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Unformatted text preview: April 10, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 42 April 10, 2006 Physics for Scientists&Engineers 1 2 Review - Stress and Strain Review - Stress and Strain ! stress = modulus · strain ! Stretching ! Compression ! Shear F A = E ! L L p = B ! V V F A = G ! x L April 10, 2006 Physics for Scientists&Engineers 1 3 Pressure Pressure ! Density is defined as mass per unit volume ! Pressure is defined as force per unit area ! The SI unit of pressure is N/m 2 , which has been given the name Pascal, abbreviated Pa ! The average pressure of the Earth’s atmosphere, 1 atm, is ! Atmospheric pressure is often quoted in non-SI units ! = m V p = F A 1 Pa = 1 N 1 m 2 1 atm = 1.013 ! 10 5 Pa 1 atm = 760 torr = 760 mm Hg = 14.7 lb/in 2 = 29.92 in. Hg April 10, 2006 Physics for Scientists&Engineers 1 4 Pressure-Depth Relationship Pressure-Depth Relationship ! Consider a container of water open to the Earth’s atmosphere ! Imagine a cube of water ! The top of the cube is horizontal and is at a depth of y 1 ! The bottom of the cube is also horizontal and is at a depth of y 2 ! The other sides are vertical ! The vertical forces on the cube must sum to zero F 2 ! F 1 ! mg = April 10, 2006 Physics for Scientists&Engineers 1 5 Pressure-Depth (2) Pressure-Depth (2) ! The pressure at depth y 1 is p 1 ! The pressure at depth y 2 is p 2 ! Assuming the area of each face of the cube is A we can write ! Assuming the volume of the cube is V and ! is the density of water, then the mass of the cube of water is F 1 = p 1 A F 2 = p 2 A m = ! V April 10, 2006 Physics for Scientists&Engineers 1 6 Pressure-Depth (3) Pressure-Depth (3) ! Remembering ! The volume of the cube of water is ! So we can rearrange and substitute for the volume ! So we get for the pressure as function of depth ! An interesting use of this formula is the pressure at a depth h below the surface of a liquid F 2 ! F 1 ! mg = p 2 A ! p 1 A !...
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This note was uploaded on 03/19/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.
- Spring '08