熒煬 1

 

尺傘褽捄唲竻卄找侜

 

л肫ˍ疺腕鮈竻頖 (Fluid Mechanics) 鉬蝜邯﹥Ⅰ序啋皊墅閫卄序埱ョ藤褶涷я珒橶          ˍ疺腕鮈竻鉖龔慞苤縓 ÷蠅婄勻眓咘佬銧橧狳牷÷羶譜贅△憼嘎夭 侜恁÷轔瓚&菔狶  煬魬芷蓍÷蠅婄勻眓咘ˍ疺腕鮈竻и絮嵑 ̄蝘 鉬蝜菟嘎骳 &÷蹴勿郯芧煬鋡竻墊З揤慞倓竊﹛疰芧媄恁扥卄岐Э弅 鏡Щ×滿恥竻阹傚嬝疺腕 &匹畛佴袨卄完堌萃嫗瓚侜恁÷蹴<餔ョ挹股暽卄箋6卄坎竻頖

 

1.1    侜恁÷璽竻ˍ疺腕鮈竻頖

л肫ˍ疺腕鮈竻頖襯倞痋奿煤擏卄找侜煬駖挬萃ы湧慞倰挬萃ы錘銧 塾頩尤祂竻頖韁涷轅匹畛佴砡寡嫣錘之煬魨瓚煬餑掑й賸境廜頩之煬 庠閫岍瓴匹畛鉬蝜並唭塾暽卄找侜煬駖挬萃ы錘銧歖鷓佬靾餑梠蹙魬嫖禳 漺邃僩涷塹擉凅芷太я眝挬萃ы錘銧憿挹卄找侜煬魰酷涷繒廙襲匹畛佴砡寡   銧暽樿穡嘟畛疰項挬煜擏銧歖避駖轅÷蹴酷涷繒廙襲匹畛棋 卄找侜煬頞谹я砫餌嗾ョ迕斯捚靾鳼湧塾暽銧殧∟卄抉侜Й堙疚埭 弝佸挹㏒珓園皊牷匹畛棋僩涷 ̄郱荂挹㏒珓塾暽轅方珗樿臏牷鉡郯侲煬繙×漱й蟈揤庍褽棆喬慞橶  ∠迗邑谹銧橶骳㏒珓塾暽鉬蝜卄找侜煬駖挬萃ы錘銧歖芾嫩椎藉×

 

1.1.1 岏碧菠煉均畟檠麩竻卄扭Y 卄抉侜 慞苤縓

巠疰植癟萃е蹙魬 3 妎珗 尤 卄扭Y (Solid) 卄抉侜 (Liquid) 慞苤縓 (Gas) 庠閫卄抉侜ш瓚㏒珓佬鈱梒 ̄Щ я 卄找侜 (Fluid) 匹畛廘△骳岔倓я狶妎珗苠竻巠疰佬苂湆煬隤駖序骳扭瓚愨妥盓棻棺倓я狶煻鉣≦ ˍ骳リ谹 卄扭Y岐晡駖序骳岔倓я狶煻鉣≦饕樿 卄抉侜Щ晡駖序骳岔倓я狶煻鉣≦鰻牷H暽 抌Л㏒珓轅芾竻я狶譜侞骳把醜禳媗轄◎涷忐       蓍煉孝癟×飾橏 ㏒珓轅愨妥盓棻棺倓я狶煻鉣≦饕樿 卄抉侜Щ涫癟棉妥棷譜侞骳把醜禳媗轄﹜紩 慞凊癟棉妥棷譜侞骳把醜禳媗轅轄◎涷忐氬飾竻屣蝘

鉡郯芴唻疰勞妎珗苠竻卄扭Y扭瓚卄找侜蓍鄋唭ˍ 例◆耽√譎觴擋暽曼飾竻巠疰煬魰√捶牷愨孝骳扳 鄋頩  愨妥盓 (Tension) 愨彤挬 (Compression) 慞凊癟鄔谹 (Shear)      佬噥я砫避駖卄扭Y找湧識筵癟鄔谹麂冓√插疰鉬纓餔嘔棡廕睿鎔狶募Ы 抌Л卄找侜佬靾駔畛疰亂挹愨抉抿芧銧歖鷓靾駍骳佬轅Ⅰ珒鈮骳蒮∠菸 鉧證冓避駖銧橨挹愨抉抿芧慞橶卄找侜     佬遄埭÷蹴酷涷繒贊酵骳弄譙侲√插疰頖韁揤煬 ÷繩涷ˍ骳Я骳卄找侜靾駔畛疰亂挹愨妥盓銧暽桄 蓍煉均畟檠麩竻頖戀畛疰亂挹愨妥盓銧暻橏抉驗★樿 鉧證釓涫癟謫毯佴涷藉譜侞骳把醜禳媗  廘餑掑骳菔蚆牷併孜谹鉌避芧я牶竻頖饜錘弅轄繹識筵癟棉找湧 庠閫鉬蝜岏遽菠曼飾竻煉序埱ョ藤褶涷膋殪朝煤駍 隞

 

1.1.2 酵牷砥疰喬蜆藪肫菠菔矷囌疺腕鮈竻頖

                   漺繚桎ы遘藤薊珛唲竻卄找侜佬廕閫迋﹤餌 卄找侜煬銵棹挬銧殧瓚        卄找侜煬 ●迕港錘銧 ˍ骳リ谹

卄找侜煬銵棹挬銧 (Compressible Fluid) 佹畟勣 卄找侜疚埭煬餑梬譎轄腕鉬纓餔嫗酷找鄘牷鉡郯芩掑й蟈揤鉬纓餔嫗酷 佸谹ˍ骳ы湧я牶竻頖韁涷●迕港湧 鉬蝜卄找侜煬餑掑骳匹畛佴砡寡嫩酷涷繒廙襲隞鉡郯秅й蟈揤鉬纓餔 漺罈△唲竻頖驍譜鈶溯淶 ㏒珓蓍蜆藪肫菠 庠閫㏒珓佬轅尺傘褽捄婄餌嫣輓畛*卄均縓 P"/T 鉡郯 P 匹畛棋 " 酵埡珛 T 阹傚濟轂

 

佸谹弅轄繹太嘎喃湧例             =    

 

 


萃е鎔狶煬 1.1 寣褖來嘎嘈墅閫轅酵埡珛 560 m3 轅阹傚濟轂 30°C 轅匹畛棋 100 kN/m2 園珛樿均疰墓寣褖來嘎凳淶隞疑癡崳嘛猁塵來嘎嘈墅閫 庠閫轅酵埡珛 150 m3 慞凅呯阹傚濟轂卄扭㏒岍畟蓍檠疚凈錘遄埳 50°C 豆太嘎傚狺й蟈揤煬魬芷疑癡嵎㏒囧蚢Л塹

 

л試照             例﹋薄疰                             =      

廗馱骳               =      

 

                   匹畛棋                    P2      =       355.34       kN/m2

 


卄找侜煬銵棹挬靾鳼湧 (Incompressible Fluid) 佹畟勣 卄找侜煬餑捸疰     鉬纓餔嫗酷坎竻酵埡珛羅樿臏牷鉡郯芩掑й蟈揤鉬纓餔嫗酷 庠閫弅轄繹煬閮凈錘太墅孜盓÷蹴酷涷繒廙襲卄宏譎轄腕銧 佸谹ˍ骳ы湧я牶竻頖韁涷●迕港錘銧 尤 卄找侜煬餑掑й賸境廜頩之煬駎譙侲酷涷繒廙襲鉧梒抉驗★樿轉避駖匹畛棋嫩酷涷繒廙襲 漺繚桎ы辣谹я牶竻鉖龔鉬蝜        卄找侜煬銵棹挬靾鳼湧

 

                嗶”牷塾暽覲廷畛疰嗤箄坎竻頖饜湧菸豁恁伈苠竻÷蠅婄勻眓咘 棋完淶

卄找侜蓍侃給牷疰 (Ideal Fluid) 佹畟勣 卄找侜煬鳼錘轅匹畛佴袨 匹畛萋尬堌慞苤棹挬靾鳼湧 併找錘轅愨抉彶織煉嘔倓я狶÷蹴勿郯芧煬 匹畛棋飾竻卄找侜佬 ̄郱茧桄妝牷×獐堌煬鋡竻頖戀捘槽怀湧鉌趨 靾駍骳卄找侜佬鄐纔駖僩涷佸谹苂湆×熒涷∠菸

卄找侜並唭 (Real Fluid or Practical Fluid) 佹畟勣 卄找侜煬餑掑堻岏碧菠菸襄藤薊珛婛瓚遄埭H暽並唭菸豁恁伈苤疰膋擏珗 鄋頩 匹畛萋尬堌慞苳й購畛疰嗚飽疰 迕斯捚銧

 

1.2 轂菠慞倓寡Ъ

酵埡珜煉均畟檠噸涷膋殫嘎啋牷囌疺腕嚌梠蹙 2 疚埭 尤 酵埡珜忺ˍ疰 (Scalar) 慞郅譎轄喪リ鉞芤 (Vector) 漺罈譎轄傘遄籤鏈佬轅鄔懊苠境毯瑁珗桄 鄋頩 鉲籤 豳戀疰 慞郋竊壯珗 庠閫酵埡珜忺ˍ疰鴩倇畛疰亂Щ×嫣湧漺繕癟湧Ъл試÷藤Щ×嫘嫩肴抉籠仇埽蜆藪棍 抌Л酵埡珜鉲戈腴鏈佬轅煤擏Ⅰ珒慞郱埱煉 鄋頩 愨 匹畛鈱褘 匹畛鈱閫慞凄醜褸萃 ÷藤Щ卄宏譎轄喪リ鉞芤鴩凅芷侜恁÷藤Щ廕箋籠仇埽靾鳼湧 廘閮豻餌僱樿彤疿捔&遄陰憵肴        鉲戈腴鏈 (åFx = 0, åFy = 0, åFz = 0)

 

1.2.1 轂菠煉均畟檠

轂菠 (Dimensions) 尤 庍倩恁伈鼒涷膋歖餌僱捚廗飾竻佴駍 漺繚桎ы頗箄找湧鉬蝜 2 酵冓懋 尤       

1.) 轂菠趕謊椑 (Primary Dimensions) 尤 轂菠萃ш酵煬鳼錘H暽×瑭埽奜郯寞 銧殧∟ 豳戀疰 (mass, M) 匹畛觴 (length, L) 鉲籤 (time, T) 慞凊癟 (Force, F) 漺臏埽堇偭濟轂卄岔郕熊骳扳 銧殧妠找①蓍菸岔狶煬 1.1

 

 

 

菸證孚涷 1.1 轂菠

 

酵埡珜                                                                              轂菠

匹畛觴                                                                              L

 

 鉲籤                                                                                     T

 

                                                                                     M

 

                                                                                       F

 

 

2.) 轂菠煥菠臍椑 (Secondary Dimensions) 尤 轂菠煬餑淀溴蕾竻轂菠趕謊椑奜鎔狶寥苂 2 鈮芩H暽隞 庠閫佬慲揮菸薄 墊觴賸譙虮薄疰菔狶 鄋頩 匹畛鈱褘 (Velocity, V) 佹畟勣 譜覆煉孝駖鉲籤轅轂菠鉬蝜 LT 1 鉬蝜菟 漺臏埽埸媯堎濟轂卄宏譎轄陬骳扳 塾暽 銧殧妠找①蓍 菸證孚涷 1.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

菸證孚涷 1.2 轂菠煥菠臍椑唲竻酵埡珜菔狶 煬魰<餔ヨ樿扼嘎啋牷囌疺腕鮈竻頖

 

酵埡珜

庍倩恁伈

轂菠

譜犖閟怀

譜犖迕均馨

 ±竊壯珗

P

ML2T-3

N.m/s (watt)

ft-lb/s

 佴駍轍癟鄔谹

t

ML-1T-2

N/m2 (Pa)

lb/ft2

 匹畛棋

p

ML-1T-2

N/m2 (Pa)

lb/ft2,psi

 匹畛勢

f

T-1

s-1

s-1

 匹畛鈱褘

u, v, w

LT-1

m/s

ft/s

 匹畛鈱褘鄋唭遽

w

T-1

s-1

s-1

 匹畛鈱閫

a

LT-2

m/s2

ft/s2

 匹畛佴砡寡

r

ML-3

kg/m3

slug/ft3

 匹畛佴袨 (庍褽棆喬)

m

ML-1T-1

kg/m.s

lb/ft.s

 匹畛佴袨乳寢

n

L2T-1

m2/s

ft2/s

 

W

ML2T-2

N.m

ft-lb

 寥蚎塾”豻憶

g

ML-2T-2

N/m3

lb/ft3

 酵埡珛

"

L3

m3

ft3

嬝悝忌

E

ML2T-2

N.m

ft-lb

 擋暽煬

A

L2

m2

ft2

 煻棻竊吨й謝袨侁嵙

E

ML-1T-2

N/m2 (Pa)

lb/ft2, psi

 煻鉡僱

M

ML2T-2

N.m

ft-lb

 煻鉡僱鴗й醜抿駖

I

L4

m4

ft4

 煻鉡僱捘

 -

ML2T-2

N.m

ft-lb

 

F

MLT-2

N

ft

 愨孝盓樊

s

MT-2

N/m

lb/ft

 愨宋埭 (torque)

G

ML2T-2

N.m

ft-lb

 迕腕牷疰頖鑠肴宏譎轄腕

Q

L3T-1

m3/s (cms)

ft3/s (cfs)

 阹傚濟轂庍褽棆喬

T

 -

Kelvin (°K)

Rankine (°R)

佹畟鉖華     1 ° K       273 + 1 °C               1 ° C    =     32 °F

                     1 °R       460 + 1 °F 

1.2.2 佴駍邃嘔郕箋蟋譎﹥瓚迕均馨

佴駍邃劂悃佩碧嘗 2 譜犖 尤 譜犖迕均馨 (English system) 慞倓寡Ъ譜犖弅ˍ (International system, SI) 佸谹譜犖閟怀 庠閫憾硃畛狳牷譜犖佴駍轉蟋譎 (Metric system) 棋扭妠扼僱疰狶煬 1.3

 

菸證孚涷 1.3  佴駍瞽竻譜犖菔狶

 

酵埡珜       轂菠

譜犖閟怀

譜犖迕均馨

譜犖鉡腕唌

佴駍

庍倩恁伈

佴駍

庍倩恁伈

佴駍

庍倩恁伈

  匹畛觴      L         

鉡腕

m

ft

鉡腕

m

     鉲籤          T

л境煬

s

л境煬

s

л境煬

s

               M

√牄 ̄捘

kg

岒栴

slug

√牄 ̄捘

kg

                F

墊З揤

N

銓僑

lb

√牄 ̄捘(愨)

kgf

 

佹畟鉖華              1.) 例﹋薄疰      W            =            

                                      鉡郯   g                         迕腕砫鏡抉塽駖夾牷愨把寥褻駍坎竻牄         m/sec2

                                                g0                       迕腕皊寡ロ鈱婰蟋暽               9.81 kg-m / kgf sec2

                                                                W            =            

                                     棋完桄嘈寡Ъ卄 W 併抉餌 kgf

                                2.)           1 slug     =    1

 

鉧郯秅й購迡ョ蓍÷蹴G繒鉣◢蚢Л轄⊥ 佸谹寥苂 蓍煉序埱ョ藤薇盓膋樿恁卍墓佴橏佴駍 棋扭妠扼僱疰狶煬 1.4

 

 

 

 

 

 

菸證孚涷 1.4 迕﹎羅蚎寥皊寡Ъ (Prefixes)

 

溜棋疚

太墓佴橏

迕﹎藕駖

太侳珗

1018

exa

E

閟‵

1015

peta

P

鉧菩

1012

tera

T

鈮譜

109

giga

G

√-

106

mega

M

鉡﹛

103

kilo

k

√牄

102

hecto

h

閜﹦

10

deca

da

鉥夫

10-1

deci

d

鉥帟

10-2

centi

c

鄎僱

10-3

milli

m

轂齬

10-6

micro

m

靾滮

10-9

nano

n

境漡

10-12

pico

p

戰滮

10-15

femto

f

鉯鎂

10-18

atto

a

慴菊

 

 

 

 

 

 

 

 

1.3    墊觴褶涷遄涷藉a竻慞釓珛簸珗卄坎竻頖

卄找侜 鉬蝜臥駖煬魬芷弝佸挹鈱梒﹜竻鉖龔慞苤縓 卄找侜鉬蝜巠疰煬餑旍蚢Л豳聾孚涷廜頩芧 廘餑桼棡鏡狶靾魨寡嗶 鉧證虼冓酷涷繒廙襲隞菸謄棡鏡狶卄尾猁塵煬餖竻識 菸謠珛簸珗卄坎竻頖饜湧寣 匹畛佴砡寡 寥蚎塾”豻懊 匹畛嗉ロ來鉧眓 酵埡珛癡豻懊 匹畛佴袨 匹畛豐森贅頩 匹畛萋尬堌 慞苳й蟈揤颮 鉬蝜菟 棋完桄僎盓徶橶骳檠疚郱涷襖岔挹塾暽佬轅Ⅰ珒煬魨窗菔狶×飽蝯畛 弅轄繹煬閮苤譜例繕捚佸谹供斯捚銧歖萇謊猁塵煬餖竻識犒桄 煤擏卄抉侜ш瓚㏒珓菔狶轅匹畛弅轄繹蓍÷繹骳繚芫匹畛棋嘈譙虮閫溴握й蟈揤例”奡佴紬找鄞悝邯”奡佴紬找湧 慞冓塽駖夾牷卄找侜蟬覬識熊捚遉橏×疑棡鏡狶卄尾猁塵煬餖竻識 棋完桄麂盓弅轄繹膋暺栴購閫卄找侜隞菸褶駖慞冓抎僩狶煬銴毯孔樲З骳扳 銧殪朝庈棗

 

                1.3.1 匹畛佴砡寡 寥蚎塾”豻懊 匹畛嗉ロ來鉧眓慞郅譎轄腕來鉧眓

                                匹畛佴砡寡 (Density, r)

鉬蝜迕腕疺駍嘔倓я狶酵埡珜豳籠竻巠疰菔豖墅閫湧Ъ酵埡珛 棋完桄嘈寡Ъ卄坐й賸境廜頩併抉餌嘈寡Ъ卄岐Э弅繭駖酵埡珛  鄋頩  kg / m3    slug / ft3

                               

匹畛佴砡寡                                    r             =                                                                     (1.1.a)

 

鉆郯竻例                                               m            =                                                                     (1.1.b)

 

棋完桄                                                    r             =                     =                                   (1.1.c)

 

鉡郯         r                        匹畛佴砡寡

                                m                       豳戀疰

                                "                       酵埡珛

                                W                       寥蚎塾

g                         匹畛鈱閫鉆郯竻例﹥癟漡橧嗉ロ卄把禳

g  =  9.81 m/s2 =  32.20  ft/sec2

 

 

佴駍瞽竻匹畛佴砡寡嘟畛疰傷砪湧例

 

譜犖迕均馨

譜犖 SI

(m)

酵埡珛 (")

匹畛佴砡寡 (r)

Slug

ft3

Slug/ft3

kg

m3

kg/m3

 

漺繚涷      r  卄完橔 煬駖堻侚椑 4 °C  =   1.937   slug/ft3   =   1000    kg/m3    =    1   g/cm3

 

                                寥蚎塾”豻懊 (Specific weight, g)

鉬蝜迕腕疺駍嘔倓я狶寥蚎塾﹜竻巠疰菔豖墅閫佴駍罈譎轄腕 佴駍瞽竻寥蚎塾”豻懊虼盓鉬蝜佴駍瞽竻寥蚎塾△駖酵埡珛 鄋頩 N/m3 慞 lb/ft3

 

寥蚎塾”豻懊                                    g              =                                                                     (1.2.a)

 

鉆郯竻例                                               W            =             mg                                                          (1.2.b)

 

                                                        r             =                                                                     (1.2.c)

 

棋完桄                                                    g     =        =      =    rg                                         (1.2.d)

                    

 佴駍瞽竻寥蚎塾”豻懊倇畛疰傷砪湧例

 

譜犖迕均馨

譜犖 SI

寥蚎塾 (W)

酵埡珛 (")

寥蚎塾”豻懊 (g)

lb

ft3

lb/ft3

N

m3

N/m3

 

         g     卄完橔 煬駖堻侚椑 4 °C   =   62.4   lb/ft3     =   9.81   kN/m3

 

匹畛嗉ロ來鉧眓 (Specific gravity, S)

鉬蝜迕腕疺駍嘔倓я狶寥蚎塾﹜竻巠疰菔芧橔佴恁卄完橔煬餑梬譎轄腕鈮骳× 佸谹迕腕疺駍飾竻寥蚎塾”豻懊迮駖寥蚎塾”豻懊 佸谹 匹畛佴砡寡飾竻巠疰菔秅й    佴砡寡飾竻寥 庠閫匹畛嗉ロ來鉧眓鉬蝜萃ч籠煬鳼錘轅轂菠棋廷薄疰

 

匹畛嗉ロ來鉧眓                                 S             =                              酵埡珛蹴瑁牷揤     (1.3.a)

 

鉆郯竻例                                               r             =                =         =      (1.3.b)

 

棋完桄                                                    S             =               =                               (1.3.c)

                        

                                酵埡珛癡豻懊  (Specific volume, "S)

鉬蝜迕腕疺駍嘔倓я狶酵埡珛繭駖佴紬弄寡Ъ豳戀疰佸谹酵埡珛癡豻懊 尤虮駍飽竊滯竻匹畛佴砡寡 塾頩尤  

 

酵埡珛癡豻懊        "S         =                  =                     =                                   (1.4)

 

 


萃е鎔狶煬 1.2      園珗橔蹊鼓墊森墅閫轅酵埡珛 200 蘸◇疿∫諷 慞倓塾 10520 銓僑 豆太嘎傚狺骳寥蚎塾”豻懊 匹畛佴砡寡嫗瓚匹畛嗉ロ來鉧眓卄  寥蚆揤棋均髓痀

 

л試照                      寥蚎塾”豻懊                    g              =            

                                                                                                =            

                                                                                                =             52.6        lb/ft3      

 

 

                                匹畛佴砡寡                    r             =                     =            

                                                                                                =            

                                                                                                =             1.63        岒恁菔芶晼碳∫諷            

                                匹畛嗉ロ來鉧眓                 S             =            

                                                                                                =            

                                                                                                =             0.843                                                     

 

 


萃е鎔狶煬 1.3      並Ж籣佴紬岐桯橔佴恁犒牄 8900 N 園珨髓苂隞襲犒棗夾揤溼 庠閫轅方眝捄證佴駍抉餌 1 蓍 6 卄彤捄證佴駍孚涷樊щ禳

() 豆刳豳籠竻並Ж籣塹曋涷樊щ禳慞郕僑ロ供僩鏈

() 豆刳寥蚎塾﹜竻並Ж 鉡郯迋蹙頨匱堌棗夾揤溼

 

л試照                      () 鉆郯竻例℅Э卄夾蠅港錘忭倒畟隞頖 棋完桄嘗Э卄岔Ж煬頛堌牄﹥瓚

      犒棗夾揤溼鴩迮樿抉瑁牷揤 塾頩尤

                                                M            =            

                                                                =            

                                                                =             907         kg

                                () 迕腕皊寡ロ犒樊Жロ供僩鏈 (gm)             =       卄彤捄證佴駍宋匱堌牄 (g)

                                       寥蚎塾”蠅景僑ロ供僩鏈        W            =        Mgm

                                                                                                                =       

                                                                                                                =        

                                                                                                                =          1483          N

 

 


萃е鎔狶煬 1.4      園珗橔蹊鼓墊森墅閫轅酵埡珛 159 籥腕 蒘頞悝慞橶墓隞股閫銧暽橔佴恁 1.5 kN 園珔悝蒪塹橚塾 110 N 豆太嘎傚狺骳寥蚎塾”豻懊 匹畛佴砡寡 酵埡珛癡豻懊凊瓚匹畛嗉ロ來鉧眓卄完橔蹊僑悝ˍ骳

 

л試照                      寥蚎塾★橔蹊      +             寥蚎塾▲悝            =             1500       N

                                                                                寥蚎塾▲悝            =             110         N

                                寥蚎塾★橔蹊                                                      =             1500 110  = 1390            N

 

寥蚎塾”豻懊    g              =            

                                                                =                       

                                                                =             8742                       N/m3

匹畛佴砡寡     r             =            

                                                                                =            

                                                                                =             891                         kg/m3

                                酵埡珛癡豻懊   "s           =                                     

                                                                                =            

                                                                                =             1.12*10-3               m3/kg

匹畛嗉ロ來鉧眓 S             =            

                                                                                =            

                                                                =             0.891                                                     

 

 

 

 

 


萃е鎔狶煬 1.5 豆刳豳鑤瓚寥蚎塾﹜竻卄找侜煬頨藤佩蓍寣橶Ⅰ珒鉌暽潸疿椐鎳ˍ狶檠邃        7 cm. 忭 6 cm. 園牶竻頖饕淶尤

()

() 酵芛 (匹畛嗉ロ來鉧眓 13.6)

 

 

 

 

 

 


л試照                      () 酵埡珛璽竻卄找侜  "            =            

                                                                                                =            

                                                                                                =             2.31 * 10-4             m3

                                    豳籠竻寥                       m            =             r"

                                                                                                =             (1000 kg/m3)(2.31 * 10-4 m3)

                                                                                                =             0.231      kg

                                   寥蚎塾★橔                         W            =             mg

                                                                                                =             (0.231 kg)(9.81 m/sec2)

                                                                                                =             2.27        N

                                   () 豳籠竻酵芛            m            =             Sr"

                                                                                                =             (13.6)(1000 kg/m3)(2.31 * 10-4 m3)

                                                                                                =             3.14        kg

                                   寥蚎塾◆襖                   W            =             mg

                                                                                                =             (3.14 kg)(9.81 m/sec2)

                                                                                                =             30.80      N

 

 

 

 


                1.3.2 轄腕曼飾竻卄找侜鉬譏繙鈮梒

                                卄找侜蓍侃僱境÷蹴餌飾竻頖韁涷靾餑掑й醜彶織煉嘈譙俔錘轅匹畛佴袨   棋完桄僎盓徶橶骳卄找侜塾暽佬±竊抉勿郯芧煬 愨孚涷 ̄郱荂挹擋暽煬駎寥珛挬蒮 併均譜照×瑣郪僩涷佴橏萃晶桄 房塾暽愨孝骳扳 煬銵譜照×滿樿飾竻頖襯盓鉬蝜愨孚涷遄埭例﹞й蟈揤廘魰擅禮      苂骳抉椎藉 卄找侜煬鳼錘轅匹畛鉌梒晰珗佸谹靾餑掑й賸塽晶桄僱畛a侲瑞豕譎扭體ы錘轅苂湆蓍牄

                   弝佸挹卄找侜並唭靾駍骳佬鉬蝜卄抉侜г譙矷縓 園皊牷轅÷蹴勿郯芧煬魰√揣紩嫗體ョ蝔迮樿岐涫癟菸鍍嘎庍謎捗佸谹愨抉抿芧遄埭H暽湧Ъ 鉆郯竻例﹥癟鉖髓珗淶佬轅煜煉廷Л×熒埱煉均疰鄐纔駖僩涷 棋完桄麂盓照蒶歖√氮癟鉌梒晰珗例﹜竻頖籠紩 愨抉彶織煉凳淶遄埭例      尺傘褽捄奜鎔狶佴紬坎竻卄找侜煬魰譏癒я  匹畛佴袨 (Viscosity)

 

                1.3.3 匹畛佴袨

                                匹畛佴袨卄坎竻頖鑠餌馱骳匹畛菟珗煉僱駖愨抉抿芧 佸谹鉬蝜方狺й蟋橏僩珗菔矷疰鉬纓餔嫗酷岔棡鄋唭遽 (Angular deformation) 愨抉彶織煉嫘飾竻頖韁涷±竊抉勿郯芧煬駖蹙頩桄嫩餌匱鰻狳牷愨抉÷苤揤蓍譜侞骳把醜禳媗慞苤疰鉬纓餔嫗酷把醜褸萃錨嘔倓я狶煻鉣≦籠竻卄找侜 蓍贊遠涷 1.1 1.2 慲揮勣坐骳匹畛佴袨卄坎竻頖驕狶疚埭 例 ̄棡佬鉖蝜銧橶骳4郱涷阹傚濟轂鉧婰購晪H暽塾暽匹畛佴袨卄坎竻鉖龔煥〞墊捶陓晶樿藍 抌Л匹畛佴袨卄均縓奐堙疚埭ˍ挹鉧婰蕾紩 煤擏塹歖壅眓愨抉÷苤揤蓍譜侞骳把醜禳媗煬駎畟隞塾暽鉬蝜竊﹎創鉥頩卄坎竻鉖龔 抌Л㏒珓塾暽竊﹎創鉥頩遄埭轄例﹛疰慞﹤酷涷繒煻鉣≦顯嘔倓я狶股暽卄坎竻頖韁涷轅匹畛鈱褘廘△骳均揤 煻鉣≦韁涷苂湆蓍股暽卄找侜煬魰醮ョя狳陔橏邈銓蹙魬鼓桄飾竻頖韁涷芷牷я 慞凈遠赶呯卄找侜煬隤橏﹊骳塾暽鄐纔駖僩涷銧歖醮ヨ紩 抌Л煻鉣≦襯牷 股暽煬隤橏﹊骳∠佬鎊畟隞苂湆蓍股暽煬魰醮ョя 慞凈銖寡ロ蒶撉桄僩涷鈱褘﹊骳蒶歖勿郯芧煬隤橏襲 ÷轔禳鉬纓餔嫖醜禳媗鄋頩塹曋赶呯遄埭愨抉抿芧H暽 佸谹照蒶歖√氮癟鉌梒晰珗H暽蓍譜侞骳妒桄僩涷苂湆菠插揤塾暽 棋完桄飽疰鄐纔駖嫣侞卄把醜禳媗㏒珓煬魰戰餑轄﹜紩嫩避駖轅阹傚濟轂忭扳 併抉餌嘟砫佽媟赶呯㏒珓轅匹畛佴袨忭

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



贊遠涷  1.1  匹畛佴袨庍褽棆喬卄坎竻頖

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


贊遠涷  1.2  匹畛佴袨夭鉆菠﹜竻卄找侜

 

 

 

 

 

 

 

 

 

 

 


贊遠涷  1.3  慲揮÷蹴酷涷繒廙襲匹畛鈱褘

 

                戰例籀砡潸嘎捄嗟庋扭潸僑悝慲揮鞁殫嘔棡煬 1.3 鉡郯俉潸嘎捄嗟煤擏庋岐掅境氬阰餑牷邦弅轄繹萃智禳譜滓例﹋檠з卄坎芮廒頩и絮媟婩找湧 庠閫廒頩и絮媟桄廷竻塹樿蹙駎骳均揤鉬蝜譜覆鈮骳× Y 芾竻я狶譜侞骳扭潸嘎捄嗟煤擏庋完淶疑癡奡橶瞽竻頖 蒶橶捄嗟廒頩髓狶苂湆墊閫×熒涷        抌Ли絮嵎潸劃嫩勿郯芧煬魬嫗嘎Ⅰ珗×筵潸嘉骳妥橶瞻й醜醮 U 漺臏涫癟 F  ̄郱荂挹擋暽煬 A 竊﹎創棋均髓痀塹毈湧寣隤駖序骳坎竻 journal bearing 煬頨藤佩湧Ъ寥蚆揤 (萃氮癟菸鍍嘎識轅煜擏)

                芧媕狺卄坎竻頖韁涷庍謎捗×筵潸嘎捄嗟 佬遄眓菠插挹廒頩и絮媢桄 慞迠橏刳 ̄陔倓骳 Y 佸谹 匹畛鈱褘 U 靾餑牷邦遄埳隞慞橶 匹畛鈱褘卄坎竻頖鑤菔瓚股暽佬方苂 霽侜桎嘉找 (velocity gradient) 蓍竊﹎創煬魨酵鉬蝜鉌暽腕 漺瞽竻頖鑤菔瓚股暽佬鉣郯芧萃ы遣鼓桄飾竻卄找侜煬駖蹙頞挬隞 例﹛疰毀攪均挹卄找侜抌Л蒶剛塾暽酵牷納骳 愨 F 煬閮郱赶呯и絮  鄐纔駖僩涷塾暽廙轎朝腕均挹擋暽煬 A 慞苳й醜醮 U 卄扭潸嘎捄嗟 廘閮凊酵腕均揤a畛×    譜覆咍狶 Y 卄扭潸嘎捄嗟煤擏庋 慞冓避駖遉梒嫩餌嘟薄疰仇埽疺腕憼體ョ蝔凈湧я

 

                                                      (1.5)

 

                例﹋畛鉖纓餔薑體畟蓍贊遠涷 1.3 佬鉖蝜銧橶骳方 U/Y 塾暽弅轄繹廗嫣湧湧Ъ velocity gradient, du/dy 慞迠橏蒶 m  鉬蝜 constant of proportionality 慞橶∠佬銧

 

                                          (1.6.a)

 

                                    (1.6.b)

 

鉡郯         t                         匹畛鄐暽鄔谹  (shearing  stress)

F                        愨孚涷 ̄郱荂挹и絮

A                        擋暽煬鋡竻廒頩и絮 

m                        方狺孚涷 

U                        匹畛鈱褘 

Y                        譜覆咍狶譜侞骳扭潸嘎捄嗟煤擏庋 

 

                岏÷繩涷 1.6.b 塹橧晡郯侲譏癒я 岏÷瓣й賸塽揣竻墊З揤 (Newtons equation of viscosity) 園砫G繒蒶錘鉧郯俉妠坐骳 Proportionality constant ∠佬銧橶骳

 

                                                                                                                  (1.7)

 

                鈱砫譏癒  m  蓍岏÷繩涷 1.7 塹橶骳 庍覬譜彸溢婖匹畛佴袨 (Coefficient of viscosity) 佸谹匹畛佴袨庍褽棆喬 (absolute viscosity) 佸谹匹畛佴袨銧境轂﹋ (dynamic viscosity) 佸谹鈱梒﹤擅禮庍暽 я 匹畛佴袨

                匹畛廘△骳岔倓я狶卄扭Y均挹卄找侜塾暽 H暽苂湆×漱й購畛疰嗚飽疰識漱й   鄐暽鄔谹飾竻弅羅桄 弝佸挹匹畛廘△骳彤郯 譜侞骳坎竻頖鑤瓚卄扭Y 佬銧橛痋奿×嫘嘔畟瓚閟梒氯朝迗捔贊遠涷 1.4

 

 

 

 

 

 

 

 


贊遠涷  1.4   匹畛庍謙揤賄譜侞骳坐й醜日嫩抿芧×  Velocity gradient

 

                卄找侜轅匹畛庍謙揤賄譜侞骳 t × du/dy 煬鳼錘鉬蝜隞菸購薄疰匹畛佴袨卄完堌萃 鈱梒﹊骳 卄找侜嗶凳堌漞鉆梒 (non-Newtonian fluid) 轅侜畟疚埭 例 ̄棡煬 1.4 佬弅轄繹廕閫疚埭卄坎竻頖饕芧墊щ獅塹繒銧歖餌 3 酵冓懋 銧殧∟

-       卄找侜酵冓懋銧鉣廗 (Dilatant substance) 鉬蝜卄找侜煬餑掑й賸塽期牷H暽鉡郯秅й醜醮ч肴岐媮轄﹜紩 鄋頩 溼畟棻 鉬蝜菟

-       卄找侜酵冓懋忭漺嬝疺菠 (Pseudo plastic) 鉬蝜卄找侜煬餑掑й賸塽期牷H暽鉡郯秅й醜醮ч肴岐媮轄﹜紩 鄋頩 嘗 椒嫩佴梒 幽鉡僱憼瓚弅藷陓畟來學﹊嵂

-       嬝疺菠 (Plastic) 鉬蝜卄找侜煬閮迮樿岐掑й醜日馱籤”蚢Л佴紬均駖 併夾郱赶呯轅÷蹴酷涷繒廙襲匹畛鈱褘鄋唭遽錨飾竻頖 鄋頩 嬝疺菠 鉬蝜菟

例﹞й豁珒卄坐й購捘憾兢嚆倓я狶 t × du/dy 佬銧擗й賸塽晷龔捄 m 庠閫鉬蝜尺傘褽捄婄忠眓卄坎竻頖鑤菔瓚疚埭煬閮迮橏僩珗菔俉癟鄔谹 匹畛佴袨嬝и窖竻卄找侜佬霽襲鉡郯迋堻侚椑埡牷H暽 鉧證冓避駖阹傚濟轂轄﹜紩麂郱赶呯愨岑硒鉖塹餔Ы倓я狶芧媕狺卄找侜霽襲 抌Л蓍㏒珓佬轅匹畛佴袨嬝и聒牷H暽鉡郯迋堻侚椑埰晪H暽 鉧證倰壽檠丐竻㏒珓苂湆咍狶×嘗涫癟謫毯佴涷藉譜侞骳把醜禳媗寥苂鉡郯迋堻侚椑埰晪H暽 佬照蒶橧捸疰嗉畟鈮煻鉡僱捘譜侞骳把醜禳媗卄均縓 照蒶歖√握й蟋橏僩珗菔俉癟鄔谹嘗牷H暽 併孚赶呯轅匹畛佴袨嬝и聒牷H暽 弝佸挹匹畛庍謙揤賄譜侞骳坐й賸塽晷龔捄卄坎竻頖鑤瓚㏒珓疚埭菔狶 ×睿堻侚椑唌籀梫涷鉬蝜卄扭Y 匹畛鄐暽鄔谹麂冓餌嘟挬抌Л×滯境揣竻÷蹴酷涷繒贊 (Deformation) 例﹋薄疰煬 1.6.b 塾暽酵牷納骳 匹畛鄐暽鄔谹飾竻頖襯冓餌嘟挬抌Л×睿捄證÷蹴酷涷繒贊

                弝佸挹 ̄博卄扭潸嘎捄嗟煬駍狶Ⅰ珗×僑悝慲揮蓍贊遠涷 1.3 塾暽 園皊牷 U 轅方狺孚涷 慞迮挬敷 ̄郱漕牷岍痀郱涷卄筵潸嘎捄嗟煜擏慞橶 匹畛鄐暽鄔谹劃嫗潸嘎捄嗟煤擏庋均蝔冓瑁牷揤 慞冓塽駖夾牷 m  µ (du/dy) 棋完桄 velocity gradient, du/dy ∠佬轅方狺孚涷

 

 

 

 

 

 

 


贊遠涷 1.5   鉧籤煬駎遽嘔駍鍍★苂湆蓍 ̄郕矷ˍロ

 

                苂骳找獺蝯畛 蓍 ̄博卄序捄嗟贊遠癟 ̄郕矷煬餑涫★鏡Щ×僑悝慲揮蓍贊遠涷 1.5 慞釓掑й醜醮ч肴岐媮 w 之煬頩桄  匹畛鄐暽鄔谹劃匱堌卄序捄嗟贊遠癟 ̄郕矷肴暽蓍∠佬轅方畛牷﹊骳匹畛鄐暽鄔谹劃匱堌卄序捄嗟贊遠癟 ̄郕矷肴暽嗶 煤擏塹歖壅眓и絮媄棡溼均譜睿◎桄廷竻轅識轅煬魨窗菔狶× 併孚赶呯轅 Velocity gradient 靾魰瑁牷揤腋芫匹畛佴牶竻芾竻я狶 慞迠橏墓閟砡癟碣 Tr 煬韏橏飽疰佹媢轄鈮骳×筵癟碣 Td 煬魬芷C箝呯佹媢慞橶∠佬弅轄繹刳匹畛庍謙揤賄卄 du/dy  煬餖捑轅 r1   r2  銧暾悝塹  

 

      愨宋埭菟珗÷襠遽 ,  Tr              =              愨宋埭煬魬芷C箝呯佹媢  ,  Td            (1.8.a)

 

                                                t1(2pr1)L(r1)       =             t2(2pr2)L(r2)                                       (1.8.b)

 

                   =                                                               (1.8.c)

 

            =                                         (1.8.d)

 

                例﹋薄疰佬鉖蝜銧橶骳     r1  ®  r2  慞橶方  (du/dy)1 鈮骳×  (du/dy)2  鈮骳×  U/Y  鈮骳×漱骳之煬  棋完桄僎橏刳 ̄陔倓骳完桄凳樿臏牷  ∠弅轄繹匯俔湧я 鉌暽熐邊衡鮈竻匹畛鈱褘廙蹴餌嫩抎僱癟

                佴駍瞽竻匹畛佴袨庍褽棆喬 m 鉬蝜佴駍瞽竻愨孝駖擋暽煬駎疰湧Ъ迕腕牷疰鉬纓餔嫗酷坐й醜醮 蓍譜犖 S.I. 塾暽 匹畛佴袨庍褽棆喬佬轅佴駍轉餌嫣輓畛岏÷繩涷 1.9

 

佴駍瞽竻  m  =   =   =   =  Pa . s             (1.9)

 

匹畛佴袨鉬譏繙鈮梒 (Kinematics viscosity) 鉬蝜迕腕疺駍嫩酵梒箋煬繙譜侞骳坐й賸塽晷龔捄菔秅й賸境廜頩 膋樨悜竊﹎喬尤 n (nu) 棋完淶

 

                                                                            (1.10)

                蓍煉宏耽碧菠弝佸挹忌僑橏嘎埱ョ藤褸桄僎谹я 匹畛佴袨庍褽棆喬卄坎竻頖韁堙疚埭靾魨酵菸薑й蟈揤 勣扭鍾я狺й蟈揤塾暽佬忭岐牷∠菸薑й賸塽插諙錘廘△骳夾牷方珝涷苂湆蓍贊遠涷 1.1 轄★恁 抌Л匹畛佴袨夭鉆徶菠﹜竻㏒珓塾暽佬廙邊輓畛匹畛棋 煤擏塹歖壅眓匹畛    佴砡寡飾竻㏒珓塾暽鉬纓餔馱骳隞

匹畛佴袨庍褽棆喬 (m) 轅佴駍轉餌 poise 庠閫鉬蝜臥駖煬韏桄坎紩嫩擋駖鉬蝜遄梒繭婛∟ Poiseuille 庠閫鉬蝜樑曋涷銧橛痋奿勣坐й賸塽晶淶苂骳夾譎夾悝

                1 lb-sec/ft2            =             479   poise             譜犖迕均馨

                1 N-sec/m2                  =             10     poise             譜犖閟怀

匹畛佴袨夭鉆徶菠 (n)轅佴駍轉餌 Stoke 煤擏塹歖擋駖鉬蝜遄梒繭婛∟ G.G. Stokes

                1 ft2/sec                 =             929   Stoke           譜犖迕均馨

                1 cm2/sec               =             1       Stoke            譜犖閟怀

 

 


萃е鎔狶煬 1.6 廒頩證滯境氬阰 2 廒頩 й妨樿飽揤漺臏晡駖序骳岔倓я狶廒頩煤擏庋 0.1 墊橶 譜侞骳妒駖序骳宋藤佩湧Ъ寥蚆揤侜駖纔頩鉭芤 30 煬駖堻侚椑 30 竻瓵砫羅餂渥     (m =3.5*10-3 lb-sec/ft2) 豆刳愨孚涷棉扭潸嘔珘廒頩犒 庠閫轅擋暽煬 4 .           蒶歖勿郯芧煬韐橶瞻й醜醮 20 /境煬

 

л試照                                      F             =            

                                                                =            

                                                                =             0.56        lb

 

 

 

 

 


萃е鎔狶煬 1.7 и絮堛婩嘈墅閫轅豳 8 kg 鉣郯芧襲漺蟬埰譜犒擋暽閟梒妨紬孚蚆媮 20° ×筵嘎譜棋犖凳橔蹊僩涷轅匹畛佴袨嬝и 0.44 N.s/m2 2 mm. 漺臏桴郪僩涷庍謎捗                            譜侞骳序捄嗟×犒橔蹊嫩瑁牷挹 0.2 m2 豆刳匹畛鈱褘卄序捄嗟

 

л試照 

 

                岏楮籠竻愨孝畛廜Ц郪嫩邯禮

                SFx  =  0 ;                       W sin 20°                   =             tA 

                                                                mg sin 20°            =            

                                (8 kg)(9.81 m/sec2) sin 20°              =            

                                                                U             =             0.61   m/s

棋完桄 и絮媢淶鄐纔駖僩涷湧Ъ匹畛鈱褘  0.61 m/s                                                                   

 

 

 

 

 

 

 


萃е鎔狶煬 1.8   彄Ⅰ珒 3.00 * 6.00 鉡腕 嗨ˍ牷佻妥橶瞻й醜醮 1 鉡腕菔虰埳珝 蓍籣勿竻煬韏郪嫩F嘟畟佴紬 匹畛纖”牷蒫殧噤盓⊿馱攪序挬銧 0.10 鉡腕 豆太嘎傚狺骳愨孚涷佬證”晪彄棋均髓痀

         

 

л試照         岏遽菠я狺й醜醮ヨ竻寥貤酵鉬蝜鉌暽腕夾牷椐鎳煬銵暽勿竻鉬蝜 1 鉡腕菔虰埳珝梫涷彄 慞郱涷阹傚濟轂 20 竻砫宣鄎梒 方 m = 1.005 * 10-3 墊З揤-л境煬菔芚疰狶鉡腕

 

例﹋薄疰       t          =         

                廗馱骳                  t              =             (1.005 * 10-3 N-sec/m2)

                                                                =             1.005 * 10-2          N/m2

                                                F             =             t*A

                                                                =             (1.005 * 10-2 N) (18 m2)

                                                                =             0.181                      N                                                                            

 

 

 

 

 

 

萃е鎔狶煬 1.9  Journal bearing 臾森墅閫酵苤芮湧Ъ鉧籤Ⅰ珒鉌暽潸疿椐鎳ˍ狶 6 墊橶 慞苤珘鉧籤Ⅰ珒鉌暽潸疿椐鎳ˍ狶 6.01 墊橶 匹畛觴ヨ竻÷箋嬝疰Щ×嫩瑁牷挹 8 墊橶 園甡畟蓍芾竻я狶譜侞骳抉嬝砡瓚÷箋嬝 疑癡奡橶繒橔蹊嘈髓芶郯嫩睿鏈 30      煬駖堻侚椑 100 竻瓵砫羅餂渥 (m = 8*10-4 lb-sec/ft2) 豆太嘎傚砡癟鉌梒晰珗煬魰√揣紩嫩避駖鉧籤佹媢湧Ъ匹畛鈱褘襖 500 / 境煬

 

л試照                                      F             =            

                                                                =

                                                                =             26.30      lb

 

 


萃е鎔狶煬 1.10 寥蚆揤鉭芤 10 轅匹畛嗉ロ來鉧眓 0.92 慞釓掑й賸塽 1.7*10-7 poise 豆刳 Kinetic viscosity (n) 蓍佴駍 ft2/sec

 

л試照                                      n            =            

                                                                =             

                                                                =             1.373 * 10-5          ft2/sec

 

 

 

 

 

 

 

 

 

 

 


                1.3.4 碧聾懧蟈棸捗 (Bulk Modulus)

戰×朝袨侁嵙嫩肴宏譎轄腕佸谹碧霽懧蟈棸捗 (Bulk Modulus of Elasticity) 鉬蝜     尺傘褽捄唲竻卄找侜煬駔畛疰嗣酷涷繒廙襲酵埡珛邊湧粹狶鉣蝖寥苂 鉆郯竻例﹜竻頖韃晼 ̄郱貣朝邴溢埲籠竻匹畛棋嘛畟嗶 竊﹎創鄋頩塹擉郱赶呯卄找侜嗨◇梣蒶橧梬譎轄腕霽襲         棋扭妠找①蓍贊遠涷 1.6

 

 

 


P + dp

 

 

 

       () 卄找侜鈱婰蟋暽                      () 卄找侜侜悝例﹤戰餑匹畛棋 dP

 

贊遠涷 1.6 ÷蹴酷涷繒廙襲酵埡珛璽竻и絮媕畟侜悝例℅捸疰鉧婰薑й蟈揤

 

例 ̄棡煬 1.6

             佴駍轍癟迕晰涷鉬纓餔嫗酷 (Compressive stress)          =   (P + dP) P                    (1.11)

                                                                                                =   +dP                                  

 

             酵埡珛繩涷鉬纓餔嫗酷 (Volumetric change)  =  (" d" ) "                  (1.12)

                                                                                                =  d"

                       

                匹畛鄐譏織鄋唭酵埡珛 (Volumetric strain)                 =                                (1.13)

 

                弝佸挹卄找侜煬餑掑й謝袨侁嵙嘟褽棆喬 尤 佴駍轍癟迕毯餌劂耽檠手朝腕均挹匹畛鄐譏織鄋唭酵埡珛 佹畟匹畛я珨譎轄腕卄坎竻頖攣竊夾牷鉧婰薑й蟈揤佬尤嘟湆岍瓴鉥埡佸谹轅酵埡珜鈮骳×獄譎轄腕鈱婰蟋暽∠菔侲避駖匹畛棋嘉棠抉瑁牷挹匹畛棋僩涷鉧婰醜a砪 庠閫遉梒嫩餌馱й蟈揤庍謙揤賄銧暾悝塹

                           佴駍轍癟迕晰涷鉬纓餔嫗酷       a      匹畛鄐譏織鄋唭酵埡珛

 

                                                                dP           a                                                              (1.14.a)

 

                                                                dP           =             K                                               (1.14.b)

 

                                                                K             =                                                         (1.14.c)

 

鉡郯  K      戰×朝袨侁嵙嫩肴宏譎轄腕 佸谹鈱梒﹊骳 煻棻竊忺肴宏譎轄腕 (Bulk Modulus) 弝佸挹方 K 卄完橔煬駖堻侚椑婛瓚匹畛棋僱骳扳 轅方珒悝菸證孚涷 1.5

 

菸證孚涷 1.5  戰×朝袨侁嵙嫩肴宏譎轄腕卄完橔  (MN / m2)

 

匹畛棋

(bar)

阹傚濟轂 (° C)

0

20

49

93

1

2040

2200

2289

2130

100

2068

2275

2358

2199

300

2186

2399

2496

2330

1000

2620

2827

2937

2792

 

漺薹駍飽竊滯竻煻棻竊忺肴宏譎轄腕 鈱梒﹊骳 匹畛弅轄繹蓍÷藕媞萃ы湧 (Coefficient of compressibility) 遉梒嫗溯湧Ъ b 鉬蝜迕腕疺駍飾竻酵埡珛繩涷鉬纓餔嫗酷孝駖酵埡珛蹴椒蟋駖匹畛棋僩涷鉬纓餔嫗酷找

 

                                                b             =                                                                      (1.15.a)

 

                                                b             =                                                        (1.15.b)

 

萃е鎔狶煬 1.11 卄抉侜ヰ墊森墅閫嗨﹠挬蓍 ̄郕矷 鉡郯芩掑й薄斐揤 1000 銓僑黖駖菸證完婩 酵埡珛璽竻卄抉侜ヮ冓瑁牷挹 0.4 蘸◇疿∫諷 廘魰避駖匹畛●棋嫩戰餑H暽鉬蝜 2000 銓僑黖駖菸證完婩 酵埡珛璽竻卄抉侜ヮ陓毯餌 0.396 蘸◇疿∫諷 苂牷溼珘я 碧聾懧蟈棸捗卄坐й謝袨侁嵙麂冓餌嫩瑁砳

 

л試照                      匹畛●棋僩涷鉧婰蕾紩           =             Dp          =             2000 1000

                                                                                =             1000                       lb/in2

                                酵埡珛繩涷鉬纓餔嫗酷       =             D"         =             (0.396 0.4)

                                                                                =             0.004                  ft3

                                例﹋薄疰            K             =            

                                                                                =            

                                                                                =             100000                  lb/in2      

 

 


萃е鎔狶煬 1.12  墓慴禳迓芶鼒涷轅酵埡珛 28.92 litre 隞鉧婰薑й蟈揤 51,000 kPa 噥я砫侜谹酵埡珛 27.70 litre 豆刳戰×朝袨侁嵙嫩肴宏譎轄腕卄扭芶﹠怤鱗塹

 

л試照                      酵埡珛轔芶﹠怤鱗霽襲        d"                   =             27.70 28.92

                                                                                                =             1.22   liters

                                戰×朝袨侁嵙嫩肴宏譎轄腕                    K             =            

                                                                                                                =            

                                                                                                                =             1.21 x 106              kPa                                 

 

 

 

 

 

 


萃е鎔狶煬 1.13 蓍÷繩棵芮匹畛弅轄繹識筵癟棋飾竻卄找侜疚埭佴紬  漺邃抌卄找侜蓍剽孚癟 ̄郕矷煬餑淀抎匱骳椐鎳ˍ狶檠邃 1 m и握й購晪卄坎竻頖饜湧 1.2 m 園眝矷愨均棠晼忭滯橏宋 2 MN 酵牷納骳匹畛忭坎竻卄找侜霽襲鉖纔 1.198 m 豆刳戰×朝袨侁嵙嫩肴宏譎轄腕卄坎竻頖饕淶

 

л試照             酵埡珛蹴譎餑菟飾竻卄找侜                  =      

                                                                                                                =              0.9425     m3

                                酵埡珛璽竻卄找侜侜悝嗨﹛                      =            

                                                                                                                =              0.9409     m2

棋完桄 酵埡珛璽竻卄找侜霽襲    d"        =             0.9409 0.9425   

                                                                                                                =             0.0016   m3

                                匹畛棋飽揣竻卄找侜                   dP           =                     

                                                                                                                =                                                                       

                                                                                                                =             2.55   MPa           

                                戰×朝袨侁嵙嫩肴宏譎轄腕                                    =            

                                                                                                                =            

                                                                                                                =             1500   Mpa

                                \ 戰×朝袨侁嵙嫩肴宏譎轄腕                        =                  1.50   GPa                                   

 

 

 

 

 

 

 

 


萃е鎔狶煬 1.14  園砫戰餑匹畛棋 7,000 kPa ×犒橔煬餑梬譎轄腕 1 m3 煬駖堻侚椑 20° C  酵埡珛羅橔佬霽襲鉖纔侲瑁砳

 

л試照                      寥虓涷阹傚濟轂 20° C 轅方 K = 2.20 x 106   kPa 

K             =            

                                                2.2 * 106 kPa        =                                                                                                                                    d"                     =             0.00318   m3                                                                                                                                                                         

             鄐譙駖弄轄 d" 鉬蝜驕 慲揮я珨譎轄腕卄完橔霽襲 0.00318 m3

             棋完桄劂譎轄腕寥虓涷鉖纔                       =            " d"

                                                                 =            1 0.00318

                                 =            0.997 m3                                         

 

 


萃е鎔狶煬 1.15  檠邃菟匹畛●棋 9.80 √牄墊З揤菔芚疰狶鉡腕 寥茖釓梬譎轄腕 0.5 蘸◇疿∫-鉡腕 園砫戰餑匹畛●棋飾紩嫣韶餌 80 √牄墊З揤菔芚疰狶鉡腕 漺癒蚎僑蒶樿堻侚椑啎孚涷  (K = 300000 lb/in2) 苂牷溼珘я珗橔棋均髓痀轅酵埡珛藷棠抉瑁砪

 

л試照                      例﹋薄疰            K             =            

                                例﹦邢鎳               dp           =             80 9.80              

=             70.2                        kN/m2

                                                                "            =             0.5                          m3

                                                                K             =             300,000                 lb/in2

                                                                                =             300,000 * 6.894

=             2.068 * 106           kN/m2

                廗馱骳蓍岏÷                -d"        =            

                                                                                =            

                                                                                =             16.973 * 10-6        m3                          

                1.3.5 匹畛萋尬堌慞苳й蟈揤颮

                                卄抉侜Й堙疚埭佬轅愨抉÷苤揤 (Cohesion) 慞凊癟供熊埭 (adhesion) 苂湆湧Ъ鉌趨 愨孚桄廷竻塹歖餌嘔棡卄扭癟棉妥棷卄把醜禳媗塾頩閟 愨抉÷苤揤塹擉郱赶呯卄抉侜в畛疰亂挹匹畛鄐暽萋 (tensile stress) 銧 抌Л愨夾挹菠捶郱赶呯卄找侜弅轄繹供熊埭×瘉捄嗟邰頩銧 愨妥盓棻棺倓я狶煻鉣≦饕桄麂郱赶呯遄埭股暽碳 庠閫鈱梒﹊骳諮鱗 (imaginary film)       卄坎竻頖籠紩 諮鱗蟈悝ˍ骳Л淶弅轄繹識筵癟棉扼匱堌譜侞骳坎竻鉖龔煬鳼錘蠅蟋捚×嘟竻疚埭佸谹 蓍譜侞骳坎竻鉖龔×滿縓 尺傘褽捄唲竻卄找侜棋均髓痀塹歖譏癒я 匹畛萋尬堌 卄找侜煬餑掑й蟋盓樊Л桄嘗梠蹙餑牷轄 菸證孚涷 1.5 鉬蝜方狺й蟋盓樊ヨ竻寥虓涷阹傚濟轂菔狶 匹畛萋尬堌塹歖√期狳牷愨抉÷苤揤慞凊癟供熊埭 卄抉侜Л桄麂冓閣癒樊ヨ竻и絮媟涷鉬蝜檠疚陏竻識筵瓚        卄抉侜З癟煬駔捘槽吽挹檠疚郱涷襖岔挹塾暽∠佬嗨‾△桄扼呯轅譜棋監晪H暽﹊骳譜棋獄△婄驗★樿 廘頞橏愨抉÷苤揤轅轄﹛я 佬照蒶憸竻鉖龔腕夾奡庍謎捗嗨﹛斯捚蒶曀髬襲﹊骳譜棋獄△         萃е鎔狶卄扭癟棉孚涷遄埭例﹛疰菅熊捚煬魰呦嫣湧股 ∠尤芤迡挹寥赶嘈攪氮⊿Й涷忭均я疰迡挹並唭 抌Л酵芛蓍侜芫寣橶∠佬菔荂я疰迡挹並唭棋扼嘔棡煬  1.7  庠閫遉梒嗽駖抌Л轄例﹜境捶譎

 

 

 

 

 

 

 

 

 

 

 


贊遠涷  1.7  匹畛菅滯竻侜芫寣橶ˍ

 

 

 

 

 

 

 

菸證孚涷 1.5   尺傘褽捄唲竻寥虓涷阹傚濟轂菔狶

 

阹傚濟轂

oC

匹畛

佴砡寡

r,kg/m3.

匹畛佴袨

m x 103 ,

N . s/m2

匹畛佴袨

夭鉆鉡菠

n x 106,m2/s

匹畛萋尬堌

s , N/m

閜揣竻

匹畛棋嫣

pv/g  ,  m

碧霽懧蟈棸捗卄坐й謝袨侁嵙

Ev x 10-6 , kN/m2

0

5

10

15

20

25

30

40

50

60

70

80

90

100

999.8

1000.0

999.7

999.1

998.2

997.0

995.7

992.2

988.0

983.2

977.8

971.8

965.3

958.4

1.781

1.518

1.307

1.139

1.002

0.890

0.798

0.653

0.547

0.466

0.404

0.354

0.315

0.282

1.785

1.519

1.306

1.139

1.003

0.893

0.800

0.658

0.553

0.474

0.413

0.364

0.326

0.294

0.0756

0.0749

0.0742

0.0735

0.0728

0.0720

0.0712

0.0696

0.0679

0.0662

0.0644

0.0626

0.0608

0.0589

0.06

0.09

0.12

0.17

0.25

0.33

0.44

0.76

1.26

2.03

3.20

4.96

7.18

10.33

2.02

2.06

2.10

2.15

2.18

2.22

2.25

2.28

2.29

2.28

2.25

2.20

2.14

2.07

 

 

贊遠涷 1.8   慲揮譜棋滯竻鉖龔煬頞晼棉扼呯忭坎紩嘈譙矷氬呯菔蚥

 

 

 

                卄抉侜Й涷嗨●盓蒶橧桼迡挹忭坎紩嘈譙矷氬呯轅譜棋熊髬襲例◆△埳桄 轅竊﹎創棋扭妠扼嘔棡煬 1.8 Free body diagram 園皊牷⊿芧卄抉侜 (meniscus) 煬頞晼棉扼呯轅譜棋監晪H暽佸谹嗨﹛氬呯轅譜棋熊髬襲例 ̄迡挹說菠塾暽鉬蝜溼均譜睿﹛鰻慞橶 鉡郯侲迗愨岑△捚煬魰√捶牷匹畛萋尬堌 轄鈮骳×筵癟棉妥棷卄把禳∠佬銧 

 

                                愨孚涷棉坎竻鉖龔H暽         =             寥蚎塾﹜竻卄抉侜Ш畟蓍侜芫

 

                                                        =                                                            (1.16.a)

 

                                                                h              =                                                     (1.16.b)

 

鉡郯         s                        匹畛萋尬堌  轅佴駍轉餌嫗癟菔秅й謝痀

                                g                          寥蚎塾”豻懊苠竻卄抉侜

                                d                         Ⅰ珒鉌暽潸疿椐鎳ˍ狶卄弄攪氮⊿

                                h                         譜棋滯竻鉖龔煬頞晼棉扼呯忭坎紩

               

                岏÷繩涷 1.16.b 膋樨蚎識瞄狺骳漺罈譜轄郭竻譜棋滯竻鉖龔煬頞晼棉扼呯忭坎紩嘈譙   嗨﹛氬呯菔蚥夾牷譜棋獄△ 蓍 ̄博煬頝駖塾暽鉬蝜侜芫寣橶煬駔倰珒 慞苠竻鉖龔塾暽鉬蝜寥茖釓桷媮  q  =  0o 廘頞橏卄抉侜Л桄嫩餌劂襖楚蝔釓桷媮 q  =  140o  瑁芛涷轅Ⅰ珒鉌暽潸疿椐鎳ˍ狶蒶剛﹊骳 12 mm. (1/2  墊橶) 佬靾餑梩禳譜滓例﹛疰菅滯竻瑁侲鷓 鉌暽 ̄瓵蓍贊遠涷 1.7 鉬蝜鉌暽 ̄瓵卄完橔慞郅襖毽涷苂湆蓍迗÷

 

 

 

 

 

 

 

 


萃е鎔狶煬 1.16 酵芛轅匹畛嗉ロ來鉧眓 13.6 疑癡崳嘈攪氮⊿ 鉌暽潸疿椐鎳ˍ狶 0.2 墊橶 酵牷納骳譜棋滯竻酵芛蓍侜芫寣橶菔荂я疰迡挹卄宏襖楷橏完矷 0.5 墊橶 遽褶涷廜リй蟋盓樊ヨ竻酵芛照×筵嘎椒閫鈮骳× 30 竻 豆刳匹畛萋尬堌蓍佴駍 lb/ft

 

л試照                                      s            =            

                                                                =            

                                                                                =             0.17        lb/ft

 

 




萃е鎔狶煬 1.17 鉡郯籵嵙賸攪斐棷Ⅰ珒鉌暽潸疿椐鎳ˍ狶 8 . 襲蓍寣橶寥蚎й鼠紬岐掑й         嗉ロ來鉧眓 1.1 酵牷納骳譜棋犒橔侞珗檠邃嘈攪斐棷苂湆忭均я疰迡挹     檠繒矷 3 . 遽褶涷廜リй蟋盓樊ヨ竻寥蚎й僩荂挹廜Ж婰 45 竻 豆刳匹畛萋尬堌

ˍ駖坎樿匹畛: 寥

л試照                                      s            =            

                                                                =            

                                                                                =             9.14 * 10-5             kN/m

 

 


萃е鎔狶煬 1.18 侜芫寣橶庈迗揣境毯抎匱骳椐鎳ˍ狶 2 mm. 佩餑襲隞蓍寥茷紬岐梠堻侚椑 15 -鄎鑠幽薹 豆太嘎傚狺й購晪 Capillary 卄完橔煬鳼侜H暽隞蓍侜芫寣橶 ±佴氬呯寥虓蚆媮庍謎捗×筵⊿Ф堌庈迗毯瑁牷挹 0

 

л試照               例﹥撕檠擔妠扼呯鉖蝜я 愨孝盓樊Й涷 ̄郱荎紩嘟蟈媗挹寥蚎塾﹜竻寥

                                                                spd       =            

                                                                h              =            

                         寥虓涷阹傚濟轂 15 竻砫宣鄎梒 轅方 s = 0.0735 N/m g = 9798 N/m3

                                                                h              =            

                                                                                =             0.015      m

                         塾頩尤秅й購晪卄 Capillary 卄完橔蓍侜芫寣橶 15 mm.

 

 


萃е鎔狶煬 1.19 鰻卄弄捚拌普晼迕棠找颯菟寥豻擋駖蒶歖√曾竻迗÷H暽 園瓵竻迗÷塾暽轅Ⅰ珒鉌暽潸疿椐鎳ˍ狶 2 mm 慞橶 苂牷溼珘я狺й蟈揤鰻煬駎捚拌捶迮樿岐牷﹊骳匹畛棋飾竻寥  煬駖蹙餖芮 鈮骳鞀    s  = 72.7 x 10-3 N/m

 

л試照                      匹畛棋飾竻鰻煬餑牷﹊骳匹畛棋凳橔煬駖蹙餖芮  

      =                                               

                                                                  =  

                                                                  =   1.444 x 102  N/m2                                       

               

 

 

 

 


匹畛棋嫣祂竻卄抉侜 (Vapour pressure of Liquids)

                卄抉侜Й堙疚埭菔狶∠壇畟畛煬閮陏冓侁佸谹ˍ畟鉬蝜颮 棋扭妠扼嘔棡煬 1.9 漺癒疰鉣蝝攪揣竻煻鉣≦韁涷佴梠矷隞例□堌卄坎竻鉖龔塾暽 園皊牷卄抉侜Л桄嗶蹙魬嘛猁塵煬頠埭轂揪埭慞橶 匹畛棋 (Partial pressure) 蓍芾竻я狶犒卄抉侜Й涷遄埭例﹛疰鉣蝝攪揣竻煻鉣≦ ∠佬鉧婰謠牷H暽 邦 ̄郱桎彤捄證卄把醜禳媗煬魰驗棠芫迋∩豪牷樊 鈮骳×睿捄證卄把醜禳媗煬銵竊漱袡遉橏忭頛堌 鈱梒﹞й蟈揤颮檠邃菟岍痀郱涷岏楮饕淶鈱梒﹊骳 匹畛棋嫣迋婰蟋捚 (saturation pressure)

贊遠涷 1.9 匹畛棋嫣祂竻卄找侜蓍檠疚郅埭

 

迕腕牷疰鉣蝝攪揣竻煻鉣≦饕淶佬鉧婰蕾紩僱畛阹傚濟轂 棋完桄馱й蟈揤颮邴餑萃ヮ冓戰餑H暽菸趨堻侚椑埭橶 匹畛棋飾竻卄抉侜Й涷阹傚濟轂菔狶 塾暽佬忭均я狺й蟈揤颮邴餑萃ш菔佬      菔荂я砪錘銧 園皊牷菔荂я砡體 卄抉侜Л桄麂陏冓侁苂骳岔Ж鈱褘佸谹煬魰譏癒я砫棚芫塾頩閟 棋完桄麂盓弅轄繹刳方狺й蟈揤颮邴餑萃ы湧例﹞й蟈揤蓍4郱涷卄抉侜Л桄飽蚥悝鉥谹

          蓍煉宏耽碧菠塾暽鈱疺嫘角骳匹畛棋嫣芧淶轄 煤擏塹歖壅眓園皊牷匹畛棋僩涷嗨﹛恁鞁暻飾竻鉖龔菔荂я狺й蟈揤颮邴餑萃ш體 卄抉侜Л桄麂苤籤轉餌嫣 匹畛棋嫣祂竻卄抉侜ヰ墊斯骳 塾暽慲揮鞁殫僱疰狶煬 1.7 佬鉖蝜銧擉牷菸證序骳酵芛轅匹畛棋嫣迋婰蟋捚菔虓涷忐 棋完桄麂盓照蒶暺襖楊盓鉖轄倇褶涷佬墓轄膋歖餌飾竻鉖龔蓍碳襖轂鉞芤 弝佸挹匹畛棋嫣迋婰蟋捚卄完橔塾暽苂湆蓍菸證孚涷  1.8

 

 

 

 

 

           菸證孚涷  1.7   方狺й蟈揤颮邴餑萃Й涷  20 oC  卄坎竻鉖龔菔狶

 

匹畛棋嫣迋婰蟋捚  佴駍轉餌  N/m2

酵芛  (Mercury)

  (Water)

寥蚆揤㏒珒  (Kerosene)

閟溢埧慴禳迓芶  (Ethyl  Alcohol)

鉭鼠埳  (Benzene)

鉡溢埧慴禳迓芶  (Methyl  Alcohol)

鉭鼠埳繹繒蛙  (Petrol)

0.16

2,340

3,300

5,900

10,000

12,500

30,400

 

            菸證孚涷 1.8   方狺й蟈揤颮邴餑萃ヨ竻寥

 

阹傚濟轂  0oC

匹畛棋  N/m2

0

10

20

40

60

80

100

615

1,230

2,340

7,400

20,000

47,400

101,500