fluid_statics_1

# fluid_statics_1 - Fluid Statics 1 Pressure on Inclined...

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Unformatted text preview: Fluid Statics 1 Pressure on Inclined Plane 2F), 2 —0'SAsAxsin«9+ O‘yAZAx = 0 ZFZ = USASAxcosﬁ—UZAyAx—yAV : O assint9=0yAz/As ascosé’zasz/As—yé-AyAz/As szAxAyAz/Z cosﬁsz/As sin¢9=Az/As 1 as = 0—2 +§7Assin6 Letting AS ——> 0 While keeping the orientation the same as = 0'), 2 0‘2 and all the stresses are equal aszayzazz—p Hydrostatic Equation , (Pi-'gédz) olx dz 3min. /: / g /’ -‘-z9.a The vertical pressure change is _ dp _ 5]? dp —;)EdZ——a§dz For equilibrium 5 ZFx = pdydz— (p +£dxmydz = 0 2F), 2 pdxdz—(p+g—ygdy)dxdz = 2 F Z = pdxdy — (p + g—gdzﬁxdy — ydxdydz = 0 6—!)20, a—p=0, and ap— 5x 0y 62 —7 The pressure doesn’t change With X and y, i.e. the pressure is constant on horizontal surfaces. The pressure only changes with z dp___. a?“ 7 Pressure Distributions Constant speciﬁc weight [7:191 atZ=Z1 Hydrostatic Pressure Distribution [91 — p = 7(2—21) =998N/m3(10)m _—. 9880N/m2 iolk 93a, Atmospheric and Liquid Pressures p=pa+7(h—z) pa=101,OOON/m2=101kPa pozpaH/h atz=0 pzpa +y depth Atmospheric Pressure Barometer pa : pv + 7k pv = 13 80P6l for mercury h: (p, —pv)/;/=(101000—1380)/(13.6x9810)=0.747m= 747mm For water pv = 2760N/m2 h=(pa—pv)/7:(101000—276O)/981O=10.0m For a gas with variable speciﬁc weight dp__ __ __ p _ E— 7— pg— ﬁg p—pRT dp__ g ?‘ ﬁdz For constant temperature —i(z—z) P _ g p _ 1 lnplp1——ﬁ(z—Zl) and E4 RT For AZ : 10m , Ap : —O. 12% Pressure ~ constant I Atmospheric Pressure Variation Linear temperature variation in the troposphere, 0 < z < 11km T=T1 +m(z—Zl) gdZ p RT R[T1+m(z—zl)] — / R p : T1+m(z——zl)] g m 191 T1 For the troposphere Z £1 1.0km T=288—6.Sz p=101300(1—0.02257z)5-25 For the stratosphere 11.0 s z 3 20.0111 T1: —56.50C = 216.50K p :2263090.1577(Z-11-0) 11.0szs20.0 60 50 47.3 km 40 Troposphere I '30 Stratosphere Altitude. km . ' 20 10 O r — BO — BO — 4O — 20 O +‘20 Temperature, ° C Properties of the U.S. Standard Atmosphere (SI Units)a W Dynamic Acceleration Density, viscosity, Altitude Temperature of gravity, Pressure, p p u (m) (°C) 9 (m/sz) [N/m2(abs)] I (kg/m3) (N-s/mz) -1,000 21.50 9.810 ' 1.139 E + 5 1.347 E + O 1.821 E y 5 0 15.00 9.807 1.103 E + 5 1.225 E + 0 1.789 E —- 5 1,000 8.50 9.804 8.988 E + 4 1.112 E + 0 1.758 E — 5 2,000 2.00 9.801 7.950 E + 4 1.007 E + 0 1.726 E — 5 3,000 14.49 9.797 7.012. E +4 9.093 E — 1 1.694 E — 5 4,000 —10.98 9.794 6.166 E + 4 8.194 E — 1 1.661 E — 5 5,000 —17.47 9.791 5.405 t E + 4 7.364 E — 1 1.628 E — 5 6,000 —23.96 9.788 4.722 E + 4 6.601 E — 1 1.595 E — 5 7,000 , —30.45 9.785 4.111 E + 4 5.900 E — 1 1.561 E — 5 8,000 —36.94 9.782 3.565 E + 4 5.258 E — 1 1.527 E —' 5 9,000 ~43.42 9.779 _ 3.080 E + 4 4.671 E — 1 1.493 E — 5 10,000 —49.90 9.776 I 2.650 E + 4 4.135 E — 1 1.458 E — 5 15,000 ~56.50 9.761 1.211 E + 4 1.948 E — 1 1.422 E — 5 20,000 —56.50 9.745 5.529 E + 3 8.891 E — 2 1.422 E — 5 25,000 ~51.60 9.730 2.549 E + 3 4.008 E — 2 1.448 E — 5 30,000 —46.64 9.715 1.197 E + 3 1.841 E — 2 1.475 E — 5 40,000 ~22.80 9.684 2.871 E + 2 3.996 E — 3 1.601 E — 5 50,000 . —2.50 9.654 7.978 E + 1 1.027 E — 3 1.704 E — 5 60,000 . —26.13 9.624 2.196 E + 1 - 3.097 E — 4 1.584 E — 5 70,000 —53.57 9.594 5.221 E + 0 8.283 E — 5 1.438 E — 5 80,000 —74.51 9.564 1.052 E + O 1.846 E —' 5 1.321 E — 5 =51?" 1.. a Data from Standard Atmosphere, 1976, US. Government Printing Office, Washington, D.C. Manometry and Pressure Measurement Manometer - For the left leg p1 —p3 =—;/g(z1 —z3) For the right leg 192 —p3 :_yg(z2 _Z3) p1“p2 :7g(22 ”' 1>:7gh For oil (speciﬁc gravity of 0.7) with h=lOcm p1 — p2 = 0.7(9810)(O.10) = 687Pa. ForPZZPa P1"P2=P1“Pa=plg=ygh. Measurement of Pressure in 21 Tank with Liquid £3le in .i #mmﬁ G 2:33“ pc 21961 Where pc :pb+y(h1 +h2) gand pd :gpaﬂ/gh pb _pa ...
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