Ch2 Fluid Statics. sin = 2. cos. θ is arbitrarily chosen

Transcription

1 Ch lud Stt lud ether t ret or mong n mnner tht there no relte moton between djent rtle. No herng tre n the flud Onl reure (fore tht deelo on the urfe of the rtle). Preure t ont N/m (ore/re) m θ n P P Y : ρ P P o γ θ Z: ρ ) ( n o γ ρ ρ θ θ : : ; Wht hen t t.? 0,, θ rbtrrl hoen Preure t t. n flud t ret, or n moton, ndeendent of dreton long there re no herng tree reent. (Pl lw)

2 . B equton for Preure eld How doe the reure n flud whh there re no herng tree r from t. to t.? Surfe & bod fore tng on mll flud element Preure weght Surfe fore: ) ( ) ( : Smlrl, n nd dreton: ) ( ) ( k j k j k j Newton eond lw W m ρ γ k γ ρ

3 Generl equton of moton for flud n whh there re no herng tree.. Preure rton n flud t ret 0 γk 0 γ d γ d (Eq..4).. Inomreble γ ρg ont d γ d γ ( ) γh Hdrott Dtrbuton γ h *ee g.. h γ reure hed 0 E: h. ft or 58mmHg ( γ 6.4lb ft ) ( γ KN m ) γ h 0 Preure n homogeneou, nomreble flud t ret ~ referene leel, X e or he of the ontner. The requred eqult of reure t equl eleton Throughout tem. ( g..5) Trnmon of flud reure

4 .. Comreble lud erfet g: ρt ume T T 0 d d γ ρg g, ont.( oer d [, ] g( e T0 g T g Z d ln ) Z T otherml ondton ).4 Troohere: 4

5 T T K β loe rte m ft T g β β ( ) T.5 Meurement of Preure See g..7 eln the gge nd bolute reure γ h tm or N (Merur brometer) Emle. ( l) m.6 Mnometr. Peometer Tube:. >. h reonble 不大. lqud, not g. U-Tube Mnometer: γ h γ h. Inlned-tube mnometer ee emle *eln g.. Dfferentl U-tube mnometer E..5 γ Emle.5 B h γ h γ h 5

6 Δu, Δ, Δ Q( the olume rte of γ h B γ h h γ ( h h ( γ γ ) the flow) k B ) B B.6. g.. Inlned tube mnometer l B γ l B γ nθ nθ Smll dfferene n g reure If e & B ontn g.7 Mehnl nd Eletron Preure Meurng Dee. Bourdon reure gge (elt truture) Bourdon Tube, ured tube trght deformton dl. ero redng on the gge ndte tht the meured reure. nerod brometer-meure tmoher reure (bolute reure). Preure trnduer-reure V.S. tme 6

7 Bourdon tube onneted to lner rble dfferentl trnformer (LVDT), g..4 ol; oltge Th oltge lner funton of the reure, nd ould be reorded on n ollogrh, or dgted for torge or roeng on omuter. Ddntge-elt enng elementme. reure re tt or onl hngng lowl (qu-tt). reltel m of Bourdon tube <dhrgm> *trn-gge reure trnduer * g..5 (rterl blood reure) eo-eletr rtl. (ef., 4, 5) H.8 Hdrott ore on Plne Surfe g..6 Preure nd reultnt hdrott fore deeloed on the bottom of n oen tnk. Storge tnk, h. or flud t ret we know tht the fore mut be erendulr to the urfe, ne there re no herng tre reent. 7

8 . Preure re lnerl wth deth f nomreble d γ ρg γh for oen tnk, g..6 d The reultnt fore t through the entrod of the re dθ τ 0 * Eere.66 dτ τd torque herng tre d ( dθ )l dτ Τ lτ lτdθ 0 π dθ πlτ w ume elot dtrbuton n the g lnerτ μ 0 Τ π lμw 0 8

9 d γhd γhd γ nθd f θ, γ re ontnt. γ nθ d d frt moment of the re γ nθ γh Inde. Of θ C The moment of the reultnt fore mut equl the moment of the Dtrbuted reure fore d γ nθ d Q γγ nθ C d I d eond moment of the re (moment of nert) I ; I I 9

10 I I I >, I et ee g..8 Note: I-the rodut of nert wrt the & re. I-the rodut of nert wrt to n orthogonl oord. tem ng through the entrod of the re. If the ubmerged re mmetrl wrt n e ng through the entrod nd rllel to ether the or e, the reultnt fore mut le long the lne, ne I 0. Center of reure (eultnt fore t ont) Emle.6 求. ;(, ) b. M ( moment ) 0

11 . b. Eq..8 Eq..9, M 0 (hft ; wter) M ( 6.6m N ) N m.9 Preure Prm Preure re lnerl wth deth. See g..9

12 h Pe γ ( ) olume of reure rm h ( γh)( bh) γ No mtter wht the he of the reure rm, the reultnt fore tll equl n mgntude to the olume of the reure rm nd t e through the entrod of the olume. rt, drw the reure rm out. Emle.8 d d γ γ 0 ( γh h h γ ( ) N 5.4KN 0 0 (0.m) (0.m) 0.96m ) N

13 .0 Hdrott ore on Cured Surfe. Eq. Deeloed before onl l to the lne urfe mgntude nd loton of. Integrton: tedou roe/ no mle, generl formul n be deeloed.. g.. ; W lne urfe γv; through C.G(enter of grt ) H, V The omoment of fore tht the tnk eert on the flud. or equlbrum, H ; ollner. through t V W Emle.9 排水管受力情形 See g..8

14 γh lb 6.4 ft 8lb ft ( ft ) lb π ω γ ρg 6.4 ft ft 44lb t C.G (Centrod; ft 4 enter of reure, CP; enter of grt) 4 I C C ft ft ft 4 4 Smlrl. 7 ft.7 ft π π 8lb; ω 44lb; 0 H tnθ H V H V θ tn V 5lb - H V.5. Buon, lotton, nd Stblt.. 阿基米德原理請看圖.4, 來分析其受力情形 γv 任意 形狀的物體之體積.. Stblt tble equlbrumeln g..5; 6; 7; 8 B 4