u open paren r close paren equals the fraction with numerator cap G and denominator 4 mu end-fraction open bracket open paren cap R sub 1 squared minus r squared close paren minus open paren cap R sub 1 squared minus cap R sub 2 squared close paren the fraction with numerator l n open paren cap R sub 1 / r close paren and denominator l n open paren cap R sub 1 / cap R sub 2 close paren end-fraction close bracket Problem 2: Force Exerted by a Converging Nozzle A pipe of area cap A sub 1 carries an incompressible fluid at density and velocity cap V sub 1 . A converging nozzle at the end reduces the area to cap A sub 2 , discharging the fluid into the atmosphere ( cap P sub a t m end-sub ). Find the force cap F sub x exerted by the nozzle on its support. MIT OpenCourseWare 1. Apply Continuity Equation
The pressure increases logarithmically toward the hinge as the gap narrows, driven by the viscous resistance of the fluid being squeezed out. MIT OpenCourseWare Recommended Resources Advanced Fluid Mechanics - Video #7 - Laminar Flow 2 advanced fluid mechanics problems and solutions
u(y)=Uyhu open paren y close paren equals cap U y over h end-fraction u open paren r close paren equals the