Static Surface Forces. Forces on Plane Areas: Horizontal surfaces. Forces on Plane Areas. Hydrostatic Forces on Plane Surfaces
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1 Hdrostti ores on Plne Surfes Stti Surfe ores ores on lne res ores on urved surfes Buont fore Stbilit of floting nd submerged bodies ores on Plne res Two tes of roblems Horizontl surfes (ressure is ) onstnt nlined surfes d dz Two unknowns Totl fore Line of tion Two teniques to find te line of tion of te resultnt fore Moments Pressure rism d ores on Plne res: Horizontl surfes Wt is te fore on te bottom of tis tnk of wter? d weigt of overling fluid! is norml to te surfe nd towrds te surfe if is ositive. sses troug te entroid of te re. Side view Vertil distne to free surfe To view
2 ores on Plne res: nlined Surfes Diretion of fore Norml to te lne Mgnitude of fore integrte te ressure over te re ressure is no longer onstnt! Line of tion Moment of te resultnt fore must equl te moment of te distributed ressure fore ores on Plne res: nlined Surfes ree surfe? entroid B enter of ressure Te origin of te is is on te free surfe Mgnitude of ore on nlined Plne re d Emle Conrete (.6 kn/m ) Plwood orm (.m.m) d d ( ) (,6*.*)*(.*.) 85.8kN. m. m is te vertil distne between free surfe nd entroid is te ressure t te entroid of te re
3 ores on Plne res: Center of Pressure: Center of Pressure: Te enter of ressure is not t te entroid (beuse ressure is inreg wit det) oordinte of enter of ressure: d Moment of resultnt fore sum of moment of distributed fores d d d d d Produt of inerti Prllel is teorem Center of Pressure: Proerties of res d d d + d Sum of te moments d + Prllel is teorem b b d b b b+ d b b 6 b b- d 7 ( )
4 b Proerties of res b 8 b 6 nlined Surfe indings Te orizontl enter of ressure nd te orizontl entroid oinide wen te surfe s eiter orizontl or vertil is of smmetr Te enter of ressure is lws below te entroid Te vertil distne between te entroid nd te enter of ressure dereses s te surfe is lowered deeer into te liquid ( inreses) Wt do ou do if tere isn t free surfe? > Emle n ellitil gte overs te end of ie m in dimeter. f te gte is inged t te to, wt norml fore lied t te bottom of te gte is required to oen te gte wen wter is dee bove te to of te ie nd te ie is oen to te tmosere on te oter side? Neglet te weigt of te gte. Solution Seme Mgnitude of te fore lied b te wter Lotion of te resultnt fore ind ug moments bout inge wter inge m b m Mgnitude of te ore Det to te entroid b N 98 m π. m.5 MN m wter. b m inge m
5 Lotion of esultnt ore ore equired to en Gte. b b Slnt distne to surfe b b...5 m r wter. b m inge m How do we find te required fore? Moments bout te inge M inge l tot - l l l tot 6.5 N.6 89 kn l.6 r wter. b m inge m l tot ores on Plne Surfes eview Te verge mgnitude of te ressure fore is te ressure t te entroid Te orizontl lotion of te ressure fore ws t (WHY?) Te gte ws smmetril bout t lest one of te entroidl es. Te vertil lotion of te ressure fore is below te entroid. (WHY?) Pressure inreses wit det. ores on Plne res: Pressure Prism simler ro tt works well for res of onstnt widt ( ) retngles f te lotion of te resultnt fore is required nd te re doesn t interset te free surfe, ten te moment of inerti metod is bout s es
6 ores on Plne res: Pressure Prism Emle : Pressure Prism ree surfe d d d ore Volume of ressure rism Center of ressure is t entroid of ressure rism Dm is wide w /os m º Dm Volume (/os)()(w)/ ( m/.95)(98 N/m * m)()/ 6 MN Emle : Pressure Prism wter inge Solution : Pressure Prism Mgnitude of fore (98 N/m )( m)()( m).96 MN Lotion of resultnt fore mesured from inge w m m m (retngulr onduit) m w w m m 6 w w w m m
7 Eerise:.6,.67,.7,.77 irst Moments d Moment of n re bout te is d d ò Lotion of entroidl is or lte of uniform tikness te intersetion of te entroidl es is lso te enter of grvit Seond Moments lso lled moment of inerti of te re d is te nd moment wit reset to n is sg troug its entroid nd rllel to te is. Prllel is teorem Produt of nerti mesure of te smmetr of te re d Produt of inerti f or is n is of smmetr ten te rodut of inerti is zero.
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Stti Surfe ores Stti Surfe ores 8m wter hinge? 4 m ores on plne res ores on urved surfes Buont fore Stbilit of floting nd submerged bodies ores on Plne res Two tpes of problems Horizontl surfes (pressure
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