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Solids and Fluids

Solids and Fluids. Summary. Elastic deformation of solids – Basic concept: . Stress = Force per unit area , causes the deformation Strain = Measure of the deformation Elastic modulus = The larger it is the harder to deform . We’ve seen three different types of deformation: .

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Solids and Fluids

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  1. Solids and Fluids Summary PHY231

  2. Elastic deformation of solids – Basic concept: Stress = Force per unit area , causes the deformation Strain = Measure of the deformation Elastic modulus = The larger it is the harder to deform • We’ve seen three different types of deformation: • Young’s modulus (Y): Elasticity in length • Shear modulus (S): Elasticity of shape • Bulk modulus (B): Elasticity of Volume

  3. Density = Mass / Volume • Density of an object: • Pressure : (from force perpendicular to surface) Pressure = Force / Area Pressure in Pa = N/m2 • Pressure in a static fluid Pressure increases with depth. If location 2 is deeper by a height h compare to a higher location 1 in the fluid, one has: Open tube manometer Measure P of the fluid Barometer Measure atm. pressure Gauge pressure = P-P0

  4. Pascal’s principle • Application: • Lifting of heavy objects using small forces Change in pressure is transmitted everywhere in an enclosed fluid Pressure transmitted to the right • Buoyant force B (supportive force from a fluid) Add pressure on the left A small force F1 creates a large force F2 because area A1 is much smaller than area A2 (same pressure F1/A1=F2/A2) Enclosed fluid Buoyant force is equal to the weight mfg of the fluid displaced by the object • Object denser than the fluid sinks • - Object less dense than the fluid floats: • - To float, the object must displace a mass of fluid equals to its own mass

  5. Flow rate: How much volume of fluid is transported every second in the fluid • Equations for incompressible and non-viscous fluid in motion: Continuity equation: Typically, fluid flowing in a pipe. If the cross-section of the pipe changes from A1 to A2, the velocity of the fluid must change. Pipe gets smaller, velocity increases. Bernouilli’s equation: At two different locations in the fluid. Comes from energy conservation. P is the static pressure seen before. v is the velocity of the fluid and y the height. Typically when fluid speeds up the static pressure decreases. • For viscous fluids, use Poiseuille’s law: Flow rate depends very strongly on the radius R of the pipe it is flowing through. Flow rate increases also with pressure drop DP and decreases for larger fluid viscosity h and larger pipe length L

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