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/m3 Water (liquid): 1.000 x 103 kg/m3 Nitrogen (gas): 1.251 kg/m3

Pressure The unit of pressure is the pascal. 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

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 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)

Under Pressure 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= -V DP / B Substitute values: (-0.50 m3)(2.0 x 107 Pa) / (6.0 x 1010 Pa) DV = -1.6 x 10-4 m3

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 Fg Fb

Deep Sea Force 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! 1 bar = 1.00 x 105 Pa 1 atm = 1013 millibar 1 atm = 14.7 psi

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.