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Chapter 9 Fluid Dynamics 9.3 The density of a substance of uniform composition is defined as mass per unit volume m ρ= V Molten Granite Water 9.3 Common Density Units and Substances Volume: 1 cm3 = 1 ml 1000 ml = 1000 cm3 = 1 liter 1 m3 = 1,000,000 cm3 1 m3 = 35.3 ft3 1 gallon = 231 in3 Density: 1 gram/cm3 = 1000 kg/m3 = “62.4 lb/ft3” Substance g/ mL 1. Water 1.0 2. Glycerin 1.3 3. Iron 7.9 4. Silver 10.5 5. Lead 11.3 6. Gold 19.3 7. Platinum 8. Air 21.4 .0013 Pressure is defined as force per unit area F P= A Units: lb /in2 = PSI N/m2 = Pascal (Pa) Hydrostatic Pressure 1. Fluids exert pressure in all directions 2. Fluids exerts pressure perpindicularly to any surface that it contacts 1. 2. Variation of “P” w/ Depth 1. All points at same depth have = Pressure 2. As depth increases , P increases but why? F mg P= a) P = A A m ρ = → m = ρ V b) A block of fluid in a fluid!!! V ρ g(A • y) c) P = A P = ρgΔy y F F Absolute Pressure Takes into account air pressure above water plus the pressure from the water! P0 = 1 x 105 Pa P = P 0 + ρgh absolute P = 3 x 105 Pa Sometimes called gauge pressure Buoyancy:the difference in pressure on the upper and lower surfaces of an object immersed in a liquid results in an upward force on the object Archimedes’ Principle: “ Any submerged body will be buoyed up by a force equal to the weight of the fluid displaced!” Fb = ρVg FB FW Boat weighs 20 tons, put it into the beaker and collect the run -off water 20 ton boat =20tons water displaced!!! 9.6 Fluid Flow Continuity:the flow rate of a liquid through its cross section is the same at any point along its path A1v1 = A2v 2 9.7 Bernoulli’s Principle where fluid flow is fast, internal pressure is low, and vice versa. But Why??? 9.7 Conservation of Work Energy Theorem Applied to an airplane wing W=KE + PE Work in + Potential energy at the bottom + kinetic energy and the bottom = 1 2 P + ρv + ρgy = k 2 Work out + Potential energy at the top + Kinetic energy at the top.