StaticsDefinitions and ApplicationsMotivation?Upstream face of Hoover DamWhat do you think?What do we need to know?Pressure Variation with Direction (Pascal’s law)Pressure FieldSlide 9Simplify the expression for the force acting on the elementApply Newton’s Second LawPressure Variation When the Specific Weight is ConstantExample: Pressure at the bottom of a Tank of Water?Units and Scales of Pressure MeasurementMercury BarometerA few important constants!Pressure MeasurementStandard ManometersManometers for High PressuresDifferential ManometersProcedure to keep track of pressuresPressure TransducersSummary for StaticsStatics exampleStaticsStaticsCVEN 311CVEN 311Definitions and ApplicationsDefinitions and ApplicationsStatics: no relative motion between adjacent fluid layers.Shear stress is zeroOnly _______ can be acting on fluid surfacesGravity force acts on the fluid (____ force)Applications:Pressure variation within a reservoir Forces on submerged surfacesTensile stress on pipe wallsBuoyant forcesStatics: no relative motion between adjacent fluid layers.Shear stress is zeroOnly _______ can be acting on fluid surfacesGravity force acts on the fluid (____ force)Applications:Pressure variation within a reservoir Forces on submerged surfacesTensile stress on pipe wallsBuoyant forcespressurebodyMotivation?Motivation?What are the pressure forces behind the Hoover Dam?What are the pressure forces behind the Hoover Dam?Upstream face of Hoover DamUpstream face of Hoover DamUpstream face of Hoover DamUpstream face of Hoover DamUpstream face of Hoover Dam in 1935Upstream face of Hoover Dam in 1935Tall: 220 m (726 ft)Crest thickness: 13.7 m (50 ft)Base thickness: 201 m (660 ft - two footballs fields) WHY???What do you think?What do you think?Lake Mead, the lake behind Hoover Dam, is the world's largest artificial body of water by volume (35 km3). Is the pressure at the base of Hoover Dam affected by the volume of water in Lake Mead?What do we need to know?What do we need to know?Pressure variation with directionPressure variation with locationHow can we calculate the total force on a submerged surface?Pressure variation with directionPressure variation with locationHow can we calculate the total force on a submerged surface?Pressure Variation with Direction(Pascal’s law)Pressure Variation with Direction(Pascal’s law)yyxxpsspxypyxyxs2yx2yxBody forcesSurface forcesEquation of MotionxFxFF = ma02 mxx ayxa02 mxx ayxay sin sy sin s0y p -y psx0y p -y psxpxy - pss sinIndependent of direction!Pressure FieldPressure FieldIn the absence of shearing forces (no relative motion between fluid particles) what causes pressure variation within a fluid?In the absence of shearing forces (no relative motion between fluid particles) what causes pressure variation within a fluid?p1p2p3Which has the highest pressure?ppzzx yFHIK 2Pressure FieldPressure Fieldppyyx zFHGIKJ 2    m x y zjizzyyxxkppzzx yFHIK 2ppyyx zFHGIKJ 2Small element of fluid in Small element of fluid in pressure pressure gradientgradient with arbitrary __________. with arbitrary __________.Forces acting on surfaces of elementPressure is Pressure is pp at at center of elementcenter of elementaccelerationMass…Mass…Same in Same in xx!!Simplify the expression for the force acting on the elementSimplify the expression for the force acting on the element   Fpyx y zy    Fpxx y zx    Fpzx y zz    F i j k FHGIKJpxpypzx y z   pxpypzp  i j k   F    p x y zSame in Same in xyzxyz!!This begs for vector notation!This begs for vector notation!Forces acting on element of Forces acting on element of fluid due to pressure gradientfluid due to pressure gradient  F ppyyx z ppyyx zy FHGIKJ FHGIKJ2 2Apply Newton’s Second LawApply Newton’s Second Law F a m  p x y z x y z      a  pa   F    p x y z    m x y zMass of element of fluidMass of element of fluidSubstitute into Newton’s 2nd LawObtain a general vector expression Obtain a general vector expression relating pressure gradient to relating pressure gradient to accelerationacceleration and write the 3 component equations.and write the 3 component equations.x y zp p pa a ax y zr r r� � �= =- -�=-� �  dpdzg ˆp r g- � = +a kText version of eq.Text version of eq.At rest (independent of At rest (independent of xx and and yy) ) 3 component equations3 component equationsPressure Variation When the Specific Weight is ConstantPressure Variation When the Specific Weight is ConstantWhat are the two things that could make specific weight () vary in a fluid?What are the two things that could make specific weight () vary in a fluid? dzdp dzdpconstant zp constant zp constant z pconstant z p2211zp zp2211zp zp = gCompressible fluid - changing densityChanging gravityPiezometric head is constantExample: Pressure at the bottom of a Tank of Water?Example: Pressure at the bottom of a Tank of Water?2211zp zp2211zp zpDoes the pressure at the bottom of the tank increase if the diameter of the tank increases?hp = hNO!!!!1122 zzpp2112 zzpp2112hpp12hpp126894.76 Pa = 1 psiUnits and Scales of Pressure MeasurementUnits and Scales of Pressure MeasurementStandard atmospheric pressureLocal atmospheric pressureAbsolute zero (complete vacuum)Absolute pressureGage pressure1 atmosphere101.325 kPa14.7 psi______ m H20760 mm HgSuction vacuum(gage pressure)Local barometer reading10.3410.3429.92 in HgWhat is the local atmospheric pressure (in kPa) when R is 750 mm Hg?Mercury BarometerMercury Barometer2211zp zp2211zp zp6.13HgS6.13HgSR12 1221zzp pHg 1221zzp pHg p2 = Hg vapor pressureR pHg1R