phy53 lecture dr. brown 11 november 2010 review -- flow [laminar,uniform] ... venturi effect ... develop bernoulli equation flow: I_v = A v = "volume" current ; multiply by density to get "mass" current conservation of mass and incompressible fluid gives A_1 v_2 = A_2 v_2 venturi effect: the pressure decreases where fluid velocity increases explains airplane upward thrust on wing [airfoil], etc. paper rises as air blown across top of dangling piece of paper bernoulli: P + \rho g h + \frac{1}{2} \rho v^2 = constant comes from work = \Delta K or work by fluid = \Delta E_{mechanical} energy per unit volume = units of pressure [to get more precise - handling more complex fluid flow would need Navier-Stokes thm] problem examples: pressurized tank with spout above tank Torricelli's Law...coming open tank with small hole [facuet] near bottom -- velocity of fluid coming out is \sqrt{2gh} Drag forces at inside surface of pipe...velocity gradient from outside to; requires work to keep fluid moving..so (P_1 - P_2) = I_v R where R is the "resistance" of the pipe "Ohm's Law" for fluid in pipe what if large diameter? what if pipe longer? viscocity ... reynold's number ... laminar vs turbulent flow ... you can hear turbulent flow in blood vessels via stethescope [sp]... blood thinners reduces viscocity introduce...new topic,,,picture of solid...atoms connected via springs; apply force to each end look at amount it stretchs...