4.6PressureMeasurementandManometers4)Inclined-tubemanometer（斜管压力计）(1)Asshown above,thedifferential readingisproportional tothepressure difference. If the pressure difference is very small, thereading may be too small to be measured with good accuracy.Toincrease the sensitivity of the differential reading, one leg of themanometer can beinclined at an angle
4.6 Pressure Measurement and Manometers 4) Inclined-tube manometer (斜管压力计 ) As shown above, the differential reading is proportional to the pressure difference. If the pressure difference is very small, the reading may be too small to be measured with good accuracy. To increase the sensitivity of the differential reading, one leg of the manometer can be inclined at an angle
4.6PressureMeasurementandManometersand the differential reading is measured along the inclined tube.As shown above, h, = L , sin O and hencePA-P=2l,sinO+Y,h,-y,hObviously, the smaller the angle A , the more the readingis magnified
4.6 Pressure Measurement and Manometers and the differential reading is measured along the inclined tube. As shown above, 2 2 h sin and hence 2 2 3 3 11 sin A B pp h h 2 Obviously, the smaller the angle , the more the reading is magnified
4.6PressureMeasurementandManometers5）Multifluidmanometer（多流体压计管）OilThe pressure in a pressurizedtank is measured by aAIRmultifluid manometer,asisshown in the figure. ShowWATERhithattheairpressureinthetank is given byh3Pir = Patm + g(Pmercury h, - Poih, - Pwaterh)Mercury
4.6 Pressure Measurement and Manometers 5) Multifluid manometer (多流体压计管 ) The pressure in a pressurized tank is measured by a multifluid manometer, as is shown in the figure. Show that the air pressure in the tank is given by Pair atm mercury 3 oil 2 water 1 P g hh h
4.7 PressureDistributions1)FlatSurfacesOilaaWaterrWYRYhy(a
4.7 Pressure Distributions 1) Flat Surfaces
4.7PressureDistributions2)CurvedSurfacesWhen the curved surface is a circular arc (full circle or any part of it)the resultant hydrostatic force acting on the surface always passesthrough the center of the circle. This is because the elemental pressureforces are normal to the surface, and by the well-known geometricalproperty all lines normal to the surface of a circle must pass through thecenterofthecircle.PressureenvelopeSeawaterPressureforcesBuoyResuitantforceFRCableCircularsurface(a)(b)(c)
4.7 Pressure Distributions 2) Curved Surfaces When the curved surface is a circular arc (full circle or any part of it), the resultant hydrostatic force acting on the surface always passes through the center of the circle. This is because the elemental pressure forces are normal to the surface, and by the well-known geometrical property all lines normal to the surface of a circle must pass through the center of the circle