Capter FLUID STTICS by mat Sairin Demun Learning Outomes Upon ompleting tis apter, te students are expeted to be able to: 1. Calulate te pressure in pipes by using piezometers and manometers.. Calulate te ydrostati pressure fore for submerged plane surfaes (magnitude, loation and diretion and te related reation fore) inlined or vertial position.. Calulate te ydrostati pressure fore for submerged urved surfaes (magnitude, loation and diretion and te related reation fore). Study on non-moving fluid fluid at rest..1) Pressure Density Heigt Relationsip Pressure unit = N/m or Pa or Bar 1 kpa = 1 kn/m = 1000 Pa = 1000 N/m 1 Bar = 100 kpa P g = vertial eigt downward from te fluid surfae (m). If te fluid is gas or air, te pressure at all plaes are te same te pressure NOT depends on eigt. If someone says te pressure is 5 m Merury, means tat te pressure is: 1. 5710009. 81 0. 05 P g = 6.66 kpa.) Relationsip Between bsolute and Gauge Pressure P abs P gauge P atm atmosperi pressure = 101. kpa = 760 mm Hg
.) Pressure Measurements Various types of equipments used to measure pressure. 1. Barometer to measure atmosperi pressure.. neroid to measure air pressure in tyres.. Bourdon to measure fluid pressure. Bourdon pressure gauge to measure pressure of fluid in a pipe.. Piezometer to measure fluid pressure in pipes. 5. Manometers to measure fluid pressure in pipes, if piezometri tube is not pratial (pressure too ig) Te following figures sow examples of manometers.
SIMPLE MNOMETER DIFFERENTIL MNOMETER Calulation Proedures: 1. Divide te manometer into setions aording to te known vertial eigt.. Draw an arrow pointing DOWNWRD for ea of te setion.. For ea drawn arrow, mark (+) or ( ) sign. (+) for te arrow tat te diretion LEDS to te point were te pressure is to be known (referene point). ( ) for te arrow tat te diretion LEVES te referene point. If te sign is (+), te pressure for te arrow is +g and if te sign is ( ), te pressure for te arrow is g ; were is te vertial eigt of te setion ontaining te arrow wile is te fluid density in te manometer were te arrow is loated.. Canel two pressure wi ave te same magnitude but opposite diretion. Same magnitude means tat tey ave te same eigt and te same fluid density,. 5. Sum up all of te pressures taking te pressure at te referene point as te eading. If te manometer end is open, te pressure at te end is zero. If te manometer end is anoter pipe (for differential manometer), add (+) te pressure value.
.) Hydrostati Pressure Fore on Submerged Plane Surfaes Hydrostati pressure is te fore due to te fluid ating on te submerged plane surfae. Fore = Pressure x rea F = P = g unit = Newton (N) or kg.m/s Fore is a vetor tat must ave items: 1. Magnitude. Loation of at. Diretion n inlined submerged plane surfae, B is as sown in te following figure. Note:- C = Center of gravity of te Submerged Surfae G = Center of gravity of te wole Plane Surfae P = Center of Pressure (te plae were te pressure fore ats) Magnitude: F g = rea of te submerged surfae (m ). = Vertial eigt from te fluid surfae to te enter of gravity of te submerged plane surfae (C) (m). Loation: F is ating on te enter of pressure tat is at a vertial distane p from te fluid surfae were: I sin p were: = I =? te inlined angle (see figure) Moment of inertia about te orizontal line troug te enter of gravity of te submerged surfae (m ) see Table.1 Diretion: F ats at te plane surfae perpendiular (90 0 ) to te wetted surfae.
.5) Hydrostati Pressure Fore on Submerged Curved Surfaes Curved surfaes B submerged in a fluid are as sown in te following figures. Compare bot figures and spot te differenes. Two fore omponents: Horizontal fore and Vertial fore. 1) Horizontal Component, F H (a) Magnitude: F H is te fore equivalent to te fore ating on te vertial plane surfae projeted from te urved surfae (te retangular image). F H g = = area of te vertial plane surfae projeted from te urved surfae (area of te retangular image). vertial eigt from te fluid surfae to te enter of gravity of te vertial plane surfae projeted from te urved surfae (te image). (b) Loation: F H ats orizontally at te urved surfae troug te enter of pressure of te vertial plane surfae projeted from te urved surfae, tat is at te vertial eigt p from te fluid surfae, were: p I beause sin 90 0 = 1 (vertial plane surfae) I = Moment of inertia about te orizontal line troug te enter of te plane surfae projeted from te urved surfae. (m ) See Table.1. and is as (a) above.
) Vertial Component, F V (a) Magnitude: F V is te fore equivalent to te weigt of te fluid above te urved surfae. F V gv were, V = fluid volume above te urved surfae (m ) up to te fluid surfae line. (b) Loation: F V ats vertially at te urved surfae troug te enter of gravity of te fluid volume above te urved surfae (up to te fluid surfae), tat is at te orizontal distane x from a referene vertial line, were: x 1 x1 1 x ) Resultant Fore, F 1 = rea of sape 1 = rea of sape x 1 = orizontal distane from te enter of gravity of area 1 to te referene vertial line. x = orizontal distane from te enter of gravity of area to te referene vertial line. Te resultant fore of omponents F H and F V is: Magnitude: Loation: Diretion: F F H F V F ats at te urved surfae troug te intersetion point of F H and F V lines. F ats at an angle from orizontal; tan 1 F F V H.6 Te HSTTIC Computer Program HSTTIC stands for HydroSTTIC is a medium sized exeutable omputer program to solve any ydrostati pressure fore problem. It is developed by Mr. mat Sairin Demun using MS DOS based Fortran programming language. It is able to alulate te pressure fore and te reation fore of fluid ating on a submerged plane and urved surfaes. Te students an opy te file from Mr. mat Sairin Demun at no ost. To run te omputer program, te students will ave to double lik te HSTTIC file and just follow te instrutions appear on te omputer sreen. If you ave diffiulties running te omputer program, please feel free to ontat Mr. mat Sairin Demun.
TBLE.1: Geometri Properties of Plane Surfaes I I y Sape Sket rea, Lo.of M. of Inertia, I or I Centroid y b Retangle = b b I x 1 Triangle b y b I 6 Cirle d d y d I 6 Semiirle d 8 d I r y 18 I 6.8610 d Ellipse b y b I 6 Semi b Ellipse Parabola b y b x 8 y 5 b I 16 b I 7 8b I 175 Quadrant d 16 r y r x I d I 56.10 d Trapezoid a b y a b a b a ab b I 6 a b