Civil and Environmental Engineering 2224 Study Guide - Final Guide: Free Surface, Hardy Cross, Pipe Networks

• School: Western University
• Department: Civil and Environmental Engineering
• Course: Civil and Environmental Engineering 2224
• Professor: Craig Miller

Document Summary

Internal flow: assume developed flow velocity profile (laminar) or flow characteristics (turbulent) constant in flow direction exclude entrance region, laminar flow between parallel plates, laminar flow in a circular pipe, friction loss for turbulent flow. , max. velocity at y=a(cid:2870), then v =(cid:2870)(cid:2871)u(cid:2923)a(cid:2934), shear: radius r0, separated by distance a, upper plate velocity u, velocity profile u(cid:4666)y(cid:4667)=u(cid:2935)a (cid:2869)(cid:2870)(cid:2972)[(cid:2914)(cid:2914)(cid:2934)(cid:4666)p+ gh(cid:4667)](cid:4666)ay y(cid:2870)(cid:4667, top plate fixed: u(cid:4666)y(cid:4667)= (cid:2869)(cid:2870)(cid:2972)[(cid:2914)(cid:2914)(cid:2934)(cid:4666)p+ gh(cid:4667)](cid:4666)ay y(cid:2870)(cid:4667), K=(cid:4672)(cid:883) a(cid:3117)a(cid:3118)(cid:4673)(cid:2870: hl=kv(cid:3117)(cid:3118)(cid:2870)(cid:2917, hydraulic diameter d(cid:2918)=(cid:2872)a(cid:2900, hydraulic radius r(cid:2918)=a(cid:2900, pipe exit to a reservoir, k = 1, friction losses in non-circular ducts just use hydraulic radius & diameter in normal equations. (cid:2902)(cid:2915)x: skin friction drag coefficient, c(cid:2916)=(cid:2868). (cid:2874)(cid:2872)(cid:2874) (cid:2902)(cid:2915)x where rel=(cid:2977)u(cid:3116)l(cid:2972, drag force for the plate, f(cid:2888)=(cid:2868). (cid:2874)(cid:2872)(cid:2874)(cid:2977)u(cid:3116)(cid:3118)l. Friction drag: friction drag is only important for thin, streamlined objects, main drag forces on blunt objects are caused by change in pressure around the body, particularly when flow separation occurs.