssteadilyintoatwo-dimensional

tubeatauniformvelocityv.Sincethe

tubebendsanangleof900,velocity

distributionattheoutletbecomes

.Assumingthewidthh

ofthetubeisconstant,findconstantC.

如圖3-25所示，水以均勻速度v

定常流入一個(gè)二維通道，由于通道彎

曲了900,在出口端速度分布變?yōu)?，。?/p>

o設(shè)通道寬度h為常數(shù)，F(xiàn)ig.3-25Problem3.9

求常數(shù)C。(C=v/3)

3.10Waterisflowinginariver,as

showninFig.3-26.TwoPitottubesare

stackedandconnectedtoadifferential

manometercontainingafluidofspecific

gravity0.82.FindvAandvB.

水在河道中流動(dòng)，如圖3-26所示。

兩個(gè)重疊的皮托管與一裝有比重為

0.82Page

的流體的壓差計(jì)連接。試求vA及vB。

(vA=1.212m/s,vB=1.137m/s)Fig.3-26Problem3.10

3.11AsshowninFig.3-27,a

pipeofdiameterlmisinstalled

horizontally,ofwhichapart

bendsanangleof300.Oilof

specificgravity0.94flowsinside

thepipewithaflowrateof2m3/s.

Assumepressureinthepipeis

uniform,thegaugepressureis

75kPa,findthehorizontalforce

exertingontheelbowpipe.

直徑為lm的水平裝置的管Fig.3-27Problem3.11

道有一段300的彎管，如圖3-27

所示。管內(nèi)比重為0.94的油以2m3/s的流量流動(dòng)。設(shè)彎管內(nèi)壓強(qiáng)均勻，

表壓為75kPa,求彎管受到的水平力。(Fx=8.64kN,Fy=31.9kN)

3.12Theheightofthemercury

columninll-tubeis60mm,asshownin

Fig.3-28.Assumethediameterofthe

conduitis100mm,findthevolumeflow

rateofwaterthroughtheconduitat

sectionA.

如圖3-28所示，U形管內(nèi)汞柱高度

為60mmo設(shè)排水管的直徑為100mm,

求在截面A處通過(guò)排水管的體積流量。

(0.0314m3/s)

Fig.3-28Problem3.12

3.13Anozzleisconnectedatoneendofawaterpipe,asshowninFig.

3-29.Theoutletdiameterofthewaterpipeis

dl=50mm,andthatofthenozzleis

d2=25mm.Thenozzleandthepipe

areconnectedbyfourbolts.The

gaugepressureatinletofthenozzle

is1.96?105Pa,volumeflowrateis

0.005m3/s,trytofindthetension

appliedoneachbolt.

在水管的端部接有噴嘴，如圖

3-29所示。水管出口直徑dl=50mm,

噴嘴出口直徑d2=25mm。噴嘴與Fig.3-29Problem

3.13管之間用四個(gè)螺栓連接。噴嘴入口

處的表壓為1.96?105Pa,流量為0.005m3/s,求每個(gè)螺栓所受到的拉

力。

(86.75N)

Page

3.14Acentrifugalpumpdrawswaterfroma

well,asshowninFig.3-30.Assumetheinner

diameteroftheslouchisd=150mm,volumeflow

rateisqv=60m3/h,andthevacuumvalueatpoint

Awheretheslouchandthepumpareconnected

ispv=4?104Pa.Neglectheadloss,whatisthe

suctionheightHsofthepump?

離心式水泵從井里抽水，如圖3-30所示。

設(shè)吸水管內(nèi)徑d=150mm,流量為qv=60m3/h,

吸水管與水泵接頭處A點(diǎn)的真空值為

pv=4?104Pao不計(jì)水頭損失，求水泵的吸水高

度Hso(4.03m)

Fig.3-30Problem3.14

3.15AsshowninFig.3-31,anoilof

specificgravity0.83rushestowardsa

verticalplateatvelocityv0=20m/s,findthe

forceneededtosupporttheplate.

如圖3-31所示，相對(duì)密度為0.83

的油水平射向直立的平板，已知v0=20m/s,

求支撐平板所需的力Fo(652N)

Fig.3-31Problem3.15

3.16AhorizontaljetflowwithvolumeflowrateqvOrushestowardsan

inclinedplateatvelocityvO,asshowninFig.3-32.Neglecttheeffectsof

gravityandimpactlossofthefluid,thepressureandvelocity

ofthejetflowremainthesameafterit

splitsintotwodistributaries.Findthe

formulasofthetwodistributaries'flow

rateqvlandqv2,andtheforceactingonthe

plate.

如圖3-32所示，一股速度為v0、體

積流量為qvO的水平射流，射到傾斜的光

滑平板上。忽略流體撞擊的損失和重力

的影響，射流的壓強(qiáng)與速度在分流后也

沒(méi)有變化，求沿板面向兩側(cè)的分流流量

qvl與qv2的表達(dá)式，以及流體對(duì)板面的

作用力。Fig.3-32

Problem3.16

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0

3.17AsshowninFig.3-33,acart

carryinganinclinedsmoothplatemoves

atvelocityvagainstajetflow,the

velocity,flowrateanddensityofthejet

flowarevO,qv,and?respectively.Ignore

thefrictionbetweenthecartandground,

whatisthepowerWneededfordriving

thecart?

如圖3-33所示，帶有傾斜光滑平

板的小車(chē)逆著射流方向以速度v運(yùn)動(dòng)，

射流的速度和流量分別為vO和qv,射

流的密度為?，不計(jì)小車(chē)與地面的摩擦

力，求推動(dòng)小車(chē)所需的功率W。Fig.3-33Problem

3.17

0

3.18Acrookedpipestretchesoutfroma

bigcontainer,asshowninFig.3-34,thediameterofthepipeis150mm,

andthatofthenozzleis50mm.Ifneglecttheheadloss,trytofindtheflow

rateofthepipe,andpressuresatpointA,B,C,andD.

從一大容器引出一彎曲的管道如圖

3-34所示，管徑為150mm,噴嘴直徑為

50mm,不計(jì)水頭損失，求管的輸水流量，以及A、B、C、D各點(diǎn)的壓

強(qiáng)。

(0,0174m3/s,68.2、-0.47、-20.1、38.8kPa)Fig.3-34Problem

3.18

3.19AVenturiflowmeterisinstalledbias

asshowninFig.3-35,diameterattheinletisdl,anddiameteratthe

throatisd2,trytodeduceitsflowrateexpression.

文丘里管流量計(jì)傾斜安裝如圖3-35所

示，入口直徑為dl,喉部直徑為d2。試推導(dǎo)出其流量的計(jì)算公式。

(

)

Page

F

ig.3-35Problem3.19

3.20AsshowninFig.3-36,waterflowsout

fromabigcontainerandintoanothersmall

container.Supposethatthefreesurface

elevationsofthetwocontainerskeepunchanged,

findthevelocityveattheoutlet.

如圖3-36所示，大容器中的水由小孔流

出，流入另一盛水小容器。若兩容器的水面

高度保持不變，求小孔流出的速度ve

0Fig.3-36Problem3.20

3.21APitottubeissubmergedinaprismaticpipeline,whichisshownas

inFig.3-37.Ifthedensityofthefluidinsidethe

pipelineis?,andthatintheU-tubeisthe

elevationdifferenceintheU-tubeis?h,findthe

velocityinthepipeline.

一皮托管置于等截面的管路中，如圖

3-37所示。U形管內(nèi)流若管內(nèi)流體的密度為？，

體的密度為？'，液面高度差為?h,求管流速

度。0

Fig.3-37Problem3.21

3.22AsshowninFig.3-38,transportwater

fromcontainerAtocontainerBbymeansofa

siphon.Ifthevolumeflowrateis100m3/h,

Hl=3m,z=6m,andneglecttheheadloss,find

thediameterofthesiphonandthevacuumvalue

intheupperpartofthesiphon.

如圖3-35所示，利用虹吸管把水從容

器A引到容器Bo已知體積流量為100m3/h,

Hl=3m,z=6m,不計(jì)水頭損失，求虹吸管的

管徑，以及上端管中的真空值。Fig.3-38Problem

3.22(0.068m,5.89?104Pa)

3.23AwatersprinklerisshownasinFig.3-39,thelengthsofitstwoarms

arell=lmand12=1.5mrespectively,ifthe

diameterofthenozzleisd=25mm,donot

takethefrictionalmomentintoaccount,find

therotatingspeedn.

灑水器如圖3-39所示，兩臂長(zhǎng)分別

為ll=lm、I2=1.5m,若噴口直徑d=25mm

，Page

每個(gè)噴口的流量qv=3L/s,不計(jì)摩擦阻力矩，求轉(zhuǎn)速n。(44.9r/min)

Fig.3-39Problem3.23

3.24AsymmetricalsprinklerisshownasinFig.3-40.Therotatingradius

isR=200mm,?=450,thenozzlediameteris

d=8mm,thetotalflowrateisqv=0.563L/s,

ifthefrictionalmomentis0.2N?m,findthe

rotatingspeedn.Andwhatisthe

magnitudeofthemomentneededtohold

thesprinkleratrestwhileitisin

operation?

對(duì)稱(chēng)灑水器如圖3-40所示。旋轉(zhuǎn)半徑Fig.3-40Problem

3.24R=200mm,?=450,噴口直徑d=8mm,總

流量qv=0.563L/s,若已知摩擦阻力矩為0.2N?m,求轉(zhuǎn)速n。若噴水時(shí)

不讓其旋轉(zhuǎn)，應(yīng)受到多大的力矩？(103r/min,0.441N?m)

Page

Problems

1.1Thevelocityfieldofarotationalflowisgivenby

Findtheaverageangularrotatingvelocityatpoint(2,2,2).

已知有旋流動(dòng)的速度場(chǎng)為

求在點(diǎn)(2,2,2)處平均旋轉(zhuǎn)角速度。(?x=0.5,?y=?2,?z=?0.5)

1.2Determinewhetherthefollowingflowfieldisrotationalflowor

irrotationalflow.

確定下列流場(chǎng)是有旋運(yùn)動(dòng)還是無(wú)旋運(yùn)動(dòng)：

(1)

(2)

((1)有旋，(2)無(wú)旋)

4.3Thevelocitydistributionofaflowfieldisdescribedby

v=x2yi?xy2j

Istheflowirrotational?

流場(chǎng)的速度分布為

v=x2yi?xy2j

該流動(dòng)是否無(wú)旋？(有旋)

4.4Foracertainincompressible,two-dimensionalflowfieldthevelocity

componentintheydirectionisgivenby

vy=x2+2xy

Determinethevelocitycomponentinthexdirectionsothatthe

continuityequationissatisfied.

某一不可壓縮平面流場(chǎng)在y方向的速度分量為

vy=x2+2xy

確定x方向的速度分量，以滿(mǎn)足連續(xù)性方程。(vx=?x2+C)

4.5Foracertainincompressibleflowfielditissuggestedthatthevelocity

componentsaregivenbytheequations

vx=x2yvy=4y3zvz=2z

Isthisaphysicallypossibleflowfield?

某一不可壓縮流場(chǎng)流場(chǎng)的速度分量由下列方程給出

Pagevvxx

vx=xyvy=4yzvz=2z

試問(wèn)該流場(chǎng)在物理上是否可能？(不可能)

4.6Itisknownthatstreamlinesareconcentriccircles,andvelocity

distributionis已知流線為同心圓族，其速度分布為

Findthevelocitycirculationalongcirclex2+y2=R2,wheretheradiusesof

thecircleare

(1)R=3；(2)R=5；(3)R=10respectively.

求沿圓周x2+y2=R2的速度環(huán)量，其中圓的半徑R分別為(1)R=3；(2)

R=5；(3)R=10o

((1)18?/5,(2)10?,⑶10?)

4.7Assumethereisavortexof?=?0locatingatpoint(1,0),andanother

vortexof?="?0atpoint(-1,0).Findthevelocitycirculationalongthefollowing

routes:

(1)x2+y2=4；

(2)(x-l)2+y2=l；

(3)Squareofx=?2,y=?2；

(4)Squareofx=?0.5,y=?0.5.

設(shè)在點(diǎn)(1,0)處置有?=?0的旋渦，在點(diǎn)卜1,0)處置有?=-?0的旋渦。試

求下列路線的速度環(huán)量：

(1)x2+y2=4；

(2)(x-l)2+y2=l；

(3)x=?2,y=?2的方形框；

(4)x=?0.5,y=?0.5的方形框。((1)0,(2)?0,(3)0,(4)0)

4.8Forincompressiblefluid,determineifthereexiststreamfunctionsin

thefollowingflowfields,whereKisaconstant.

對(duì)于不可壓縮流體,試確定下列流場(chǎng)是否存在流函數(shù)？式中K為常數(shù)。

(1)vx=Ksin(xy),vy=-Ksin(xy)

(2)vx=Kln(xy),vy=-Ky/x((1)不存在，⑵存在)

4.9Demonstratethefollowingplanarflowofanincompressiblefluid

satisfiescontinuityequation,andisapotentialflow,thenfindthe

potentialfunction.

Page

滿(mǎn)足連續(xù)性方程，是有勢(shì)流動(dòng)，并求勢(shì)函數(shù)。(？=x2/2+x2y?y2/2?y3/3)

4.10Avelocityfieldisgivenbyvx=x2y+y2,vy=x2?xy2,vz=0,questions：

(1)Ifthereexiststreamfunctionandpotentialfunction?

(2)Findtheexpressionsofstreamfunctionandpotentialfunctionifthey

exist,給定速度場(chǎng)vx=x2y+y2,vy=x2?xy2,vz=0,問(wèn)：

(1)是否存在流函數(shù)和勢(shì)函數(shù)？

(2)如果存在，求其具體表達(dá)式。

((1)存在流函數(shù)，不存在勢(shì)函數(shù)；(2)?=x2y2/2+y2/3?x2/3)

4.11Thevelocitypotentialinacertainflowfiledis

?=4xy

Determinethecorrespondingstreamfunction.

某流場(chǎng)的速度勢(shì)為

?=4xy

求相應(yīng)的流函數(shù)。(？=2x2?2y2)

4.12Thevelocitypotentialforanincompressible,planarflowis

?=x2?y2+x

Finditsstreamfunction.

不可壓縮流體平面流動(dòng)的勢(shì)函數(shù)為

?=x2?y2+x

試求流函數(shù)。(?=2xy+y)

4.13Thestreamfunctionforanincompressible,planarflowis

?=xy+2x?3y

Findthepotentialfunction.

不可壓縮流體平面流動(dòng)的流函數(shù)為

?=xy+2x?3y

試求勢(shì)函數(shù)。(?=(x2?y2)/2?3x?2y)

4.14Demonstratethefollowingtwoflowfieldsareidentical:

(1)thepotentialfunctionis?=x2+x?y2

(2)thestreamfunctionis?=2xy+y

證明下列兩個(gè)流場(chǎng)是相同的。

⑴勢(shì)函數(shù)？=x2+x?y2

(2)流函數(shù)?=2xy+y

4.15

Giventhevelocitydistributionofaflowfieldas

vx=Ax+By

vy=Cx+Dy

Pagevx

Iftheflowisincompressibleandirrotational,find

(1)WhatrelationshipshouldcoefficientsB、C、Dsatisfy?

(2)Thestreamfunctionoftheflowfield.

已知流場(chǎng)的速度分布為

vx=Ax+By

vy=Cx+Dy

若流體不可壓縮，且流動(dòng)無(wú)旋，試問(wèn)

(1)系數(shù)A、B、C、D應(yīng)滿(mǎn)足怎樣的關(guān)系？

⑵求流場(chǎng)的流函數(shù)。

(⑴A=?D,B=C；(2)?=B(y2?x2)/2+Axy)

4.16Thereisafixedpointvortexofcirculation?anddistanceatoa

stationarywall.Findthevelocitypoten