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Chapter 10: Fluids. Fluids: substances which flow Liquids: take the shape of their container but have a definite volume Gases: take the shape and volume of their container Pressure in a fluid: force per area P = F/A
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Chapter 10: Fluids • Fluids: substances which flow • Liquids: take the shape of their container but have a definite volume • Gases: take the shape and volume of their container • Pressure in a fluid: force per area P = F/A • Force = normal force, pressure exerts a force perpendicular to the surface. • pressure of the bottom of a container on a liquid balances the pressure the liquid exerts on the container bottom • Units for pressure: • 1 N/m2 = 1 Pa • 1 Bar = 105 Pa ~ atmospheric pressure (14.7 psi)* • 1 atmosphere = 1.01 E5 Pa • 1 mm Hg = 1.33E2 Pa • 1 torr = 1.33E2 Pa • 1 lb/in2 (psi) = 6.89 E3 Pa • *atmospheric pressure varies from .970 bar to 1.040 bar
Most pressure gages detect pressure differences between the measured pressure and a reference pressure. • absolute pressure: the actual pressure exerted by the fluid. • gauge pressure: the difference between the pressure being measured and atmospheric pressure. • P = Pgauge + Patm • Some important aspects of pressure in a fluid • The forces a fluid at rest exerts on the walls of its container (and visa versa) always perpendicular to the walls. • An external pressure exerted on a fluid is transmitted uniformly throughout the volume of the fluid. • The pressure on a small surface in a fluid is the same regardless of the orientation if the surface.
Pexternal • h • P • Pressure and Depth • A fluid supports itself against its weight with pressure. • The fluid also must support itself against external pressure • P = F/A = Pexternal + weight of fluid • w = mg = r Vg V = Ah • P = Pexternal + rgh DP = rgDh • A
Example: A tank is filled with water to a depth of 1.5 m. What is the pressure at the bottom of the tank due to the water alone? Example: How high above an IV insertion point into the patient’s arm must the saline bag be hung if the density of the saline solution is 1E3 kg/m3 and the gauge pressure inside the patient's vein is 2.4E3 Pa?
F2 = PA2 F1 = PA1 p Pascal’s Principle: The pressure applied at one point in an enclosed fluid is transmitted to every part of the fluid and to the walls of the container. Example: An application of pressure in a fluid is the hydraulic press. The smaller piston is 3 cm in diameter, and the larger piston is 24 cm in diameter. How much mass could be lifted by a 50 kg woman putting all her weight on the smaller piston?
Buoyant force: • pressure balances gravity for a fluid to support itself. Fnet= rfluidVg Fnet= w = rVg • Archimedes’ principle: • Buoyant force = weight of fluid displaced • Fbuoyant = Vrg Example: An object of density r is submerged in a liquid with density r0. What is the effective weight of the object in terms of the densities and the original weight of the object.
Example: Icebergs are made of freshwater (density of 0.92 E3 kg/m3 at 0ºC). Ocean water, largely because of dissolved salt, has a density of 1.03E3 kg/m3 at 0ºC. What fraction of an iceberg lies below the surface?
F • Surface Tension: attraction of molecules in liquid for each other result in imbalance in the net force for charges near the surface. • Surface Tension is a force per unit length. • Example: lifting a ring of circumference C out of a liquid surface • Surface Tensions g = F/2C • Capillary Action: • Fy = T-mg • = 2prg cos q – rpr2hg =0 g g q
