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PHY1122 (47)
Chapter

Fluid Statics 12.1 - 12.3

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Department
Physics
Course
PHY1122
Professor
Andrzej Czajkowski
Semester
Winter

Description
• Fluid: liquid or gas • Fluid statics: study of fluids at rest in equilibrium 12.1 Density • Density (ρ) = mass / Volume • o Unit: kg / m^3 • Specific Gravity: ratio of material's density to the density of water (1000 kg/m^3) • o No units • Average density • o Human body (bones vs fat) o Atmosphere • Useful for determining battery charge Example 12.1 The Weight of a Roomful of Air Q) Find mass and weight of air at 20C in a room w/ 4.0 m x 5.0 m floor and a ceiling 3.0 m high, and the mass and weight of an equal volume of water. A) V = (4.0)(5.0)(3.0) = 60 m^3 m(air) =ρ(air)V = (1.20 kg/m^3)(60 m^3) = 72 kg w(air) = m(air)g = (72g)(9.8 m/s^2) = 700 N = 160 lb m(water) = ρ(water)V = (1000 kg/m^3)(60 m^3) = 6.0 x 104 kg w(water) = m(water)g = (6.0 x 10.4 kg)(9.8 m/s^2) = 5.9 x 10^5 N = 1.3 x 10^5 lb = 66 tons 12.2 Pressure in a Fluid • Pressure (p) = dF(perp) / dA • o If pressure is the same at all points of a finite plane then o  p = F(perp) / A o F(perp) = net normal force on one side of surface o Unit: 1 pascal (Pa) = 1 N/m^2 o  1 bar = 10^5 Pa  1 millibar = 100 Pa • Atmospheric pressure (pa): pressure of earth's atmosphere at the surface • o 1 atmosphere (atm) = 101,325 Pa = 1.013 x 10^5 Pa Example 12.2 The Force of Air Q) In the room from Example 12.2, what is the total downward force on the floor due to an air pressure of 1.00 atm? A) A = (4.0)(5.0) = 20m^2 F(perp) = pA = (1.013 x 10^5 N/m^2)(20 m^2) = 2.0 x 10^6 N = 4.6 x 10^5 lb = 230 tons • Fluid's weight usually not negligible, so pressure in fluid varies throughout volume • Pressure in a fluid of uniform density • o p2 - p1 = -ρg(y2 - y1) o  p1, p2 pressures at elevation y1, y2; ρ and g are constant o p = p0 + ρgh o  p, p0 pressures at depth, surface; h = depth of p below surface (y2 - y1)  At any given level, two points have same pressure regardless of shape • Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel • o p = (F1 / A1) = (F2 / A2) and F2 = (A2/A1)F1 • Hydraulic lift multiplies force by factor equal to ratio of the areas of two pistons • Density of air changes too much over large heights to use p =p0 + ρgh but liquids are nearly incompressible • Gauge Pressure: excess pressure above atmospheric pressure • o psig = pounds per square inch gauge • Absolute Pressure: total pressure (including atmospheric) • o psia = pounds per square inch absolute Example 12.3 Finding Absolute and Gauge Pressure Q) 12.0 m deep water in a storage tank with an open top is open to the atmosphere
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