Pressure Solids Liquids and Gases Normal matter is

Pressure

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

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/m 3 Water (liquid): 1. 000 x 103 kg/m 3 Nitrogen (gas): 1. 251 kg/m 3

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/m 2 • Same type as stress

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)

Bulk Modulus P ] 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. DV V A (surface area)

Under Pressure ] ] Steel has a bulk modulus of B = 60 GPa. A sphere with a volume of 0. 50 m 3 is constructed and lowered into the ocean where P = 20 MPa. How much does the volume change? Ø Use the relation for bulk modulus. Ø B = -(DP) / (DV/V) Ø DV= - V DP / B Ø Substitute values: Ø (-0. 50 m 3)(2. 0 x 107 Pa) / (6. 0 x 1010 Pa) Ø DV = -1. 6 x 10 -4 m 3

Surface Force ] ] ] 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.

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

Deep Sea Force ] The deepest point in the ocean is 11. 3 km. Ø Ø ] Ø h is positive with depth. What is the pressure at that depth? • P 0 = 1. 013 x 105 Pa • Water r = 1000. kg/m 3 1 bar = 1. 00 x 105 Pa 1 atm = 1013 millibar 1 atm = 14. 7 psi The pressure increases linearly with depth. Solve for P = P 0 + rgh. Ø Substitute values: Ø rgh = 1. 11 x 108 Pa. Ø This is much larger than P 0. Ø P = 1. 11 x 108 Pa Ø This is 1100 atm!

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

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.