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Unformatted text preview: 1 Solids and Fluids Chapter 9 Solids and Fluids c Solids c Definite shape and volume c Fluids c Liquids c Definite volume – Shape of container c Gases c Shape and volume of its container Solids Not really “solid” c All solids are deformable c It is possible to change the size and/or shape of an solid through the application of external forces c When the forces are removed, the object tends to return to its original shape c This is elastic behavior 2 Simple Model of a Solid Stress and Strain c Stress = Applied force per unit cross sectional area. Stress = F/A (N/m 2 ) (Related to the force causing the deformation) c Strain = Fractional change in length. Strain = ∆ L/L (no units) (A measure of the degree of deformation) Stress Vs Strain (Experimental) 3 Hooke’s Law c Elastic modulus = (F/A)/( ∆ L/L ) c Elastic modulus = stress/strain c Based on experiment c Elastic Modulus (Units N/m 2 ) c Young’s Modulus Y (Length deformation) c Shear Modulus S (Shape deformation) c Bulk Modulus B (Volume deformation) Length Deformation c Elastic Modulus c Y ≡ (F/A)/( ∆ L/L ) c Young’s modulus c Y = p/( ∆ L/L ) Shape Deformation c Elastic Modulus c S ≡ (F/A)/(x/h) c Shear Modulus c S < Y c In fact S ≈ Y/3 for many materials 4 Volume Deformation c Elastic Modulus c B =  (F/A)/( ∆ V/V ) c Bulk modulus c p = B . ( ∆ V/V ) Elastic Moduli Summary c Y = (F/A)/( ∆ L/L ) c S = (F/A)/(x/h) c S < Y c S ≈ Y/3 for many materials c B =  (F/A)/( ∆ V/V) Definition of Pressure Fig 96 c SI unit of pressure is the Pascal (Pa) c By definition we have c 1 Pa = 1 N/m 2 5 Example 92 Find the pressure required to change the volume of a liter of water by 0.10% ∆ V/V = 0.001 V = 1 Liter B water = 2.2x10 9 N/m 2 p = B( ∆ V/V ) = 2.2x10 9 N/m 2 . 0.001= 2.2x10 6 N/m 2 p = 22 atm [Not very compressible] Problem c If 1.0 m 3 of concrete weighs 5.0 x 10 4 N, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? (The maximum pressure that can be exerted on the base of the structure is 1.7 x 10 7 Pa)....
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 Spring '09
 JamesR.Boyd
 Fluid Dynamics, elastic modulus, totally submerged object

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