Physics 116 Lectures -- part 4

Physics 116 Lectures -- part 4 - Lecture 31 April 7 2010...

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Lecture 31, April 7, 2010 Last lecture: Gravitation Today: Static Fluid: pressure Fluid in motion Next lecture: (Chapter 14) Static Fluid Fluid in motion
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Fluids A gaseous or liquid fluid Can only sustain forces directed to its surface Flows to fill its container Density ρ = m/ V (kg/m 3 ) Water: 10 3 , Air ~1, Ion 10 4 , Pressure p = F / A (N/ m 2 =1 Pascal) 1 atmosphere = 1.0 x 10 5 Pascal 1 bar= 1 atmosphere = 760 mm of Hg =14.7 lb/in 2
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Fluids at rest Consider the forces on a submerged, pillbox-shaped element of fluid. Since it is in equilibrium, . Thus, So, pressure in a fluid rises linearly with depth, and does not depend on any horizontal dimension. The equation is valid for both liquid and gas. 0 i F gh p p gh p p gdh dp h p dh g dp Adh g dV g gdm dF Adp dF pA A dp p h p g g 0 or , then direction, downward in the increase and both If . So, 0 ) 0 0 0
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Pressure Absolute pressure at depth h to a liquid is P=P 0 + gh, where is the density of the liquid, P 0 is the pressure at the surface. The gauge pressure P-P 0 = gh,
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Pressure Measurements Manometers: (Shape is arbitrary) For the U-tube shown, p 0 is the reference pressure, so in the bulb, Absolute Pressure p=p 0 + ρ gh Gauge Pressure, p-p 0 = ρ gh , measures pressure above that of the reference Barometers: When the bulb pressure p=0 , then - p 0 = ρ g(-h) is the B arometric Pressure This is often quoted as height of column supported 760 mm of Hg, or 29.9 in of Hg.
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