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Pressure

This article provides a detailed explanation of matter and pressure, covering topics such as incompressible solids, compressible gases, density, volume stress, bulk modulus, and the effects of pressure on liquids and gases. It also discusses surface tension and capillary action.

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Pressure

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  1. Pressure

  2. Solid Incompressible Subject to shear force Gas Compressible Not subject to shear force Solids, Liquids, and Gases • Normal matter is made of atoms. • Atoms can interact to form three types of matter. • Liquid • Incompressible • Not subject to shear force

  3. Density • Matter has mass and takes up volume. • The ratio of the mass to the volume is the density. • Incompressible materials maintain their density. Salt (solid): 2.165 x 103 kg/m3 Water (liquid): 1.000 x 103 kg/m3 Nitrogen (gas): 1.251 kg/m3

  4. Pressure • Matter can exert the same force in all directions. • The ratio of the force exerted to the area is the pressure. • It’s a scalar, not a vector • The unit of pressure is the pascal. • 1 Pa = 1 N/m2 • Same type as stress

  5. Volume Stress • Pressure from all sides can change the volume of a solid. • Volume stress measures the pressure. • Volume strain measures the change in area. P DV V A (surface area)

  6. Bulk Modulus • Pressure changes volume, not length. • Bulk modulus B relates changes in pressure and volume. • The negative sign represents the decrease in volume with increasing pressure. P DV V A (surface area)

  7. Steel has a bulk modulus of B = 60 GPa. A sphere with a volume of 0.50 m3 is constructed and lowered into the ocean where P = 20 MPa. How much does the volume change? Use the relation for bulk modulus. B = -(DP) / (DV/V) DV= -VDP / B Substitute values: (-0.50 m3)(2.0 x 107 Pa) / (6.0 x 1010 Pa) DV = -1.6 x 10-4m3 Under Pressure

  8. Liquids and gases are fluids. Any area in the fluid experiences equal forces from each direction. This is just the law of inertia. All forces are balanced Forces are still vectors Any arbitrary volume in the has balanced forces. Surface Force

  9. Fluids at Depth • Vertical pressures are not the same. • Pressure below is higher • Pressure above is less • Include the weight Ft Fg Fb

  10. The deepest point in the ocean is 11.3 km. What is the pressure at that depth? P0 = 1.013 x 105 Pa Water r = 1000. kg/m3 The pressure increases linearly with depth. Solve for P = P0 + rgh. h is positive with depth. Substitute values: rgh = 1.11 x 108 Pa. This is much larger than P0. P = 1.11 x 108 Pa This is 1100 atm! Deep Sea Force 1 bar = 1.00 x 105 Pa 1 atm = 1013 millibar 1 atm = 14.7 psi

  11. Surface Tension • Liquid molecules attract each other. • Cohesion to self • Adhesion to other material • At the surface this force is the surface tension. • Force per length parallel to the surface: g • Constant for different liquids insect leg on water

  12. Capillary Action • Liquid surfaces adhere to adjacent solids. • The contact angle q depends on the liquid and solid. • The surface tension can support a weight of fluid.

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