Hydrostatic Pressure. To determine the center position of pressure of a plane surface immersed in water

Transcription

1 Objectives Elementa Flui Mechanics an Lab. Elementa Test Hostatic Pessue Chapte. Hostatic Pessue To etemine the cente position of pessue of a plane suface immese in wate To compae the expeimental position with the theoeticalti esults Instucto: Seo, Il Won (5-0) Web: Backgoun theo Flui pessue? The pessue at some point within a flui Flui statics? - No elative motion between flui elements - No shea stess What is flui statics? Backgoun theo Hostatic pessue? The pessue at an given point of a static flui is calle the hostatic pessue Can t suppot sheaing stesses Pessue must be acting on nomal to suface

2 Backgoun theo How to calculate hostatic pessue? p = γ h γ h ( : specific gavit, : epth) Backgoun theo How to calculate hostatic pessue? p = γ h γ h ( : specific gavit, : epth) Wh? F z F x F x F = F + W z z No shea stess & Acting nomal to suface Foce Equilibium px px F x = p p+ z = 0 x x p z p z F z = p p+ x W = 0 z z Eventuall! p F x : = 0 Pessue is constant in a hoizontal plane x in a static flui p F z : = ρg = γ z Incease of pessue with epth in a flui of constant ensit lineal incease Δ p = γ Δz Backgoun theo Summa. Hostatic pessue: Incease lineal with epth Example of hostatic pessue Hoelectic am Fom pessue iffeence with hepth, wate gets eneg to opeate tubine.. Flui at est: Pessue must be acting on nomal to the suface. Same at all points on a hoizontal plane

3 Example of hostatic pessue Basement tleaks &hostatic ti pessue Backfill becomes satuate Hostatic pessue makes a cack at the basement wall Example of hostatic pessue Thee ae man kins of poblems. - Which point shoul we choose to intake wate fom am? - Whee shoul we elease wate to get sufficient eneg? - How can we constuct safe am? - How can we potect wate leak poblem? Basic solutions o s of these poblems come fom unestaning hostatic pessue e Wate infiltates the basement wall Hostatic pessue on submege plane Pessue istibution iagam Pessue is lineal incease fom wate suface to bottom h Cente of the aea p = ρgh z =? F =?. What is foce, F?. Whee is the point of action? Hostatic pessue on submege plane Total foce acting on suface h p = ρgh Cente of the pessue z =? F =? - Pessue at p = ρ gh - Foce acting on suface h F = p A = ρ g A = ρ ga - Fist moments of aeas Foce A = A = Sum of pessue

4 Hostatic pessue on submege plane Position of the total foce O h C p = ρgh z =? F - Moment at O M = ρg A = ρgioo = Fz (Secon moment of aea: A = I oo ) M ρ gi Ioo F ρ g A A oo z = = = - Fom paallel axis theoem I = I + A oo gg b (Rectangula : I = gg ) I Igg + A Igg oo b / z = = = + = + A A A b ( /) When t=0, Cente of pessue is locate on / own fom wate suface to bottom of submege plate Obsevation fo Total Immesion - In case of ectangula plane = - Resultant Foce F= ρ ga - Cente point of pessue b / z = + b ( /) b / c = + + ( ) q b / fom wate suface fom pivot ( Fulcum) Theoetical Value fo Total Immesion Obsevation fo Patial Immesion Foce Moment am Moment am M = M FL = Fc FL c = F = mg F F ( ) ( ) = ρ g b ρg b Foce p= ρgh Foce - Cente point of pessue z = fom wate suface Foce c = a + fom pivot (Fulcum)

5 Theoetical Value fo Patial Immesion Pinciple of Expeiment Moment am Foce Foce FL M = M FL = Fc c = F F = mg b F = ρga= ρg p = ρ g Place a weight until the balance am is hoizontal. Reco the wate level on the quaant an the weight on the balance pan. Repeat this poceue until the wate level eaches the top of the quaant. Poceue Poceue Place the quaant on the two owel pins an using the clamping scew, fasten to the balance am. Measue values of a, L, epth an with b of the quaant en face. With the Pespex tank on the bench, position o the balance am on the knife eges (pivot). 4 Hang the balance pan fom the en of the balance am. 5 Connect a hose fom the ain cock to the sump an anothe fom the bench fee to the tiangula apetue on the top of the Pespex tank. 6 Level the tank using the ajustable feet an spiit level. 7 Move the counte balance weight until the balance am is hoizontal. 8 Close the ain cock an amit wate until the level eaches the bottom ege of the quaant. 9 Place a weight on the balance pan, slowl aing wate into the tank until the balance am is hoizontal. until the balance am is hoizontal. 0 Reco the wate level on the quaant an the weight on the balance pan. Repeat the above fo each incement of weight until the wate suface level eaches the top f h f Th h i f i h i i h of the quaant en face. Then emove each incement of weight noting weights an wate levels until the weights have been emove.

6 Results Discussion a Am L epth With b Mass m (kg) Measue length cm Theoetical Value ct. Confim that the cente of pessue is below the cente of aea, an iscuss wh.. Compae the theoetical value with measue length, iscuss wh oes the iffeence occus.. Discuss wh we o not consie the pessue at the suface of ac. Wh we just calculate the pessue of the ectangula section?